{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":57620,"title":"Compute frequency factors for the normal distribution","description":"In frequency analysis in hydrology, the streamflow  corresponding to a specified exceedance probability  (or return period ) can be computed as\r\n\r\nwhere  and  are the mean and standard deviation of the streamflow series, respectively, and  is the frequency factor. \r\nWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.242px 8px; transform-origin: 156.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn frequency analysis in hydrology, the streamflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"QT\" style=\"width: 20.5px; height: 20px;\" width=\"20.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.95px 8px; transform-origin: 164.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to a specified exceedance probability \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.6667px 8px; transform-origin: 32.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or return period \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"T = 1/p\" style=\"width: 55.5px; height: 18.5px;\" width=\"55.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.2917px 8px; transform-origin: 67.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"QT = mu + KT sigma\" style=\"width: 89.5px; height: 20px;\" width=\"89.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eμ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eσ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 249.592px 8px; transform-origin: 249.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the mean and standard deviation of the streamflow series, respectively, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACcAAAAoCAYAAAB99ePgAAACtElEQVRYR+1XPUsdQRR97x/EmCqlSSCNJKAiBC3SmK8mnV8/wI/CUkFLNaBF0ojGIrUJRKyUWAlGBNFCC7FRf4GanxDPkbnLdZydmV3fbh7hDRzeuntn5sy5d+69Vit1PKp1zK3SIJfXOw3lilKuBQs/Diy+Y753eexO8O0yK8mQW0nuOTAGvLEW78ff3PRIkXuH50llt4nnGUAOkIlfiJwsRlV+q5W7UzYcwvuvxo7kv2diYxnHkuvDvBUz9wy/Tx2bis0ffHutFM3NL5YcFeg1u3zC75S1oyhGNw4CmePLdYJYcleY3GQW+IDfDfPcjN9pYARwkc6tGifGkHsBu0O1yyOjDN+vAk+AtBgsnNw4dpgzu9BtbwFxI+OvBzi/F4uUyTHK/cJcSSN0HZVi/P0AeAkKGzHk/qrdeRMZewdGwZoEftrpQuTeY+K6gxxfDQPLhcmGhUPkZmEjGZ9u3AIkyTLeOoHC1AuR28fm7UYdUerUxB1f1zx9aE/4yLGuUh0ZL/HAOqpdzRgk+dBt9TUFdmQkTYKPnC5ZJPFQraJv8BLej3piT/Ik09AacAx8MYdiqCwArwCmK160DlnLR24RRsz8HDYBuxEQVV0cmRNJUA7AqnJhDHVzwPjmSEqjj5wuWa4OQ5P31VQm8W+AXBwdFlJtSIp2u0DSXqWRs0sWE68dV3ZM6prrUlDeSQa45ULXhDRyui9La5G4nlYvNjFLBpjA/HnfKVzkGBN7ANXi8OUznQdpy9TyWbnQ3lurHWwWbHK8oR+BB9aqdOk2IJ0t7VqBNsfJbVttohvSZ55D3MwJJWGf6nm+SRhENQ1lk5MMEFWXyySnM4Dr9t/xRJnkdIPq+gfpn5KTFBIqdwnJMpRjqRsAmEZksMb+rLfbmumGl6FcJkLauEEur3QN5f5L5a4BNC2HKYDzOZ0AAAAASUVORK5CYII=\" alt=\"KT\" style=\"width: 19.5px; height: 20px;\" width=\"19.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.275px 8px; transform-origin: 74.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the frequency factor. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.275px 8px; transform-origin: 373.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function KT = normFreqFactor(p)\r\n  KT = trapz(QT:inf,exp(-Q.^2));\r\nend","test_suite":"%%\r\np = 0.001;\r\nKT_correct = 3.090;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.002;\r\nKT_correct = 2.878;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.01;\r\nKT_correct = 2.326;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.02;\r\nKT_correct = 2.054;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.04;\r\nKT_correct = 1.751;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.1;\r\nKT_correct = 1.282;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.2;\r\nKT_correct = 0.842;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.3;\r\nKT_correct = 0.524;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.5;\r\nKT_correct = 0;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.8;\r\nKT_correct = -0.842;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\nT = [5 10 20 25 50 100 250 500 1000];\r\nKT_correct = [0.842 1.282 1.645 1.751 2.054 2.326 2.652 2.878 3.090];\r\nassert(all(abs(normFreqFactor(1./T)-KT_correct)\u003c1e-3))\r\n\r\n%%\r\np = rand(1,randi(15));\r\nK1 = normFreqFactor(p);\r\nK2 = normFreqFactor(1-p);\r\nassert(all(abs(K1+K2)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('normFreqFactor.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp') || contains(filetext, 'interp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-29T19:23:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-29T19:23:11.000Z","updated_at":"2026-01-04T12:13:24.000Z","published_at":"2023-01-29T19:23:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn frequency analysis in hydrology, the streamflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"QT\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_T\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to a specified exceedance probability \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or return period \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T = 1/p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = 1/p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) can be computed as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"QT = mu + KT sigma\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_T = \\\\mu + K_T \\\\sigma\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"mu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are the mean and standard deviation of the streamflow series, respectively, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"KT\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_T\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the frequency factor. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57844,"title":"Solve an ODE: draining tank","description":"Write a function to compute the time to drain a cylindrical tank of diameter  from an initial level  to a level . The outflow occurs through a small circular orifice of diameter  at the bottom of the tank, and the outflow  can be computed with , where  is a discharge coefficient,  is the area of the orifice, and  is the acceleration of gravity, which should be taken as 9.81 m/s. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 319.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 159.55px; transform-origin: 407px 159.55px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 87.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 43.55px; text-align: left; transform-origin: 384px 43.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 229.742px 8px; transform-origin: 229.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the time to drain a cylindrical tank of diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.85px 8px; transform-origin: 61.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from an initial level \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.8917px 8px; transform-origin: 31.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to a level \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.225px 8px; transform-origin: 40.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The outflow occurs through a small circular orifice of diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Do\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.667px 8px; transform-origin: 130.667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the bottom of the tank, and the outflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.9583px 8px; transform-origin: 71.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be computed with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = Cd Ao sqrt(2 g h)\" style=\"width: 99.5px; height: 22px;\" width=\"99.5\" height=\"22\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Cd\" style=\"width: 18.5px; height: 20px;\" width=\"18.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.3333px 8px; transform-origin: 82.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a discharge coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ao\" style=\"width: 17px; height: 20px;\" width=\"17\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.175px 8px; transform-origin: 92.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the orifice, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.708px 8px; transform-origin: 111.708px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the acceleration of gravity, which should be taken as 9.81 m/s\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAmCAYAAADN0BvRAAABE0lEQVRIS2NkoBAwUqifYRgbEA4Mm0IgNoeG0UkgnQvEp9HDDFsYZAAV5QPxRCB+D8RJQOwG1egOpHchG4LNgGdABbZAfBdJ4U6oISDNIEPgAN0AkE3BQJyO5lSQl1YA8Q0g1iTkAmxJA2QwyBUEXYBNM0gMFC7TgbgKiNvJccFKoCY9ILYG4nekGqAM1HAHGngoMQAyiJikfAKobiO602GuIGTATKhC9FjBGY3I3gMFnCMQZ6L7m5gwAGlOAGIvNM1C0NgApQswwOYFWKJZBZR/iGwbkB0DxKA8AooVrAaYAkX3ATEPmkYY9zmQoYPsKkKBiMMchPCoAcQlZbwBORqIo4GIqzwgmAOJKZGINmQYpEQA0UUlJ+mjkqgAAAAASUVORK5CYII=\" alt=\"^2\" style=\"width: 8px; height: 19px;\" width=\"8\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. 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\" data-image-state=\"image-loaded\" width=\"308\" height=\"223\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = drainingTank(h0,h,Cd,Do,D)\r\n  g = 9.81;    %  Acceleration of gravity (m/s2)\r\n  t = sqrt((h0-h)/g);\r\nend","test_suite":"%% Rounded orifice\r\nh0 = 3;                     % Initial depth (m)\r\nCd = 0.98;                  % Discharge coefficient\r\nDo = 0.1;                   % Orifice diameter (m)\r\nD  = 1;                     % Tank diameter (m)\r\nh  = 2;                     % Depth in question (m)\r\nt_correct = 14.6440;        % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Sharp-edged orifice\r\nh0 = 5;                                           % Initial depth (m)\r\nCd = 0.6;                                         % Discharge coefficient\r\nDo = 0.2;                                         % Orifice diameter (m)\r\nD  = 2.5;                                         % Tank diameter (m)\r\nh  = 4:-1:1;                                      % Depth in question (m)\r\nt_correct = [27.7579 59.2645 96.6372 145.3422];   % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(all(abs(t-t_correct)\u003c1e-4))\r\n\r\n%% External mouthpiece\r\nh0 = 3;                     % Initial depth (m)\r\nCd = 0.8;                   % Discharge coefficient\r\nDo = 0.1;                   % Orifice diameter (m)\r\nD  = 1;                     % Tank diameter (m)\r\nh  = 2;                     % Depth in question (m)\r\nt_correct = 17.9389;        % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Convergent mouthpiece\r\nh0 = 1;                     % Initial depth (m)\r\nCd = 1;                     % Discharge coefficient\r\nDo = 0.05;                  % Orifice diameter (m)\r\nD  = 0.3;                   % Tank diameter (m)\r\nh  = 0.1;                   % Depth in question (m)\r\nt_correct = 11.1146;        % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Re-entrant mouthpiece\r\nh0 = 4.5;                                    % Initial depth (m)\r\nCd = 0.75;                                   % Discharge coefficient\r\nDo = 0.2;                                    % Orifice diameter (m)\r\nD  = 5;                                      % Tank diameter (m)\r\nh  = [1.2 0.8 0.4];                          % Depth in question (m)\r\nt_correct = [386.0058  461.6427  560.2147];  % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(all(abs(t-t_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-01T12:15:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-28T00:41:34.000Z","updated_at":"2025-03-25T15:09:17.000Z","published_at":"2023-03-28T01:19:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the time to drain a cylindrical tank of diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from an initial level \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to a level \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The outflow occurs through a small circular orifice of diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Do\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the bottom of the tank, and the outflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = Cd Ao sqrt(2 g h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = C_d A_o \\\\sqrt{2 g h}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Cd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a discharge coefficient, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ao\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the orifice, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the acceleration of gravity, which should be taken as 9.81 m/s\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58314,"title":"Compute the normal depth of a channel","description":"For steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \r\nAs described in Cody Problem 57969, the normal depth, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) ):\r\n\r\nwhere  is Manning’s roughness coefficient,  is the hydraulic radius,  is the slope of the channel, and  is the cross-sectional area of the flow. The coefficient  is 1 for SI units and 1.49 for U.S. customary units.\r\nWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure channelStruct with the following fields and possible values:\r\n\r\nThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 850.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 425.1px; transform-origin: 407px 425.1px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.017px 8px; transform-origin: 380.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7917px 8px; transform-origin: 49.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs described in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57969\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 57969\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.55px 8px; transform-origin: 15.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.85px 8px; transform-origin: 40.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003enormal depth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 197.833px 8px; transform-origin: 197.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = (C/n) R^(2/3) S0^(1/2) A\" style=\"width: 105.5px; height: 35px;\" width=\"105.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.55px 8px; transform-origin: 112.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is Manning’s roughness coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 8px; transform-origin: 73.5167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.1833px 8px; transform-origin: 85.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the slope of the channel,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the cross-sectional area of the flow. The coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155.942px 8px; transform-origin: 155.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 1 for SI units and 1.49 for U.S. customary units.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383px 8px; transform-origin: 383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.05px 8px; transform-origin: 50.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003echannelStruct\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.3333px 8px; transform-origin: 16.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the following fields and possible values:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 64.85px; text-align: left; transform-origin: 384px 64.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 435px;height: 124px\" 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\" data-image-state=\"image-loaded\" width=\"435\" height=\"124\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.15px 8px; transform-origin: 376.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 339.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 169.85px; text-align: left; transform-origin: 384px 169.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 725px;height: 334px\" 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\" data-image-state=\"image-loaded\" width=\"725\" height=\"334\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function yn = normalDepth(Q,n,S0,units,channelStruct)\r\n%  yn = normal depth\r\n%  Q = discharge (or flow)\r\n%  n = Manning roughness coefficient\r\n%  S0 = channel slope\r\n%  units = 'SI' for metric, 'USCS' for U.S. Customary System\r\n%  channelStruct = structure with with fields 'type', 'size1', and (for trapezoidal) 'size2'\r\n\r\n   C = switch(units,[1 1.49]);\r\n   yn = solve(Q-(C/n)*R^(2/3)*sqrt(S0)*A,0);   ","test_suite":"%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyn_correct = 0.61;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.04;                                   %  Manning coefficient \r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyn_correct = 1.12;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\nyn_correct = 3.58;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 0.72;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.034;                                  %  Manning coefficient (rock)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 1.16;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nn = 0.013;                                  %  Manning coefficient (asphalt)\r\nS0 = 8e-4;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 1.7;                  %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 2.80;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nn = 0.013;                                  %  Manning coefficient (asphalt)\r\nS0 = 8e-4;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1.5;                  %  Side slope\r\nyn_correct = 3.33;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\nyn_correct = 4.52;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\nyn_correct = 7.28;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 9.76;                                   %  Discharge (cfs)\r\nn = 0.015;                                  %  Manning coefficient (concrete pipe)\r\nS0 = 1e-2;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 1.5;                  %  Diameter (ft)\r\nyn_correct = 1.36;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-18T12:36:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-05-17T14:01:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-17T13:54:07.000Z","updated_at":"2023-05-18T12:36:47.000Z","published_at":"2023-05-17T14:01:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs described in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57969\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 57969\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enormal depth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = (C/n) R^(2/3) S0^(1/2) A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = \\\\frac{C}{n} R^{2/3} S_0^{1/2} A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is Manning’s roughness coefficient, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the slope of the channel,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the cross-sectional area of the flow. The coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 1 for SI units and 1.49 for U.S. customary units.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003echannelStruct\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the following fields and possible values:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"124\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"435\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"334\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"725\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/docu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water surface profiles","description":"Problem statement\r\nWrite a function to classify the water surface profile starting at depth  in a channel with longitudinal slope , discharge , Manning roughness coefficient , and cross section specified by a structure channelStruct as in Cody Problem 58314. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity  to be either 9.81  or 32.2 . You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \r\nBackground\r\nSections of channels are classifying by the relationship between the critical depth  and the normal depth . Slopes with  are steep—that is, normal flow is supercritical (fast and shallow), whereas slopes with  are mild—that is, normal flow is subcritical (slow and deep). \r\nThe type of water surface profile in gradually varied flow then depends on the water depth  relative to these two depths, as shown in the figure below. Profile S1 has ; profile S2 has ; and profile S3 has . Profile M1 has ; profile M2 has ; and profile M3 has .  \r\n\r\nFigure by NateJonesAR - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=25698746","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 780.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 390.35px; transform-origin: 407px 390.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 106px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53px; text-align: left; transform-origin: 384px 53px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.842px 8px; transform-origin: 211.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify the water surface profile starting at depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.05px 8px; transform-origin: 112.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a channel with longitudinal slope \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.175px 8px; transform-origin: 36.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, Manning roughness coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134.183px 8px; transform-origin: 134.183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and cross section specified by a structure \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.05px 8px; transform-origin: 50.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003echannelStruct\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6667px 8px; transform-origin: 18.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58314\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The unit system will be specified in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eunits\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 252.408px 8px; transform-origin: 252.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.45px 8px; transform-origin: 54.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to be either 9.81 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAAnCAYAAAC7bZ4BAAADyklEQVRoQ+2ZuYsVQRDG3T9AxCMyMPDIBAUvEFPxClU8MBQUjRQ8UEMPNNDICzRTURAEUVETA0XwCBQMBI9AUw/wH9Dvt3YttbU9b/vN2+fM4hsoZnf6qvrq6K/7DU0ZPMMIDA1w+IvAAIgUCQMg/iMgVsnWlcne53o/y5WDNkfELin8VfKgZh2bqXEPJdMlPyVL0zy39N4r+e7nbTMQP6ToHsnNmkAAwh3J5TR+kd5PEjCH9D4zGYBYLyWvSWbUBGGuxuH5ZWE8UXZJ8jq2tTUiLiQDiIg6D0BMlbwNg6kXTycLEOT2N8kGSd36UAWeAXFSHY62PTW2SsHjkvl1QmGcMQfVflqyOEZLG1OD4vgpemyCQPmYaseoaGDutgFBbgPCGI9NABAUygNVkdY2IFB2pyRW+15xYOu8IlkrGcUfbOJOQOCd1RLbh/l/uWROGnxb789OQ4rcCsnC9O1RzMMCa14lhW3N3JC4zhd1einJ7RKMN2K1T39nWSWdIhAYu0myWQITg5Gxl1uRiYpZZceTpySwOP90U/nx2hvJvACwn89IEXXkRmpYp/cRp6vvDwjXJRTfCAJFeYSs5YCYrQ7nHBDkLJ5iYSbzDI22xwksgGDfZou6m0ChvbT6n0ggoGDVQ7HDOTF1cNThpIeNtUggJWKE4bhpkhF2WZUaPgK2eeTSKiiNF3hgcFF5Y3C0lxY+jDyWWcsMs4gh5ch1/2D0C4kHHW9vqYQ0RF4JEDlDjJiwzu4M4r49B2TUzyj1AjVki5m++zlzKYfzzMOAtqYDCNSVUWeYfwFEDqioYyml5iBmdYh5KdhVwHXAYWxTG4AgrD9IdkjGo9REzn1nBvWilxPqyFRtAKJbSm1p5Hco6gZH63jIKo6KNgBRh1ITRfslVrAxmB1qY10wmgaiG0pNX7Z2zwf4xknSdofcjlIUFU0D0ZH/BwvYNbanmhCNs63SCGCR8b5T00CUUGrT14haboutvHApRaRJICwtOlFqb0flpYo6GQEs2aqz2OSAQEFoMwrykINnJbZfU6jOu7zk/o8ctQNYzNvYborATpdIIkuscqInVBfV6Z7kl4Srei5bxlzIlkYD/SIQ/jeAOM9VfYCfcyjLPe/08X2H9ngaHY9SxzVwAOsDuNfTTp/+JNwNBsN9m7qPMO/Okg4Twgy7tjwMaAqIUkrdq33F45sCgjNDCaUuNqTXjk0AAaUmIur+eNOrzdnxTQBRh1L3xXg/aRNA/JYCpZc1fQfAFmgCCC5Nap8S+4VME0D0y5ae5h0AkeAbAJGA+ANSTOootOgcngAAAABJRU5ErkJggg==\" alt=\"m/s^2\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or 32.2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"ft/s^2\" style=\"width: 30.5px; height: 19.5px;\" width=\"30.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 258.808px 8px; transform-origin: 258.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.617px 8px; transform-origin: 211.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSections of channels are classifying by the relationship between the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58324\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ecritical depth\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc\" style=\"width: 14px; height: 20px;\" width=\"14\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 8px; transform-origin: 27.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003enormal depth\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn\" style=\"width: 14.5px; height: 20px;\" width=\"14.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 8px; transform-origin: 41.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Slopes with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003c yc\" style=\"width: 44.5px; height: 20px;\" width=\"44.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1167px 8px; transform-origin: 17.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003esteep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.275px 8px; transform-origin: 237.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, normal flow is supercritical (fast and shallow), whereas slopes with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e yc\" style=\"width: 44.5px; height: 20px;\" width=\"44.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.8417px 8px; transform-origin: 12.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003emild\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.55px 8px; transform-origin: 29.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, normal flow is subcritical (slow and deep). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 279.292px 8px; transform-origin: 279.292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe type of water surface profile in gradually varied flow then depends on the water depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.35px 8px; transform-origin: 99.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e relative to these two depths, as shown in the figure below. Profile S1 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y \u003e yc \u003e yn\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.6167px 8px; transform-origin: 48.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; profile S2 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc \u003e y \u003e yn\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.2333px 8px; transform-origin: 62.2333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and profile S3 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc \u003e yn \u003e y\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 8px; transform-origin: 37.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Profile M1 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y \u003e yn \u003e yc\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7833px 8px; transform-origin: 49.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; profile M2 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e y \u003e yc\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.4px 8px; transform-origin: 63.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and profile M3 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e yc \u003e y\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 427.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 213.85px; text-align: left; transform-origin: 384px 213.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 440px;height: 422px\" 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\" data-image-state=\"image-loaded\" width=\"440\" height=\"422\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 353.142px 8px; transform-origin: 353.142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFigure by NateJonesAR - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=25698746\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function profType = classifyGVF(y,Q,n,S0,units,channelStruct)\r\n%  profType = character string--one of S1, S2, S3, M1, M2, or M3\r\n%  y = water depth\r\n%  Q = discharge\r\n%  n = Manning roughness coefficient\r\n%  S0 = channel slope\r\n%  units = either 'SI' or 'USCS' (i.e., lengths in m or ft)\r\n%  channelStruct = structure describing the cross section--see CP 58314\r\n\r\n  y = 'S1';\r\nend","test_suite":"%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 1.2;                                    %  Depth (m)\r\nprofType_correct = 'S1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 0.7;                                    %  Depth (m)\r\nprofType_correct = 'S2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 0.34;                                   %  Depth (m)\r\nprofType_correct = 'S3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 4;                                      %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 2;                                      %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 1;                                      %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 1;                                      %  Depth (m)\r\nprofType_correct = 'S1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 0.75;                                   %  Depth (m)\r\nprofType_correct = 'S2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 0.6;                                    %  Depth (m)\r\nprofType_correct = 'S3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 4.7;                                    %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 3.5;                                    %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 2.0;                                    %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 7.3;                                    %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 7.2;                                    %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 3.7;                                    %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nfiletext = fileread('classifyGVF.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-09T21:56:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-23T01:31:32.000Z","updated_at":"2025-07-09T21:56:13.000Z","published_at":"2023-05-23T01:34:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to classify the water surface profile starting at depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a channel with longitudinal slope \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, Manning roughness coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and cross section specified by a structure \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003echannelStruct\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58314\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The unit system will be specified in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunits\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to be either 9.81 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or 32.2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ft/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm ft/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSections of channels are classifying by the relationship between the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58324\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecritical depth\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enormal depth\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Slopes with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026lt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026lt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esteep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, normal flow is supercritical (fast and shallow), whereas slopes with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emild\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, normal flow is subcritical (slow and deep). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe type of water surface profile in gradually varied flow then depends on the water depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e relative to these two depths, as shown in the figure below. Profile S1 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y \u0026gt; yc \u0026gt; yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \u0026gt; y_c \u0026gt; y_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; profile S2 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc \u0026gt; y \u0026gt; yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c \u0026gt; y \u0026gt; y_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and profile S3 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc \u0026gt; yn \u0026gt; y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c \u0026gt; y_n \u0026gt; y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Profile M1 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y \u0026gt; yn \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \u0026gt; y_n \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; profile M2 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; y \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and profile M3 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; yc \u0026gt; y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y_c \u0026gt; y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"422\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"440\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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the critical depth of a channel","description":"Problem statement\r\nWrite a function to compute the critical depth of a channel with discharge . The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity  to be either 9.81  or 32.2 . The geometry of the channel’s cross section will be specified by a structure channelStruct as in Cody Problem 58314.\r\nBackground\r\nSpecific energy for a flow is , where  is the water depth and  is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity  and differentiating with respect to depth gives\r\n\r\nThen using the definition of the top width  gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number :\r\n\r\nFlows with depths smaller than critical are supercritical—fast and shallow (), and flows with depths greater than critical are subcritical—deep and slow (). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the field, in the laboratory, and even in a kitchen sink. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 409.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 204.6px; transform-origin: 407px 204.6px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.642px 8px; transform-origin: 226.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the critical depth of a channel with discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 139.633px 8px; transform-origin: 139.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.45px 8px; transform-origin: 54.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to be either 9.81 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m/s2\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or 32.2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"ft/s2\" style=\"width: 30.5px; height: 19.5px;\" width=\"30.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.8833px 8px; transform-origin: 17.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The geometry of the channel’s cross section will be specified by a structure channelStruct as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58314\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.125px 8px; transform-origin: 87.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSpecific energy for a flow is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL4AAAAnCAYAAACxHfIWAAAIKElEQVR4Xu2d28uvUxDH9/4L5HAlSQ4XckHOiQsuEBJRiAtFTrmhHLJJytmFcuEUd4Rwo4gUhZTDBUWUQ8KlQ/IHMJ/8RrPXXmvNWut51u/9ve+znpr2731/6zjznVkzs+Z59+5d4xkcWCAHdi9wz2PLgwO7BvAHCBbJgQH8RYp9bHoAf2Agx4Fj5ctThfYT+lno5Z3CrgH8nSLJ+ffxpAx5udCnQueshv9c/r1W6MuG6a6XPr8IvdXQd/YuA/izs3RHDHi77OL4FfDZ0IFCbwudKPSO0LkNu/xD+ty0KafGAH6DBBfQ5TPZ42VCP5q94vZ8sfr5IPn39wo+nCdtXxA6oKJP16Ye8NH81gfL0HIkts635H64JIcmGPCX/P6ZyHcp2T4vbU8Rirkk/zQCH7eJB4ufemw8QZuPhT7qJVQP+MzLgl4XOsIs4in5/FOwqMPk57NNO9pbi9FrD2Pc/ziAVX3TMOOHlTxyMkBhXlr1wVBdKZSz5AAfP/+kCqbjJv0mdL5QTJkOl9+jGBpH2KGnxBTZJZYAnwEeELprNVJu4+oLAvqNOdYqhLTdm+Ki4IfzPCi0x9mQui9/rvrllOR0afOh0A1CsRMkNRXKdb/QkZEG4OU7of2FwBVKRztrZFHgS4Rm9R5KgU9goxrpMZQj9CyhlgBouwOvdP2AiOeblbBL+3ntsJw3rhp5cqKZGrQSMDM2lr7G2jMHKVDAG1NCvsNLODMANvx5XEiV+BX5jALN9pQCX307Jj5DKOd7AXzyvp61mW0T23Ag5edxgcCnboWU4dOrQTyXRK0toPTAzMnwfgSg3npxYxg/ts/cd4yr3/OZE+kooZqAOru2EuDrEVe6ABZMQDXbIj3ubsPvewHfygrAEaSm5KCng6d8KMiLQrgrtcEmikjeP6ZYJQaSE4HsEo+3zioYlADf+vepHC4bfG2AvZj3vYCvgaQuJJV2VN++xB0CfFj7Gr9e5yfmeC7RVy/HcnEFyvHIVgHfBkwxX5ANXCQ0qw9WDKF5GnJKHSx0iBBpwUcjw6LcuHCk+6aeZr2Az7K5KCJY5Em5pcRsJwt57gOnAkFlCHoySJ84fFDlmpLdU+Dj6pQkSzjxTlvtHa/jXaGoYnkWP7Qg4XHD9zDgsQhzaiGZy0XXjBUDba6/znudNNJsQph6sy7EHIFWT+DbREQshahpzytkv7naG0AP2EKDBi9ujvw+5DGeAvycYhDV1fFOJozSQ0IoPVj8WuhuIRIyeCk8KMD/9wge8G2el853mN1h/fC/2NwUrdYhrcBqgG7bllqG2Pg2tRZz6dQnbr2yt3P2BL51TUPAqKH6XhaTy7rZIDnGK09p6MMcgG9KYZueXjl8qVzCANgaK+6dPrBr8YBv02NkCV41XKCWA+ATRMVytLXgncPip24pS9diQRNjNsr5nlDtqRLO3xP4FrQI3N6W4jrcKRSmD+36UI5rHIZ5+9cSBc+Vyk2jRhdjm5rPgjtURvvdPiefB3y0Vo//mJbj/6MMHiNKgbfV7Ww9Smy/8KPkMsVTYg3YsMgoa+pp4asVuE1pEsfwM8rQO9VcUqKQk7U9mXK3ySlrz9jWAFQB34KAgWIZAoB/i1BtmmurAZ6bX5U99OX1UsXLeTP2VrptNv9tU5p6WVQSJE6Rj7qMV8kgrSXIAJqLrVw61vI5dmeh8UH0DiBn8UsuQ1jgPUJTsxxTGD1335QVAcxPFAqz1OLHap50P1PcNnvhiME6Wohyg1S9zJw8zJUolMxDf2TAra1X66WyCoFvlT8aGOeAby8Pcn5WyWZK2nhgKRmDNi3ugR3bBvSaxaqx9iXr7OnjhycOYL9PCOs/JcNSsi/a5EoUvDFqQM9Y6tbZWiO9cCOjk8zA5YBfU6agGyJ4ai1H3kr3wArEWgu9t8Clu7fQ2nvC5fvewLdJCeRBzr7EgpasPdfGK0PI9a0FvY5FIM1JDPiJN0lL8zwrlDSCKeDXlikw0dRIfg6LP8U9sEJRP59jkndNLxaas+iuN/DtjSf7WseJzTy4x7cJ1Wb5wNsbjnKiVChwmB4lE0dhHtmrX4X+FnIrOVPAt4wryVtrEROLyr1sYMG1yZ/VYuIe8JRkcmr20xv4Yc1OLRBr9mLb5koUUmMqdnLBsJa7h6eu4rTk3YO95k8B35YphLlgOwBaeKmQpue8ys1Whq67nw3se1jL3sC37tq6ZKJz1lxmKuiRLy+1px4sPZdZoQLbOBRXh5+x9m7dWAh8NAsga2krC2FAwG/zzdzakm7SemnazXWRtW6Qx+ZTi9lrT72Bz56YI2e05uYzLscJQqUuoYJe64q89cQMkLrX9LXjgNmHhYp9fI6O1qfrO5Kti2rspz7nhdK/xx3FOoBPzESR1rpSzbUlCrUxnS0OxEDfKkTlgOb6UYILhPRFHESfrPHxbm4bcbPtu00pxS3ZfK83sErm7tFGT8jav77QuhZccVyqWEkELhdpTLyR5AssA/j7sp5Tz/5NmVbhLKnf1BKFGl7pPUuuYtPGOFFlHMDfm+VTbx1rBLiT2hJ4TilRqOGFZnJywNdy+mRGcunA1+wVQSDZAHLQXn1IjZCW0FYvnnrXACkvtYYsl8LkBGJdyRht6cC3byuV/F2ZJQC5do9TShRq59L2qmzIjxtaEis8vEF3tRAWP/xLcHvNtXTg6z3ETspItYKptR8ZqllfBK9YCEH1MUKk13m+EvpWyCtuG/8xRAWTR9M4B3A93BKBTWPe0i3+psljrGdNHBjAXxOjxzSbxYEB/M2Sx1jNmjjwL4e77DeFMTLgAAAAAElFTkSuQmCC\" alt=\"E = y + V^2/2g\" style=\"width: 95px; height: 19.5px;\" width=\"95\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.7333px 8px; transform-origin: 72.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.908px 8px; transform-origin: 122.908px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHsAAAAlCAYAAABiQ5b4AAAFn0lEQVR4Xu2aOasmVRCGZ36AuIYi4hIrLmiggoELmhiIGwYGA66YueCSqagoRm5gYCCogYnglmjgKM6ooCAYuCSCkfv8gPF9sAuLpk9XnT63u2f4uqHoe78+S1W9dWrr3r9vu3ZGA/t3RtJN0H0b2DtkBBvY64J9p7b/RfT+EmxsYC+h5fIef+jRPaK3lmBjA3sJLQ/vcZ1+fkN0ylIslMA+TwycMMLEwYFnlxXGf6/ff19KoBn38Tr5Vfv83LjXS918TnbLBV9HMvyMgX2TFnikx8Wt+h/wvi2AfZt+v7t79pPu94sWiUct2hqZe4ue3SC6WYQ8P4pOFV0k+kr0vGiKC2aN30TXN+rnrI6vh3R/NtJB5MYR7uxukad0fzRY0DZn2OWiIQ8Q8XQsPMdLvd7J/pHunD5/knn+ruhk0cuix0U13gsjekJ0TqOwGBqGCA+hh4jAtsXgKQM22eUrybGNcs42/UGt/Ey3+l26v1rYCcDe7J6lTpZbB73iKaLDMyYkBvdpNwAvc3GkkQhsLzgWfm2wIJ6AhOPcSkuP+FzqOXHUwlDmtJBNc7r/FOHaM3HcvN/5Gj8UDrOyeq/LnNMinUdg960HsEvuygyjNQ5lhd3rceaVWJdTl3GxH2rcNR0jY17A88o+BzIncURAdP1w9xxj4wqNJwLbx+Ax6yHh+EF0WBSd/r0GaS/W80bNelmD9WC/rXm49uj6UgNeE5XCQzTfdE2MvsMZW8hzBDYbH3W7l6zH3B/JXMaVRQIt/dy7xCxo8OjBzsRNyqRvRC16QtfEZ+hJkVVMYU6VAdsLNGQ9JkC4WYBgVNtnDaC2AvCJVs2pZqzFbP7O5DSAA9AZDzAkr3kgq3R86AmNNAO2T1qGsk6MgfiWiXFjgHmjygLbH0eiVNuR8qe6Zn4/xGWMnb0eE02pzc2T/OWMpSojz4DtM/K+QHYqwniRQA+rvzAxbmyIV0RmKfNKNjYDmI3tewQaTmMgWnt0aqVi+/ms25ozxtNoRp4Bu2Q9bHRIRKya6pYygMw5xrtB9qlpBHmPx9woDre0Ry0poxzs1+Y+lIxm5BmwvfUDrJVfduLD+m5OtBrX7gOWlcWUb2VPFC9t/O3id0r72Eot5v/Tk/kF/U+NzzXqYTNgs4jPyFHIiSJq0drOUSM2ez69NpsuufCoxm1pj1puwEEb6nGQK6Va2lmwqQ3NenB193UbhC26CnjWyMangu2TukynraU9Co94hpKu0xl5Fux+j5zaria+ZTBfIxv3yWemTkaOfqftksKJM5lb2qOWL42553RGngXbKwUhMtacAdiPWSMbJ0N+r2OCsBQBh/f5RGSxOkrKzDge0B9TSlM8COXgmAfNdjnTHxx6pSBANpGpBXyN8d4lj8VeXCneh3AGAFeKMi8yprZHzYNkytpMlzMNts/Io3pyDcBa9vRukKz63gG3jPz0s+2jhbEXQp4XO3UZD+DnWfZOWZXxCL78KuKTdeMwgvVk41qL8teYaw0P3DNtTz4ssMu+vuE015ZOFppqXg55D+JL3ZJe+o2VksGmTzYbUZM+JzoeX3RkDAil3Sji9aOdYEqdr0WfiabUx7XtUTwBXbyTHMPs/4Go3/NnLPxe0BvP1ME5NSc7o7DjfQz1MEZN9RF+5tMJi5Fc1c3x8lt4OGbymw3s/+GxhAh3/bToOxHdqrG3aMTyd0RDH1a2tEdnOTQb2P81LF4U8eHe0AX4fJTxsejzbsDpul8h4hOmUkJE0lQb42cB2RbddbDtK1JiK2BynSm6WmQtyBIAJE/E96Hyy8JB7evWDewZNUCS87doqOeMi75UdIbIXr3yCpWmyhcFkI3VlvbobOLu+smeS7GUqdHLkbn2Lq67gT2PyvEKme7aPLsXVt3AXlTd6262gb2u/hfdfQN7UXWvu9m/az5FNYP7vlgAAAAASUVORK5CYII=\" alt=\"V = Q/A\" style=\"width: 61.5px; height: 18.5px;\" width=\"61.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and differentiating with respect to depth gives\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg 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\" alt=\"dE/dy = 0 = 1+(-2) (Q^2/2gA^3)dA/dy = 1-(Q^2/gA^3)dA/dy\" style=\"width: 257.5px; height: 36.5px;\" width=\"257.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.583px 8px; transform-origin: 127.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen using the definition of the top width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"T = dA/dy\" style=\"width: 70px; height: 18.5px;\" width=\"70\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.6px 8px; transform-origin: 211.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr^2 = Q^2T/gA^3 = 1\" style=\"width: 95.5px; height: 36.5px;\" width=\"95.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.283px 8px; transform-origin: 230.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFlows with depths smaller than critical are supercritical—fast and shallow (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr \u003e 1\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.742px 8px; transform-origin: 114.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), and flows with depths greater than critical are subcritical—deep and slow (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr \u003c 1\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 240.533px 8px; transform-origin: 240.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=qsC9FUYpHqU\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003efield\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.9417px 8px; transform-origin: 22.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://youtu.be/5etwhZ0d2GU?t=373\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003elaboratory\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.8417px 8px; transform-origin: 47.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and even in a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://youtu.be/OoA1ASjMfag?t=24\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ekitchen sink\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function yc = criticalDepth(Q,units,channelStruct)\r\n  g = 9.81*(units=='SI') + 32.2*(units=='USCS');\r\n  yc = solve(Q^2*T/(g*A^3)==1,y)\r\nend","test_suite":"%%\r\nQ = 12;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyc_correct = 0.33;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 10;                   %  Width (m)\r\nyc_correct = 0.74;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\nyc_correct = 1.26;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 0.82;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 0.82;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 1.7;                  %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 2.34;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%  \r\nQ = 45;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1.5;                  %  Side slope\r\nyc_correct = 2.84;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 14;                                     %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1;                    %  Side slope\r\nyc_correct = 1.65;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\nyc_correct = 3.72;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%  \r\nQ = 8;                                      %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 1.5;                  %  Diameter (ft)\r\nyc_correct = 1.1;                           %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-18T13:28:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-18T13:25:33.000Z","updated_at":"2023-05-18T13:28:20.000Z","published_at":"2023-05-18T13:28:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the critical depth of a channel with discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to be either 9.81 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m/s2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or 32.2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ft/s2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm ft/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The geometry of the channel’s cross section will be specified by a structure channelStruct as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58314\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSpecific energy for a flow is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"E = y + V^2/2g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eE = y + V^2/2g\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the water depth and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and differentiating with respect to depth gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dE/dy = 0 = 1+(-2) (Q^2/2gA^3)dA/dy = 1-(Q^2/gA^3)dA/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dE}{dy} = 0 = 1 + (-2)\\\\frac{Q^2}{2gA^3}\\\\frac{dA}{dy} = 1-\\\\frac{Q^2}{gA^3}\\\\frac{dA}{dy}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen using the definition of the top width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T = dA/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = dA/dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr^2 = Q^2T/gA^3 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr^2 = \\\\frac{Q^2T}{gA^3} = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFlows with depths smaller than critical are supercritical—fast and shallow (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr \u0026gt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr \u0026gt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), and flows with depths greater than critical are subcritical—deep and slow (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=qsC9FUYpHqU\\\"\u003e\u003cw:r\u003e\u003cw:t\u003efield\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/5etwhZ0d2GU?t=373\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elaboratory\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and even in a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/OoA1ASjMfag?t=24\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ekitchen sink\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57969,"title":"Compute flow in a partially full pipe","description":"Problem statement\r\nWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow  equals the diameter  of the pipe. \r\nWrite a function that takes the ratio  and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \r\nSee Test 13 for the answer to the initial question.\r\nBackground\r\nSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow  is\r\n\r\nwhere  is Manning’s roughness coefficient,  is the hydraulic radius,  is the slope of the channel,  is the cross-sectional area of the flow, and  is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient  is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 392.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 196.4px; transform-origin: 407px 196.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.35px 8px; transform-origin: 65.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e equals the diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the pipe. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.933px 8px; transform-origin: 109.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the ratio \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADsAAAAlCAYAAAD8+ZFYAAADwElEQVRoQ+1ZuaoUQRR97wvEJTJ0AQ1EQU1EY7dYVDQwcwkFFdREXEARzFxAQUyeIiaCogYmiiAaaCAmKn6AC+gH6DnQdzhTU8utnp4WmTdwmZ7XVbfuuXXurdP9Zmem6DM7RVhn5sH2tNtXsc5l2Jee1vtnO7sWAN/Blk8D2PMN0D197SrX8dYsd2I17BfscQcBfoKP07C7GV/LcG+pc62XnnE5sJvhYDvspDg6hOsbHseZMTtw7xFsCex7Aewq3D8D2xCMe9r8Xiz37uH6Dux1yq9nZ0k5A7wO1+/HBMvGxM8Rpx8m/YWM3YlrZRcBH5UYmQj6Hml8HrCk2m7YZ9gKZ4C5YT9wc38QcG78Qdy83gz4ie9FicGs/7nm3tsm5iHAHrAMbiHsWsVupIJnQNzZVMCxeZZs3iNVc03tCe5vbZyMjC2BVQqF9GmzyQycDDlVMdmSzSl7YbmmZv3A3A+VXQnsccy62MwsNZRS/Kytb7Caurfz2Hx7zuU/EsgJXF+y3yWwRgsW/TZxwsB5FP2GeRsWa+8YrKbuNdnenvEGa1j3HqJyDqztBDFqhjQAD7UsRwziJqzm6NIavOCkv85ho9ro2Vnl/xZM+AijI56N52C3YaTVkMMElykQuDMeGqoLpaS3Z2iNu8Ha+cp2v7IBqjtjTksdksHT13qYlkIiL4M/h82mVHI2URPkprFxnxMIjKCti2qXHmoCCQQeeRhOVTET9oxUokIB4mpQRjs6JVjSb8B9XGvdkuI5bWoB1HZzbTSehBqDVN66jh5VI3QSBmpNIKdoLPu18pDztDnyt/e4IoO4MfyM9JJUHTDAw82kmPi3uvDUa6085LKabE9Cwzn8PdLQUmCt+cQW0rooKZo28pCBarI9MpVM4NOO7Wp0TgysqpZYrWi9ljokpR0T533CMeorHUsJDZOTFB+xYPUpI1YrVq9GYe7eGliod9vIQwZeKxGVBeza+2DR5+QY2NIjndUrM06h8QAWk4BMAsVHjTwk2PCRjmd8LHiW0xWYScOiwoqBNTAx3mu9ki6saQqFWDA8Ou7DBkLcOJr55pH3TGqPQ9kgP8icTbjeJSAZp+stZQiWFLKnHNZrKPJJzbMwBvUcdisBtI08JBMOOBLCB/KvsFcw17sn81lqMI61o0PYxJh9FSJtfXU2b1Jg28jDzkClHE0CrHXTWnn4X4K1d0y9vgD3ZGoSO9tGHnpiHXtM12B5ND2E1bw9HBuE10HXYHk0LYD19p85L1CO6xpszdq9j50H23vKe1rwL6q22CbizNfIAAAAAElFTkSuQmCC\" alt=\"h/D\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.258px 8px; transform-origin: 251.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.917px 8px; transform-origin: 150.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee Test 13 for the answer to the initial question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.8px 8px; transform-origin: 369.8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7px 8px; transform-origin: 7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = (C/n)R^(2/3)S0^(1/2)A\" style=\"width: 105.5px; height: 35px;\" width=\"105.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.55px 8px; transform-origin: 112.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is Manning’s roughness coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 8px; transform-origin: 73.5167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAACaklEQVRYR+1WOy9EQRTe/QEKj1KFnsKjQaJB+AGIRodohYRCgwSdQkK1HRKtZ6Og8kgoRINC7ZHwA/g+mbM59+7ce+fuzmYj2Zt82dl7Z853zjfnnJlspoJPtoLcmSp5RdT/V7J3K4keMX43/1vx+w28pJHQJfImGJwFpo3hU/Pbgt8zM+a3HuDSJzkjOgdqgX1gVBmvx/gEaDfvXAIJ+Ja0gMYHgE+gzhIVVXkGboCONFFzbhw5I3szBuOMXxv5F32SM7kuFPkgxpJgmofq5IA9n+QiqdgcxuDIQsA8uAJSZXqS7Pwue84x970PuE8bYdT8pIRjtt+pxdz7kWKitDmQRM41lHVXLWZ29/twwIXc5oAXBVzJbQ6w6cwAtgpwSos05DQ4B6wpy1MYb0cwMV9qAH0GBKamJedi1jOTjo+t+bA/5IAd4BVYBjZsTtrIVzDxGIg6JHTnowMNSnqpjlW8k44nzWrMOJ6P3kbOdrkE2BqKLNT1r8nlfRsm6n7wZBZ2KUetvf0HE+L2knaEhGXHo5WP7ojhoGSrAtGHJ4kBntnj2su8VpmMll3LO4Q5h4AtDyRR9fyCyPVhMg9D64pUhlsY8PLAqLWMQhBHHvgWjlwM0HAzQAU2gS+gEZgAeL6HielYyeSTMPIAMNO5BZ1ArxmT4BaIqoSSyS0qO7+SMyBOdirJe8HfU0yTifJGatxGzt6xAATyyCc5nfoAeNnUtc/3UpqBG65vctl3Xc9SmgWK+CZnlOyQfOTSwdJkPvCKHbhqlYOcxCRjlfDqxcPlACg4estFHpWUgfdVcieZfE+qyu5bUSd7v7RmiilK8yatAAAAAElFTkSuQmCC\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.125px 8px; transform-origin: 87.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.6667px 8px; transform-origin: 39.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the cross-sectional area of the flow, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 278.1px 8px; transform-origin: 278.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182.383px 8px; transform-origin: 182.383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function f = pipeFlow(hoverD)\r\n  f = hoverD.^2;\r\nend","test_suite":"%%\r\nhoverD = 1;\r\nf_correct = 1;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.9;\r\nf_correct = 1.06580;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.8;\r\nf_correct = 0.97747;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.75;\r\nf_correct = 0.91188;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.6;\r\nf_correct = 0.67184;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.5;\r\nf_correct = 0.5;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.4;\r\nf_correct = 0.33699;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.3;\r\nf_correct = 0.19583;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.2;\r\nf_correct = 0.08757;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.1;\r\nf_correct = 0.02088;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0;\r\nf_correct = 0;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = (1:6)/7;\r\nf_correct = [0.04395 0.17812 0.38187 0.62268 0.85931 1.03672];\r\nassert(all(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4))\r\n\r\n%%\r\ng = @(x) -pipeFlow(x); \r\nhoverD_max = fminsearch(g,0.9);\r\nhoverD_max_correct = 0.93817;\r\nassert(abs(hoverD_max-hoverD_max_correct)\u003c1e-4)\r\n\r\n%%\r\nfiletext = fileread('pipeFlow.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":9,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-08T16:02:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-08T12:50:01.000Z","updated_at":"2023-04-08T16:02:01.000Z","published_at":"2023-04-08T12:50:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equals the diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the pipe. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the ratio \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h/D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh/D\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee Test 13 for the answer to the initial question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = (C/n)R^(2/3)S0^(1/2)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = \\\\frac{C}{n}R^{2/3}S_0^{1/2}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is Manning’s roughness coefficient, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR=A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the slope of the channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the cross-sectional area of the flow, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57879,"title":"Route a hydrograph through a river section with the Muskingum method","description":"Problem statement \r\nWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph , the times  at which the hydrograph is reported, the routing parameters  and , and the desired time step . If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph , and a Boolean flag that says whether the time step is within the guidelines .\r\nBonus points to anyone who can solve this problem using the FILTER command. \r\nBackground\r\nHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow  and outflow  are connected to the storage  in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\r\n\r\nThis equation is written in discretized form as \r\n\r\nwhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow  and the current storage . \r\nIn the Muskingum method, the storage, inflow, and outflow are further related by \r\n\r\nwhere  is a time scale related to travel time in the river section and  is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\r\n\r\nwhere\r\n\r\n\r\n\r\nNotice that . With the assumption that the first value of the outflow equals the first value of the inflow, this equation for  can be used to compute the outflow hydrograph. The guideline for  above ensures that the coefficients , , and  are positive.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 882.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 441.35px; transform-origin: 407px 441.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.95px 8px; transform-origin: 64.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.783px 8px; transform-origin: 383.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"I(t)\" style=\"width: 26.5px; height: 18.5px;\" width=\"26.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2167px 8px; transform-origin: 34.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 187.875px 8px; transform-origin: 187.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at which the hydrograph is reported, the routing parameters \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eX\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 8px; transform-origin: 29.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the desired time step \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dt\" style=\"width: 18.5px; height: 18px;\" width=\"18.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 284.583px 8px; transform-origin: 284.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O(t)\" style=\"width: 30px; height: 18.5px;\" width=\"30\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 234.942px 8px; transform-origin: 234.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a Boolean flag that says whether the time step is within the guidelines \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"2KX \u003c= dt \u003c 2K(1-X)\" style=\"width: 149px; height: 18.5px;\" width=\"149\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.925px 8px; transform-origin: 251.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBonus points to anyone who can solve this problem using the FILTER command. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.742px 8px; transform-origin: 368.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eI\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and outflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eO\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are connected to the storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.25px 8px; transform-origin: 97.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dS/dt = I - O\" style=\"width: 72.5px; height: 35px;\" width=\"72.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.583px 8px; transform-origin: 141.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis equation is written in discretized form as \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.95px; text-align: left; transform-origin: 384px 18.95px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"(S2-S1)/dt = (I1+I2)/2-(O1+O2)/2\" style=\"width: 156.5px; height: 38px;\" width=\"156.5\" height=\"38\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O2\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.2333px 8px; transform-origin: 76.2333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the current storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S2\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 249.317px 8px; transform-origin: 249.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the Muskingum method, the storage, inflow, and outflow are further related by \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S = K[XI + (1-X)O]\" style=\"width: 143px; height: 18.5px;\" width=\"143\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185.917px 8px; transform-origin: 185.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a time scale related to travel time in the river section and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eX\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.75px 8px; transform-origin: 156.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O2 = C0 I2 + C1 I1 + C2 O1\" style=\"width: 152px; height: 20px;\" width=\"152\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.0667px 8px; transform-origin: 19.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.2px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.6px; text-align: left; transform-origin: 384px 17.6px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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V0zomSCVtlRSbyAfhtJDCEP7PXSWtcYrBU73mDJbLIEPjIW4gS8VVhCaB/xuSuEKMHiATcs2rGfQjiaOlsmsVD69dNIaB7ACFucsUZhZEIen2defBoSAQV/zYF1/TY5XwjkxZCAf1G7kEuhoaAVxHA364R/2BB0a/tEdZQitDb452rC9o+qNrUoQx1g8j50b1Et4T9Zijx67nGv7fuDW2CJBHI2AbSA5NI+sNXwD5V+6iIFXB+JBHB2gbeAVGOMeEmmJfLWBas1SRGhnMDbG04BAEEcDWJE0EAgE/odAEEf0hEAgEGhGIIijGbJ4IRAIBII4og8EAoFAMwJBHM2QxQuBQCDwBBqkyHR7zIhNAAAAAElFTkSuQmCC\" alt=\"C0 = (dt - 2KX)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35px;\" width=\"135\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.2px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.6px; text-align: left; transform-origin: 384px 17.6px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C1 = (dt + 2KX)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35px;\" width=\"135\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.8px; text-align: left; transform-origin: 384px 17.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C2 = (2K(1-X)-dt)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35.5px;\" width=\"135\" height=\"35.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 66px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 33px; text-align: left; transform-origin: 384px 33px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.3917px 8px; transform-origin: 35.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNotice that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C0+C1+C2 = 1\" style=\"width: 108px; height: 20px;\" width=\"108\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 289.742px 8px; transform-origin: 289.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. With the assumption that the first value of the outflow equals the first value of the inflow, this equation for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O2\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 207.717px 8px; transform-origin: 207.717px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be used to compute the outflow hydrograph. The guideline for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dt\" style=\"width: 18.5px; height: 18px;\" width=\"18.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.892px 8px; transform-origin: 111.892px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e above ensures that the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C0\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are positive.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t2,O,dtOK] = Muskingum(t,I,K,X,dt)\r\n  y = x;\r\nend","test_suite":"%%  Chin example 5.38\r\nK = 40;         %  Time parameter (min)\r\nX = 0.2;        %  Weighting parameter \r\ndt = 30;        %  Time step (min)\r\nt = 0:30:600;   %  Time (min)\r\nI = [10 10 25 45 31.3 27.5 25 23.8 21.3 19.4 17.5 16.3 13.5 12.1 10 10 10 10 10 10 10];   %  Inflow (m3/s)\r\nt_correct = 0:dt:600;   %  Correct time (min)\r\nO_correct = [10 10.000 12.234 23.361 35.133 32.120 28.799 26.195 24.294 22.100 20.094 18.259 16.592 14.410 12.623 10.949 10.343 10.124 10.045 10.016 10.006];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Chin example 5.39\r\nK = 0.604;      %  Time parameter (h)\r\nX = 0.102;      %  Weighting parameter \r\ndt = 0.5;       %  Time step (h)\r\nt = 0:0.5:8;    %  Time (h)\r\nI = [42.4 46.3 51.8 56.2 57.6 65.1 80.3 90.6 103.2 81.5 78.3 65.8 59.6 56.3 50.8 53.1 50.7];   %  Inflow (m3/s)\r\nt_correct = 0:dt:8;   %  Correct time (min)\r\nO_correct = [42.400 43.327 46.510 50.893 54.574 58.266 66.191 77.540 88.774 92.714 84.880 77.757 68.741 62.190 57.167 53.698 52.750];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c5e-3))\r\n\r\n%%  Gupta example 12.7\r\nK = 3.07;       %  Time parameter (h)\r\nX = 0.39;       %  Weighting parameter \r\ndt = 12;        %  Time step (h)\r\nt = 12:12:120;  %  Time (h)\r\nI = [100 300 680 500 400 310 230 180 100 50];   %  Inflow (cfs)\r\nt_correct = 12:dt:120;   %  Correct time (h)\r\nO_correct = [100 222 573 626 373 359 235 197 123 58];  %  Outflow (cfs)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c0.6))\r\n\r\n%%  Homework problem 44a\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 30;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5.000 6.424 15.930 23.650 20.977 19.035 17.713 16.841 15.948 14.981 13.746 13.187 12.289 9.465 6.074 5.258 5.062 5.015 5.004];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44b1\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 35;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5 7.350 18.103 22.845 19.774 17.965 16.839 15.781 14.614 13.436 12.489 9.898 6.283 5.214 5.036 5.006];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44b2\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 10;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5.000 4.223 5.122 7.129 10.048\t13.062 16.139 20.271 22.245 22.793 22.094 21.428 20.785 20.119 19.543 19.027 18.519 18.104 17.751 17.450 17.150 16.850 16.550 16.250 15.950 15.687 15.344 14.948 14.442 14.073 13.796 13.597 13.398 13.199 13.167 12.773 12.140 11.404 10.444 9.334 7.865 6.894 6.252 5.827 5.547 5.362 5.239 5.158 5.104 5.069 5.046 5.030 5.020 5.013 5.009];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44c\r\nK = 35;         %  Time parameter (min)\r\nX = 0.6;        %  Weighting parameter \r\ndt = 45;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5 5.711 26.085 18.977 17.719 16.407 15.024 12.997 12.606 8.234 4.247 5.175 4.959];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-02T23:02:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-02T16:23:33.000Z","updated_at":"2024-11-11T12:36:59.000Z","published_at":"2023-04-02T16:31:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I(t)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI(t)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at which the hydrograph is reported, the routing parameters \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"X\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the desired time step \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O(t)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO(t)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a Boolean flag that says whether the time step is within the guidelines \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2KX \u0026lt;= dt \u0026lt; 2K(1-X)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2KX \\\\le \\\\Delta t \\\\le 2K(1-X)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBonus points to anyone who can solve this problem using the FILTER command. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and outflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are connected to the storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dS/dt = I - O\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dS}{dt} = I-O\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis equation is written in discretized form as \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(S2-S1)/dt = (I1+I2)/2-(O1+O2)/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{S_2 – S_1}{\\\\Delta t} = \\\\frac{I_1+I_2}{2} - \\\\frac{O_1+O_2}{2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the current storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the Muskingum method, the storage, inflow, and outflow are further related by \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S = K[XI + (1-X)O]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS = K[XI+(1-X)O]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a time scale related to travel time in the river section and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"X\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2 = C0 I2 + C1 I1 + C2 O1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2 = C_0 I_2 + C_1 I_1 + C_2 O_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0 = (dt - 2KX)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0 = \\\\frac{\\\\Delta t – 2KX}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C1 = (dt + 2KX)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_1 = \\\\frac{\\\\Delta t + 2KX}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C2 = (2K(1-X)-dt)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_2 = \\\\frac{2K(1-X)-\\\\Delta t}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNotice that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0+C1+C2 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0+C_1+C_2 = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. With the assumption that the first value of the outflow equals the first value of the inflow, this equation for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be used to compute the outflow hydrograph. The guideline for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e above ensures that the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are positive.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57605,"title":"Determine flows of given probability using empirical frequency analysis","description":"Write a function that takes as input  observations of peak streamflow  and exceedance probabilities  expressed as percentages and returns the flows  corresponding to the probabilities. \r\nUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank  (e.g., the highest flow has ). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with . Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return NaN for any probabilities that fall outside the range. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 158px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 79px; transform-origin: 407px 79px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.158px 8px; transform-origin: 109.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes as input \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.242px 8px; transform-origin: 104.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e observations of peak streamflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Qo\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5417px 8px; transform-origin: 94.5417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and exceedance probabilities \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p1\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5083px 8px; transform-origin: 45.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e expressed as percentages and returns the flows \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q1\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.925px 8px; transform-origin: 108.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to the probabilities. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 345.033px 8px; transform-origin: 345.033px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.4917px 8px; transform-origin: 31.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (e.g., the highest flow has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m = 1\" style=\"width: 40px; height: 18px;\" width=\"40\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.142px 8px; transform-origin: 311.142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 100m/(n+1)\" style=\"width: 115px; height: 18.5px;\" width=\"115\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7833px 8px; transform-origin: 63.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.2833px 8px; transform-origin: 87.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for any probabilities that fall outside the range. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Q1 = floodFreq1(Qo,p1)\r\n%  Qo = observed flows\r\n%  p1 = exceedance probabilities at which the flows are to be reported\r\n%  Q1 = flows corresponding to the probabilities p1\r\n\r\n  Q1 = Qo*log(normcdf(p1));\r\nend","test_suite":"%%  Small sample from lognormal distribution\r\nQo = [27 360 71 8798 58 122 468 638 19 114 3542 781 356 635 6093 748 8305 8 6253 875];\r\np1 = [5 10 20 50];\r\nQ1_correct = [8773 8100 5583 552];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Larger sample from lognormal distribution\r\nrng(1)\r\nQo = 10.^(randn(1,500)+1.7);\r\np1 = [0.2 1 2 4 5 10 20 50];\r\nQ1_correct = [106602 21248 6176 2975 2432 1062 326 58];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Yellowstone River at Livingston, MT\r\n%  Flows from here down are in cubic feet per second\r\nQo = [18300 15400 13100 10600 18500 30600 13500 20400 15800 20600 26800 17500 21400 20000 22800 21200 20400 14900 25800 21900 17100 24200 15700 15600 20400 20200 20200 27900 16000 24900 24600 21200 24400 29200 26700 21100 36300 25700 21400 14200 26000 20100 15000 23800 27900 18600 17900 15200 24000 7450 16200 16200 17200 23000 13800 24000 16900 23700 37100 38000 18800 23400 19300 14800 25900 27200 13300 17900 22600 15200 26300 23500 28100 40600 23500 17900 32700 15600 12800 26300 33600 22800 30600 18500];\r\np1 = [9.58 13.53 50];\r\nQ1_correct = [30000 27900 20850];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Mullica River near Batsto, NJ\r\nQo = [1190 407 815 360 382 350 384 245 287 1170 645 990 1050 435 430 630 489 1380 499 240 857 1840 380 204 420 705 946 143 419 666 269 579 490 565 401 488 578 149 401 473 747 364 335 343 201 509 452 420 449 1320 258 312 867 1860 303 332 537 387 222 342 517 676 249 285];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 1854 1564 1365 1110 747 433];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%  Charles River near Waltham, MA\r\nQo = [690 1520 1020 1370 2540 1020 2180 1020 1600 555 1470 1180 1000 1240 1360 692 1730 575 869 933 1250 1360 1550 2490 1990 957 1940 1460 1510 1850 1540 1340 890 904 637 1250 2670 1800 1790 1110 1670 1630 1090 895 4150 1610 1740 3480 1140 1220 2960 1970 2410 811 1110 2710 837 779 1240 1030 637 2180 1430 757 1430 2990 2180 1080 1090 2190 721 1170 1510 1510 1590 1250 1390 1390 4270 1770 1080 1570 1460 1640 634 1150 1250 1180 806 1520];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 4172 3166 2974 2482 1840 1367];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%  Merced River at Happy Isles Bridge near Yosemite, CA\r\nQo = [2500 3320 3180 3800 2720 2720 3240 2620 1240 2620 2240 2820 2050 2520 1870 1350 2570 2520 935 2820 2380 3020 8400 1210 2620 3220 2800 3480 1980 3040 3690 2450 3080 2480 2520 9260 3580 2180 2500 2800 9860 2910 3640 1520 1710 1080 2230 5200 1720 9240 1640 4640 1480 4980 2330 2170 2690 4240 3260 4650 1440 1800 4190 3500 4040 2100 4880 5450 2860 1600 4040 1750 1640 1910 1090 2310 1490 3140 1870 5220 5900 10100 4150 2810 2920 2330 2290 4550 1830 5680 4350 1180 2760 2750 4470 4610 2250 1750 1190 882 2490 5210 8060 4240 2160 1410];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [10083 9776 9005 8281 5213 4247 2700];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct));\r\n\r\n%%  Quashnet River near Waquoit, MA\r\nQo = [41 36 33 41 40 35 28 34 39 42 32 27 39 26 33 40 36 61 83 32 39.2 52 44 42 58 30 32 30.1 50.1 48.4 53.2 40.8];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN NaN 76.0 68.7 56.6 49.1 39.1];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(all(isnan(Q1(1:2))) \u0026\u0026 isequal(round(Q1(3:end),1),Q1_correct(3:end)));\r\n\r\n%%  Illinois River at Henry, IL\r\nQo = [104000 108000 53700 106000 95200 46300 45100 45000 40200 53700 30900 67000 47000 58900 78000 117000 88900 55000 40400 71800 88500 38400 52100 84600 32400 90300 128000 92400 58300 64000 49000 161000 65400 98500 107000 93100 111000 108000 120000 64200 51600];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN NaN 138560 127200 115800 106600 67000];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(all(isnan(Q1(1:2))) \u0026\u0026 isequal(round(Q1(3:end)),Q1_correct(3:end)));\r\n\r\n%%  South Skunk River near Ames, IA\r\nQo = [1990 600 3490 2580 3000 2890 3230 2320 3050 2530 4500 8060 4010 2270 6550 2620 3000 3820 5320 1630 980 8630 1340 376 3540 3150 1720 6210 1990 4300 1820 2170 5260 2900 2790 4890 4380 1330 3660 3030 3340 5780 5230 3580 5300 2240 4980 2720 1880 3490 5150 5020 1980 4040 3040 565 370 6600 4700 2350 11200 2340 1640 14000 2080 4760 3630 906 1990 1070 2030 2520 2310 3330 6510 11000 4560 14800 1620 730 6740 9250 11200 6420 1890 4380 6740 3260 455 4210];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 14144 11181 11060 7092 5292 3190];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%\r\nfiletext = fileread('floodFreq1.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-21T19:33:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-01-21T19:33:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-21T19:29:29.000Z","updated_at":"2023-01-21T19:33:03.000Z","published_at":"2023-01-21T19:29:55.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes as input \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e observations of peak streamflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Qo\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and exceedance probabilities \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e expressed as percentages and returns the flows \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to the probabilities. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (e.g., the highest flow has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 100m/(n+1)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 100 m /(n+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for any probabilities that fall outside the range. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57800,"title":"Compute infiltration and runoff under constant precipitation with the Green-Ampt method","description":"Problem statement\r\nWrite a function that computes infiltration, depression storage, and runoff using the Green-Ampt method. It should take as input the rainfall intensity , saturated hydraulic conductivity , initial moisture content , saturated moisture content , average suction head , maximum available depression storage , and a vector of times . If ponding occurs, the function should insert the ponding time  into the time vector. It should then compute the cumulative infiltration  and depression storage  at each of the times, as well as the runoff  during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths.  \r\nBackground\r\nTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate  is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) , and the cumulative infiltration  is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \r\nThe infiltration capacity predicted by the Green-Ampt method is\r\n\r\nThe cumulative infiltration  at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\r\n\r\nwhere\r\n\r\nis the time to infiltrate  from the start of the storm under immediate ponding.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 286.3px; transform-origin: 407px 286.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 64.5px; text-align: left; transform-origin: 384px 64.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 257.242px 8px; transform-origin: 257.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eGreen-Ampt method\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.775px 8px; transform-origin: 56.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. It should take as input the rainfall intensity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.467px 8px; transform-origin: 103.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ks\" style=\"width: 17px; height: 20px;\" width=\"17\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.4583px 8px; transform-origin: 75.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, initial moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"thetai\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.675px 8px; transform-origin: 88.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"thetas\" style=\"width: 14px; height: 20px;\" width=\"14\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, average suction head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Psi_av\" style=\"width: 23.5px; height: 20px;\" width=\"23.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.208px 8px; transform-origin: 127.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, maximum available depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Smax\" style=\"width: 27px; height: 20px;\" width=\"27\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.775px 8px; transform-origin: 70.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a vector of times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.725px 8px; transform-origin: 72.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If ponding occurs, the function should insert the ponding time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 216.25px 8px; transform-origin: 216.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e into the time vector. It should then compute the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.933px 8px; transform-origin: 130.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at each of the times, as well as the runoff \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.983px 8px; transform-origin: 169.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.5px; text-align: left; transform-origin: 384px 42.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.342px 8px; transform-origin: 378.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.025px 8px; transform-origin: 140.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"fp\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.4667px 8px; transform-origin: 96.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.408px 8px; transform-origin: 126.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.65px 8px; transform-origin: 195.65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.9px; text-align: left; transform-origin: 384px 19.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"fp = Ks(1+Psi_av(thetas-thetai)/F)\" style=\"width: 162.5px; height: 40px;\" width=\"162.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.3px 8px; transform-origin: 81.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 290.558px 8px; transform-origin: 290.558px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.5px; text-align: left; transform-origin: 384px 19.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" alt=\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\" style=\"width: 264px; height: 41px;\" width=\"264\" height=\"41\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.0583px 8px; transform-origin: 68.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the time to infiltrate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fp\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 166.85px 8px; transform-origin: 166.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the start of the storm under immediate ponding. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax)\r\n%  See tests for definitions and units of variables\r\n  F = i*t; S = min(F,Smax); Q = i*t-F-S;\r\nend","test_suite":"%%  Gupta ex. 4.2\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = zeros(size(F_correct));                     %  Depression storage (mm)\r\nQ_correct = [0 0.1680 1.4553 2.2120];                   %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, with depression storage\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = [0 0 0.1680 1.6233 3.8352];                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, i \u003c Ks\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = rand;                       %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5 \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 0.4375;                     %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 10.5;                       %  Intensity (mm/h)\r\ntp_correct = 0.5609;            %  Ponding time (h)\r\nF_correct = [0 5.8896 9.4982 14.9421 19.0537 22.5444];     %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                    %  Depression storage (mm)\r\nQ_correct = [0 1.0018 5.0561 6.3884 7.0093];               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity + depression storage \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 75;                      %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 65;                         %  Intensity (mm/h)\r\ntp_correct = 0.0138;            %  Ponding time (h)\r\nF_correct = [0 0.8961 11.1781 16.1243 20.0327 23.4058];     %  Cum. infiltration (mm)\r\nS_correct = [0 0 53.8219 75 75 75];                         %  Depression storage (mm)\r\nQ_correct = [0 0 38.8757 61.0916 61.6268];                  %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('GreenAmptConst.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-18T02:19:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-18T02:01:12.000Z","updated_at":"2023-03-18T02:19:29.000Z","published_at":"2023-03-18T02:19:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGreen-Ampt method\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. It should take as input the rainfall intensity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ks\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, initial moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetai\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetas\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, average suction head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Psi_av\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Psi_{av}\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, maximum available depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Smax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a vector of times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If ponding occurs, the function should insert the ponding time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e into the time vector. It should then compute the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at each of the times, as well as the runoff \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp = Ks(1+Psi_av(thetas-thetai)/F)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p  = K_s\\\\left(1+\\\\frac{\\\\Psi_{av}(\\\\theta_s - \\\\theta_i)}{F}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = (1/Ks)[F-Psi_av(thetas-thetai) ln(1+F/Psi_av(thetas-thetai)]+tp-t'p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = \\\\frac{1}{K_s}\\\\left[F-\\\\Psi_{av}(\\\\theta_s - \\\\theta_i) \\\\ln\\\\left(1+\\\\frac{F}{\\\\Psi_{av}(\\\\theta_s-\\\\theta_i)}\\\\right)\\\\right]+t_p-t^\\\\prime_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et^\\\\prime_p = \\\\frac{F_p}{K_s} – (\\\\theta_s - \\\\theta_i)\\\\frac{\\\\Psi_{av}}{K_s} \\\\ln\\\\left(1+\\\\frac{F_p}{\\\\Psi\\n_{av} (\\\\theta_s - \\\\theta_i)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis the time to infiltrate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the start of the storm under immediate ponding. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57765,"title":"Determine whether a hydrograph is a unit hydrograph","description":"A hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate  (or flow or discharge) as a function of time  resulting from a given excess rainfall (expressed as a depth ) for a storm of a specified duration. A unit hydrograph results from unit excess rainfall (e.g.,  = 1 cm). \r\nWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time  in minutes, the flow rate  in , and the catchment area  in . Allow for a tolerance of 0.01 cm in the excess rainfall depth.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.467px 8px; transform-origin: 333.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or flow or discharge) as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.267px 8px; transform-origin: 188.267px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e resulting from a given excess rainfall (expressed as a depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.8333px 8px; transform-origin: 82.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) for a storm of a specified duration. A \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eunit hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.9px 8px; transform-origin: 115.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eresults from unit excess rainfall (e.g., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.3583px 8px; transform-origin: 29.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 1 cm). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 330.108px 8px; transform-origin: 330.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in minutes, the flow rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^3/s\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 8px; transform-origin: 79.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the catchment area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^2\" style=\"width: 19.5px; height: 19px;\" width=\"19.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.642px 8px; transform-origin: 188.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isUnitHydrograph(t,Q,A)\r\n  tf = isequal(Q*t/A,1);\r\nend","test_suite":"%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:40:520;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2520000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 753601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 735601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 3.2 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 2.3 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-11T12:56:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-11T01:14:20.000Z","updated_at":"2023-03-11T12:56:36.000Z","published_at":"2023-03-11T01:14:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or flow or discharge) as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e resulting from a given excess rainfall (expressed as a depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) for a storm of a specified duration. A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunit hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eresults from unit excess rainfall (e.g., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 1 cm). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in minutes, the flow rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^3/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^3/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the catchment area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57635,"title":"Compute the average precipitation for a watershed using the Thiessen polygon method","description":"Several methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \r\nThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \r\nWrite a function that takes the precipitation amounts and the (, ) coordinates of the boundary and the gauges and compute the average precipitation for the watershed. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93px; transform-origin: 407px 93px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.425px 8px; transform-origin: 366.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSeveral methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190.458px 8px; transform-origin: 190.458px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the precipitation amounts and the (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.767px 8px; transform-origin: 156.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) coordinates of the boundary and the gauges and compute the average precipitation for the watershed. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Pavg = spatial_average(xd,yd,P,xb,yb)\r\n%  (xd, yd) = coordinates of the precipitation gauges\r\n%  P = precipitation values\r\n%  (xb,yb) = coordinates of the boundary of the watershed\r\n\r\n   Pavg = integral(P*dx*dy)/integral(dx*dy);","test_suite":"%% Rectangular catchment with simple gauge placement and values\r\nxb = [0 5 5 0 0];    % km\r\nyb = [0 0 10 10 0];  % km\r\nxd = [-1 6 6 -1];\r\nyd = [-1 -1 11 11];\r\nP  = [20 20 40 40];  % cm\r\nPavg_correct = 30;   % cm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.05);\r\n\r\n%% Example 3 from dreamcivil.com\r\nxb = [0 10 10 0 0]; % km\r\nyb = [0 0 5 5 0];   % km\r\nxd = xb(1:end-1);\r\nyd = yb(1:end-1);\r\nP  = [11 15 12 10]; % cm\r\nPavg_correct = 12;  % cm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01);\r\n\r\n%% Rectangular catchment with more complicated gauge locations \r\nxb = [0 10 10 0 0];\r\nyb = [0 0 30 30 0];\r\nxd = [-3 8  4 13  1 9];\r\nyd = [-2 2 12 21 25 33];\r\nP  = 132+3*(yd-33);\r\nPavg_correct = 77.65;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)/Pavg_correct\u003c0.01)\r\n\r\n%% More complicated boundary\r\nxb = 10*[0.5497 0.4705 0.3840 0.3214 0.2937 0.2882 0.3379 0.4632 0.6271 0.7284 0.7947 0.8241 0.8039 0.8039 0.7689 0.7302 0.6452 0.5497];   % km\r\nyb = 10*[0.1857 0.2512 0.3867 0.5152 0.6717 0.7909 0.9007 0.9591 0.9498 0.8797 0.7605 0.6320 0.4708 0.4708 0.3914 0.2745 0.2194 0.1857];   % km\r\nxd = 10*[0.4 0.63 0.5 0.7 0.8];\r\nyd = 10*[0.9 0.6 0.35 0.8 0.32];\r\nP  = [113 166 140 183 125]; % mm\r\nPavg_correct = 148.271; % mm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n\r\n%% Example 5.5 from Chin\r\nxb = [2.0084 2.4293 2.8156 3.0028 3.2368 3.4126 3.6713 3.8467 4.0235 4.2117 4.3540 4.5197 4.7338 4.9362 5.0688 5.2611 5.4307 5.5418 5.6399 5.7033 5.7094 5.6167 5.4566 5.3269 5.2170 5.1962 5.2033 5.2325 5.2838 5.3351 5.3630 5.3672 5.3594 5.2956 5.1854 5.0638 4.9172 4.7914 4.5239 4.2432 4.0206 3.9153 3.7154 3.4805 3.3047 3.1412 2.9657 2.6980 2.4305 2.1494 1.9034 1.6444 1.3955 1.1317 0.9849 0.8611 0.7998 0.7605 0.6858 0.5893 0.4919 0.3519 0.2515 0.1265 0.0875 0.0801 0.1796 0.3474 0.5154 0.6832 0.7618 0.8867 1.0592 1.2773 1.4249 1.5055 1.5835 1.5910 1.5914 1.6825 1.8099 1.9151 2.0084];\r\nyb = [6.4122 6.4364 6.4348 6.4401 6.4466 6.4391 6.3966 6.4015 6.3566 6.3246 6.2539 6.1839 6.0530 5.9218 5.7761 5.5824 5.3632 5.1423 4.9708 4.7859 4.5496 4.0617 3.4599 3.0456 2.7688 2.6686 2.3950 2.1719 1.9991 1.8263 1.6529 1.4912 1.3416 1.0910 0.8266 0.5494 0.3337 0.2182 0.1485 0.1406 0.1468 0.1439 0.1756 0.2064 0.2139 0.1969 0.1920 0.1347 0.0650 0.0695 0.0751 0.1301 0.2475 0.4890 0.7338 0.9917 1.5500 1.7106 1.8828 1.9921 2.1387 2.5703 2.8288 3.1364 3.2847 3.5707 3.7975 4.1008 4.3918 4.6951 4.8218 4.9746 5.0914 5.2593 5.4377 5.4897 5.6412 5.8032 6.2388 6.3409 6.3942 6.3972 6.4122];\r\nxd = [1.3 1.0 4.2 3.5 2.1];\r\nyd = [7.0 3.7 4.9 1.4 -1.0];\r\nP  = [60 90 65 35 20];\r\nPavg_correct = 59.301;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n\r\n%% C E 372 problem 11\r\nxb = [33.6241 31.3609 26.3820 25.3635 24.0062 22.8754 21.4057 19.4844 18.2414 17.5648 15.1930 15.1935 15.5336 15.8735 15.8742 15.3089 13.6128 12.9347 12.0319 11.4673 10.2237 8.8694 8.0782 7.7400 7.4023 7.4049 7.7466 8.2004 9.6732 11.4838 14.6517 15.7834 16.4627 16.8027 16.8037 15.5614 14.0926 13.0759 12.3981 12.5118 14.5502 15.4557 16.7001 19.1891 22.2439 24.2812 26.3185 27.5654 27.9054 29.1500 30.9595 32.7690 34.5782 36.2742 38.0830 39.1005 40.6836 41.9275 46.9026 47.6937 49.5021 49.8399 49.8383 49.1574 48.2507 46.8905 45.1911 44.5108 44.0567 43.4877 43.0343 42.5763 42.4619 41.2167 39.1791 38.8389 38.8379 38.3850 37.2537 36.0095 35.5567 34.6511 35.2149 35.4394 35.5514 35.5496 35.3221 35.2082 33.7370]; % mi\r\nyb = [5.2159 3.9673 1.3564 0.6755 0.5609 0.7865 1.4650 2.9363 4.1815 6.2206 9.7311 10.2976 11.2045 11.7714 12.5646 12.7907 13.1290 13.6949 15.8471 16.7530 17.3184 20.3766 20.9425 22.0753 23.7747 26.6075 29.1008 30.5743 33.2952 34.3168 35.4529 36.1339 36.9277 37.6079 38.7411 40.6662 42.2512 43.4967 44.4026 44.9693 47.6908 48.4848 48.8259 49.6215 50.7575 52.3458 53.9342 56.8815 57.5617 58.1295 58.0179 57.9063 57.4547 56.8898 56.0983 55.6460 55.3075 55.0821 53.6137 53.0479 51.6898 50.1037 48.4040 46.0238 43.9832 40.8092 37.7481 35.9344 34.1209 30.4943 29.3608 23.4680 22.1081 20.9738 19.0455 18.1387 17.0055 16.5518 16.2108 16.0963 15.6427 14.8486 13.0361 11.2233 10.0903 8.1639 6.8039 5.8973 4.9894]; % mi\r\nxd = [15.9758 6.0340 4.0115 15.4546 38.1999 50.7358 40.6553 33.7370 31.4005 19.7352 28.4331]; % mi\r\nyd = [0.3267 12.1020 26.1511 47.3517 60.0644 40.6995 25.2792 4.9894 45.8937 28.9988 17.5623]; % mi\r\nP  = [29.79 34.97 25.60 24.27 24.60 42.61 42.35 15.51 39.99 43.04 28.41]; % in\r\nPavg_correct = 35.011;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2023-02-04T01:17:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2023-02-04T01:17:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-01T17:01:04.000Z","updated_at":"2023-02-04T01:17:57.000Z","published_at":"2023-02-01T17:03:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSeveral methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the precipitation amounts and the (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) coordinates of the boundary and the gauges and compute the average precipitation for the watershed. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":57620,"title":"Compute frequency factors for the normal distribution","description":"In frequency analysis in hydrology, the streamflow  corresponding to a specified exceedance probability  (or return period ) can be computed as\r\n\r\nwhere  and  are the mean and standard deviation of the streamflow series, respectively, and  is the frequency factor. \r\nWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.242px 8px; transform-origin: 156.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn frequency analysis in hydrology, the streamflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"QT\" style=\"width: 20.5px; height: 20px;\" width=\"20.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.95px 8px; transform-origin: 164.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to a specified exceedance probability \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.6667px 8px; transform-origin: 32.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or return period \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG8AAAAlCAYAAABMBrdqAAAEZUlEQVR4Xu1aOYsVQRDe/QWekRiImgiC4ploqqKpooKBIHiF4gEegXiAYmTgKhiYeKGRoHiAgYrgBQqCiRoYGHngL9DvY6eWevN6Zrq7uh/71h74eMd0V3fX13V0zYyOlGtoNTA6tDMvEx8p5A3xJijk5SXvEsRfAL7mGKaQl0Or4zKXAO+BBYW8fErOJflMRdy2XAO0Wd4a46Dfc+0447y6us9Hgz/Az66GHfc/4/5x4JZRTmP3JvLE5KXjb3x5Xf1YWO0oufeo4f9s7iKTMkjaQWAfsBT4YBhnI/reB2Yn2ATB5O1Bj8vAbeBozYIe4vf6SuJZfB5T0ukibgJvgZWGxQ+y6ywMdqoiTca1ksdEhdf+nAtpsjya+nRgQ21wLvSH+m8Tvj+otXmD349rpOZcg0U2LWQx8BE4CayohFnJ+wU5Oxy6scy1r28TeX/R0mXy4g5EkKs/LfNi7okn1cK4sMPAuQTk0fvQ8mZmmGOPSJfy6ftXAa5AywyKbpQXY13dMvk/22hXmnsNqeSnIo96+zIIHYSe8+gSxbUcwffzqTQ3CeSkIE/CitXteqkjhLx6vBvIBL1WkaZRCvKY6B0CmJH7XtTrImAuMA24UnWUeMyfL4EXdYEh5Ol4x6NDKp9ONz3Hd6Ut7T7hnuVsloI8eqarioC2ZXHdm4HdAI9VvMaAG8A1gDqeUbt3Qq8xhDwGYZ6BePEIkapyoJVm4dDqCazkkQzGutDzLYshz5VeGZbWAVIP5WFfyF2L7xMWGEKeFrIXQsS8LQpnX26CnVYh6M8zlaUAbCWPidpywJXEtS1PztRsw/Mx+2sPoufVk2f4kie7SiYRursScJNdhJW82HIYs9Ot1epc3kPPq6co4kueVE44Bl1DSEDOrvVEA1jIE9cXUw7jmZpX09FLz2s72k0c4XzJ0/GOQTVr2ScRGaFiLOTFlsN0vGsKRboc2WOZvuSx3MPMh5erJBaqKN1+KmSbseUwXfRwhSJ9POurF/uQV3/CEOMa2sgd9mzTUg6TokeTy9TJTJ/R+JCnBTQNYrG8Yc82GYNoeaGhRFuVq1rF+68AWqTzaOZDns6GplpJTG+6mJhnKYfpokfP+a2alOQZTBBXA30FiC7yfB4BWaxuMvWNIY9e4zQQk33rJLAeiiS7bySOiusiTw/A9j2p6mTSvHEuTJr4DFIqGb4ehjHrDhBToNdFD0lWaCwHAD656ZxDE3nchcsAPpCtX0/xxzcg27sZRiJCupO0XQArI/WL1Rq+CtFUSYoth3EcXfRgHvEO4Hsz84BnwBOgs07bZXkhivjf2nKDbwFiXvfQSaAr3nnpspDnpSZno9hyGIXpJDCag+iO8WueEj3l7Bt75pWih+noVciL20vyjkrMYzFdEutMStqmV8iLIy+2HMZs8jogr04W8uL0H92LlnMPCH2TQJ6cuwa+iz+Dn0UWywvnkNbDd02ClR0+VHuPQl5qjQ5QXiFvgMpOPVQhL7VGByjvH3tR7yYA92EaAAAAAElFTkSuQmCC\" alt=\"T = 1/p\" style=\"width: 55.5px; height: 18.5px;\" width=\"55.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.2917px 8px; transform-origin: 67.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"QT = mu + KT sigma\" style=\"width: 89.5px; height: 20px;\" width=\"89.5\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eμ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eσ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 249.592px 8px; transform-origin: 249.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the mean and standard deviation of the streamflow series, respectively, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"KT\" style=\"width: 19.5px; height: 20px;\" width=\"19.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.275px 8px; transform-origin: 74.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the frequency factor. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.275px 8px; transform-origin: 373.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function KT = normFreqFactor(p)\r\n  KT = trapz(QT:inf,exp(-Q.^2));\r\nend","test_suite":"%%\r\np = 0.001;\r\nKT_correct = 3.090;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.002;\r\nKT_correct = 2.878;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.01;\r\nKT_correct = 2.326;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.02;\r\nKT_correct = 2.054;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.04;\r\nKT_correct = 1.751;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.1;\r\nKT_correct = 1.282;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.2;\r\nKT_correct = 0.842;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.3;\r\nKT_correct = 0.524;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.5;\r\nKT_correct = 0;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\np = 0.8;\r\nKT_correct = -0.842;\r\nassert(abs(normFreqFactor(p)-KT_correct)\u003c1e-3)\r\n\r\n%%\r\nT = [5 10 20 25 50 100 250 500 1000];\r\nKT_correct = [0.842 1.282 1.645 1.751 2.054 2.326 2.652 2.878 3.090];\r\nassert(all(abs(normFreqFactor(1./T)-KT_correct)\u003c1e-3))\r\n\r\n%%\r\np = rand(1,randi(15));\r\nK1 = normFreqFactor(p);\r\nK2 = normFreqFactor(1-p);\r\nassert(all(abs(K1+K2)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('normFreqFactor.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp') || contains(filetext, 'interp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-29T19:23:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-29T19:23:11.000Z","updated_at":"2026-01-04T12:13:24.000Z","published_at":"2023-01-29T19:23:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn frequency analysis in hydrology, the streamflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"QT\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_T\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to a specified exceedance probability \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or return period \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T = 1/p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = 1/p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) can be computed as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"QT = mu + KT sigma\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_T = \\\\mu + K_T \\\\sigma\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"mu\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are the mean and standard deviation of the streamflow series, respectively, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"KT\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_T\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the frequency factor. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the frequency factor for the normal distribution given the exceedance probability as a vector. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57844,"title":"Solve an ODE: draining tank","description":"Write a function to compute the time to drain a cylindrical tank of diameter  from an initial level  to a level . The outflow occurs through a small circular orifice of diameter  at the bottom of the tank, and the outflow  can be computed with , where  is a discharge coefficient,  is the area of the orifice, and  is the acceleration of gravity, which should be taken as 9.81 m/s. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 319.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 159.55px; transform-origin: 407px 159.55px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 87.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 43.55px; text-align: left; transform-origin: 384px 43.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 229.742px 8px; transform-origin: 229.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the time to drain a cylindrical tank of diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.85px 8px; transform-origin: 61.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from an initial level \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.8917px 8px; transform-origin: 31.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to a level \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.225px 8px; transform-origin: 40.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The outflow occurs through a small circular orifice of diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Do\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.667px 8px; transform-origin: 130.667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the bottom of the tank, and the outflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.9583px 8px; transform-origin: 71.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be computed with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = Cd Ao sqrt(2 g h)\" style=\"width: 99.5px; height: 22px;\" width=\"99.5\" height=\"22\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Cd\" style=\"width: 18.5px; height: 20px;\" width=\"18.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.3333px 8px; transform-origin: 82.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a discharge coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ao\" style=\"width: 17px; height: 20px;\" width=\"17\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.175px 8px; transform-origin: 92.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the orifice, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.708px 8px; transform-origin: 111.708px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the acceleration of gravity, which should be taken as 9.81 m/s\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAmCAYAAADN0BvRAAABE0lEQVRIS2NkoBAwUqifYRgbEA4Mm0IgNoeG0UkgnQvEp9HDDFsYZAAV5QPxRCB+D8RJQOwG1egOpHchG4LNgGdABbZAfBdJ4U6oISDNIEPgAN0AkE3BQJyO5lSQl1YA8Q0g1iTkAmxJA2QwyBUEXYBNM0gMFC7TgbgKiNvJccFKoCY9ILYG4nekGqAM1HAHGngoMQAyiJikfAKobiO602GuIGTATKhC9FjBGY3I3gMFnCMQZ6L7m5gwAGlOAGIvNM1C0NgApQswwOYFWKJZBZR/iGwbkB0DxKA8AooVrAaYAkX3ATEPmkYY9zmQoYPsKkKBiMMchPCoAcQlZbwBORqIo4GIqzwgmAOJKZGINmQYpEQA0UUlJ+mjkqgAAAAASUVORK5CYII=\" alt=\"^2\" style=\"width: 8px; height: 19px;\" width=\"8\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. 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\" data-image-state=\"image-loaded\" width=\"308\" height=\"223\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = drainingTank(h0,h,Cd,Do,D)\r\n  g = 9.81;    %  Acceleration of gravity (m/s2)\r\n  t = sqrt((h0-h)/g);\r\nend","test_suite":"%% Rounded orifice\r\nh0 = 3;                     % Initial depth (m)\r\nCd = 0.98;                  % Discharge coefficient\r\nDo = 0.1;                   % Orifice diameter (m)\r\nD  = 1;                     % Tank diameter (m)\r\nh  = 2;                     % Depth in question (m)\r\nt_correct = 14.6440;        % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Sharp-edged orifice\r\nh0 = 5;                                           % Initial depth (m)\r\nCd = 0.6;                                         % Discharge coefficient\r\nDo = 0.2;                                         % Orifice diameter (m)\r\nD  = 2.5;                                         % Tank diameter (m)\r\nh  = 4:-1:1;                                      % Depth in question (m)\r\nt_correct = [27.7579 59.2645 96.6372 145.3422];   % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(all(abs(t-t_correct)\u003c1e-4))\r\n\r\n%% External mouthpiece\r\nh0 = 3;                     % Initial depth (m)\r\nCd = 0.8;                   % Discharge coefficient\r\nDo = 0.1;                   % Orifice diameter (m)\r\nD  = 1;                     % Tank diameter (m)\r\nh  = 2;                     % Depth in question (m)\r\nt_correct = 17.9389;        % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Convergent mouthpiece\r\nh0 = 1;                     % Initial depth (m)\r\nCd = 1;                     % Discharge coefficient\r\nDo = 0.05;                  % Orifice diameter (m)\r\nD  = 0.3;                   % Tank diameter (m)\r\nh  = 0.1;                   % Depth in question (m)\r\nt_correct = 11.1146;        % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(abs(t-t_correct)\u003c1e-4)\r\n\r\n%% Re-entrant mouthpiece\r\nh0 = 4.5;                                    % Initial depth (m)\r\nCd = 0.75;                                   % Discharge coefficient\r\nDo = 0.2;                                    % Orifice diameter (m)\r\nD  = 5;                                      % Tank diameter (m)\r\nh  = [1.2 0.8 0.4];                          % Depth in question (m)\r\nt_correct = [386.0058  461.6427  560.2147];  % Time (sec)\r\nt = drainingTank(h0,h,Cd,Do,D);\r\nassert(all(abs(t-t_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-01T12:15:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-28T00:41:34.000Z","updated_at":"2025-03-25T15:09:17.000Z","published_at":"2023-03-28T01:19:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the time to drain a cylindrical tank of diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from an initial level \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to a level \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The outflow occurs through a small circular orifice of diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Do\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the bottom of the tank, and the outflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = Cd Ao sqrt(2 g h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = C_d A_o \\\\sqrt{2 g h}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Cd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a discharge coefficient, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ao\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the orifice, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the acceleration of gravity, which should be taken as 9.81 m/s\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58314,"title":"Compute the normal depth of a channel","description":"For steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \r\nAs described in Cody Problem 57969, the normal depth, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) ):\r\n\r\nwhere  is Manning’s roughness coefficient,  is the hydraulic radius,  is the slope of the channel, and  is the cross-sectional area of the flow. The coefficient  is 1 for SI units and 1.49 for U.S. customary units.\r\nWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure channelStruct with the following fields and possible values:\r\n\r\nThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 850.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 425.1px; transform-origin: 407px 425.1px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.017px 8px; transform-origin: 380.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7917px 8px; transform-origin: 49.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs described in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/57969\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 57969\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.55px 8px; transform-origin: 15.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.85px 8px; transform-origin: 40.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003enormal depth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 197.833px 8px; transform-origin: 197.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = (C/n) R^(2/3) S0^(1/2) A\" style=\"width: 105.5px; height: 35px;\" width=\"105.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.55px 8px; transform-origin: 112.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is Manning’s roughness coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 8px; transform-origin: 73.5167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.1833px 8px; transform-origin: 85.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the slope of the channel,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the cross-sectional area of the flow. The coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155.942px 8px; transform-origin: 155.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 1 for SI units and 1.49 for U.S. customary units.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383px 8px; transform-origin: 383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.05px 8px; transform-origin: 50.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003echannelStruct\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.3333px 8px; transform-origin: 16.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the following fields and possible values:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 64.85px; text-align: left; transform-origin: 384px 64.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 435px;height: 124px\" 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\" data-image-state=\"image-loaded\" width=\"435\" height=\"124\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.15px 8px; transform-origin: 376.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 339.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 169.85px; text-align: left; transform-origin: 384px 169.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 725px;height: 334px\" 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\" data-image-state=\"image-loaded\" width=\"725\" height=\"334\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function yn = normalDepth(Q,n,S0,units,channelStruct)\r\n%  yn = normal depth\r\n%  Q = discharge (or flow)\r\n%  n = Manning roughness coefficient\r\n%  S0 = channel slope\r\n%  units = 'SI' for metric, 'USCS' for U.S. Customary System\r\n%  channelStruct = structure with with fields 'type', 'size1', and (for trapezoidal) 'size2'\r\n\r\n   C = switch(units,[1 1.49]);\r\n   yn = solve(Q-(C/n)*R^(2/3)*sqrt(S0)*A,0);   ","test_suite":"%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyn_correct = 0.61;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.04;                                   %  Manning coefficient \r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyn_correct = 1.12;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\nyn_correct = 3.58;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 0.72;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.034;                                  %  Manning coefficient (rock)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 1.16;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nn = 0.013;                                  %  Manning coefficient (asphalt)\r\nS0 = 8e-4;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 1.7;                  %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyn_correct = 2.80;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nn = 0.013;                                  %  Manning coefficient (asphalt)\r\nS0 = 8e-4;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1.5;                  %  Side slope\r\nyn_correct = 3.33;                          %  Normal depth (m)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\nyn_correct = 4.52;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\nyn_correct = 7.28;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 9.76;                                   %  Discharge (cfs)\r\nn = 0.015;                                  %  Manning coefficient (concrete pipe)\r\nS0 = 1e-2;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 1.5;                  %  Diameter (ft)\r\nyn_correct = 1.36;                          %  Normal depth (ft)\r\nyn = normalDepth(Q,n,S0,units,channelStruct);\r\nassert(abs(yn-yn_correct)\u003c0.01)","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-18T12:36:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-05-17T14:01:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-17T13:54:07.000Z","updated_at":"2023-05-18T12:36:47.000Z","published_at":"2023-05-17T14:01:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs described in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/57969\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 57969\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enormal depth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = (C/n) R^(2/3) S0^(1/2) A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = \\\\frac{C}{n} R^{2/3} S_0^{1/2} A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is Manning’s roughness coefficient, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the slope of the channel,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the cross-sectional area of the flow. The coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 1 for SI units and 1.49 for U.S. customary units.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003echannelStruct\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the following fields and possible values:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"124\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"435\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"334\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"725\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/docu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water surface profiles","description":"Problem statement\r\nWrite a function to classify the water surface profile starting at depth  in a channel with longitudinal slope , discharge , Manning roughness coefficient , and cross section specified by a structure channelStruct as in Cody Problem 58314. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity  to be either 9.81  or 32.2 . You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \r\nBackground\r\nSections of channels are classifying by the relationship between the critical depth  and the normal depth . Slopes with  are steep—that is, normal flow is supercritical (fast and shallow), whereas slopes with  are mild—that is, normal flow is subcritical (slow and deep). \r\nThe type of water surface profile in gradually varied flow then depends on the water depth  relative to these two depths, as shown in the figure below. Profile S1 has ; profile S2 has ; and profile S3 has . Profile M1 has ; profile M2 has ; and profile M3 has .  \r\n\r\nFigure by NateJonesAR - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=25698746","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 780.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 390.35px; transform-origin: 407px 390.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 106px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53px; text-align: left; transform-origin: 384px 53px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.842px 8px; transform-origin: 211.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify the water surface profile starting at depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.05px 8px; transform-origin: 112.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a channel with longitudinal slope \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.175px 8px; transform-origin: 36.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, Manning roughness coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134.183px 8px; transform-origin: 134.183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and cross section specified by a structure \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.05px 8px; transform-origin: 50.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003echannelStruct\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6667px 8px; transform-origin: 18.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58314\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The unit system will be specified in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eunits\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 252.408px 8px; transform-origin: 252.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.45px 8px; transform-origin: 54.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to be either 9.81 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m/s^2\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or 32.2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"ft/s^2\" style=\"width: 30.5px; height: 19.5px;\" width=\"30.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 258.808px 8px; transform-origin: 258.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.617px 8px; transform-origin: 211.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSections of channels are classifying by the relationship between the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58324\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ecritical depth\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc\" style=\"width: 14px; height: 20px;\" width=\"14\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 8px; transform-origin: 27.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003enormal depth\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn\" style=\"width: 14.5px; height: 20px;\" width=\"14.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 8px; transform-origin: 41.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Slopes with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003c yc\" style=\"width: 44.5px; height: 20px;\" width=\"44.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1167px 8px; transform-origin: 17.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003esteep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.275px 8px; transform-origin: 237.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, normal flow is supercritical (fast and shallow), whereas slopes with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e yc\" style=\"width: 44.5px; height: 20px;\" width=\"44.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.8417px 8px; transform-origin: 12.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003emild\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.55px 8px; transform-origin: 29.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, normal flow is subcritical (slow and deep). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 279.292px 8px; transform-origin: 279.292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe type of water surface profile in gradually varied flow then depends on the water depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.35px 8px; transform-origin: 99.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e relative to these two depths, as shown in the figure below. Profile S1 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y \u003e yc \u003e yn\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.6167px 8px; transform-origin: 48.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; profile S2 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc \u003e y \u003e yn\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.2333px 8px; transform-origin: 62.2333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and profile S3 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yc \u003e yn \u003e y\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 8px; transform-origin: 37.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Profile M1 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y \u003e yn \u003e yc\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7833px 8px; transform-origin: 49.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; profile M2 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e y \u003e yc\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.4px 8px; transform-origin: 63.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and profile M3 has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"yn \u003e yc \u003e y\" style=\"width: 70.5px; height: 20px;\" width=\"70.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 427.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 213.85px; text-align: left; transform-origin: 384px 213.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 440px;height: 422px\" 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\" data-image-state=\"image-loaded\" width=\"440\" height=\"422\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 353.142px 8px; transform-origin: 353.142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFigure by NateJonesAR - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=25698746\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function profType = classifyGVF(y,Q,n,S0,units,channelStruct)\r\n%  profType = character string--one of S1, S2, S3, M1, M2, or M3\r\n%  y = water depth\r\n%  Q = discharge\r\n%  n = Manning roughness coefficient\r\n%  S0 = channel slope\r\n%  units = either 'SI' or 'USCS' (i.e., lengths in m or ft)\r\n%  channelStruct = structure describing the cross section--see CP 58314\r\n\r\n  y = 'S1';\r\nend","test_suite":"%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 1.2;                                    %  Depth (m)\r\nprofType_correct = 'S1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 0.7;                                    %  Depth (m)\r\nprofType_correct = 'S2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 40;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 5e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\ny = 0.34;                                   %  Depth (m)\r\nprofType_correct = 'S3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 4;                                      %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 2;                                      %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nn = 0.035;                                  %  Manning coefficient (rock)\r\nS0 = 6e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\ny = 1;                                      %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 1;                                      %  Depth (m)\r\nprofType_correct = 'S1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 0.75;                                   %  Depth (m)\r\nprofType_correct = 'S2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nn = 0.015;                                  %  Manning coefficient (concrete)\r\nS0 = 4e-3;                                  %  Slope\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\ny = 0.6;                                    %  Depth (m)\r\nprofType_correct = 'S3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 4.7;                                    %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 3.5;                                    %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 350;                                    %  Discharge (cfs)\r\nn = 0.04;                                   %  Manning coefficient (clean winding channel)\r\nS0 = 5e-4;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 12;                   %  Side slope\r\ny = 2.0;                                    %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 7.3;                                    %  Depth (ft)\r\nprofType_correct = 'M1';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 7.2;                                    %  Depth (ft)\r\nprofType_correct = 'M2';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nn = 0.024;                                  %  Manning coefficient (corrugated metal pipe)\r\nS0 = 1e-3;                                  %  Slope\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\ny = 3.7;                                    %  Depth (ft)\r\nprofType_correct = 'M3';                    \r\nprofType = classifyGVF(y,Q,n,S0,units,channelStruct);\r\nassert(strcmp(profType,profType_correct))\r\n\r\n%%\r\nfiletext = fileread('classifyGVF.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-09T21:56:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-23T01:31:32.000Z","updated_at":"2025-07-09T21:56:13.000Z","published_at":"2023-05-23T01:34:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to classify the water surface profile starting at depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a channel with longitudinal slope \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, Manning roughness coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and cross section specified by a structure \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003echannelStruct\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58314\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The unit system will be specified in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunits\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to be either 9.81 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or 32.2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ft/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm ft/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSections of channels are classifying by the relationship between the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58324\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecritical depth\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enormal depth\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Slopes with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026lt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026lt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esteep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, normal flow is supercritical (fast and shallow), whereas slopes with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emild\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, normal flow is subcritical (slow and deep). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe type of water surface profile in gradually varied flow then depends on the water depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e relative to these two depths, as shown in the figure below. Profile S1 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y \u0026gt; yc \u0026gt; yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \u0026gt; y_c \u0026gt; y_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; profile S2 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc \u0026gt; y \u0026gt; yn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c \u0026gt; y \u0026gt; y_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and profile S3 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yc \u0026gt; yn \u0026gt; y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_c \u0026gt; y_n \u0026gt; y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Profile M1 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y \u0026gt; yn \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey \u0026gt; y_n \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; profile M2 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; y \u0026gt; yc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y \u0026gt; y_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and profile M3 has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"yn \u0026gt; yc \u0026gt; y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey_n \u0026gt; y_c \u0026gt; y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"422\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"440\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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the critical depth of a channel","description":"Problem statement\r\nWrite a function to compute the critical depth of a channel with discharge . The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity  to be either 9.81  or 32.2 . The geometry of the channel’s cross section will be specified by a structure channelStruct as in Cody Problem 58314.\r\nBackground\r\nSpecific energy for a flow is , where  is the water depth and  is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity  and differentiating with respect to depth gives\r\n\r\nThen using the definition of the top width  gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number :\r\n\r\nFlows with depths smaller than critical are supercritical—fast and shallow (), and flows with depths greater than critical are subcritical—deep and slow (). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the field, in the laboratory, and even in a kitchen sink. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 409.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 204.6px; transform-origin: 407px 204.6px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.642px 8px; transform-origin: 226.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the critical depth of a channel with discharge \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 139.633px 8px; transform-origin: 139.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eg\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.45px 8px; transform-origin: 54.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to be either 9.81 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m/s2\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or 32.2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD0AAAAnCAYAAAC8L0AUAAAD60lEQVRoQ+2ZyY9NQRTGu/8AxLAjIoY1EVOEhQ3CEkHYEVOsjDFsJIhpSxALC4JYE0PCgogxYSEWhoWFlSH8A3y/Tp1OvXr16tat1++9ju6bfLnd9546db46p845dV9/3wi8+kcg575R0iPF6/+bp2fLcYuEccJX4WbMkcOF9EQZd17Y0Ea0XXDjX+q+wul5rftW4Z2vd7iQ3i6j9gszC0kf0Li53qKxiPeEecJ9YWUpaUJnjPBN+FJoXKthr/TiinCpUC/j1wd2Ye9bp2+S7j9Md5WnWbE9wgzhs7BTGC9Ew6bQ4OlON3OULuYqjb0bmf9vCWlChJBb6FYK5Xecoh1teMa374T+WS7ML1y01DBI46AG3SlPk1RuCLcEP8Gwf6YJ5zzPtFrpHB6fJHRUiGbaHAUtZJbo+ROhyTkp0hjBPglJh3MQng9cRNS10fZdw56rq6SFPNkcDzdFUIo0yYHsV0UaOfbjhAJjMYxx7ZSq2LQs5mNhmdBQrhBOkbYkkCKN0SS3X4Wkf2rcZiGWhArWcGAIyfe6cFx4GlMSkmYfLHaCp92dRHDbG/xMf38QaCYIfy5In/JkzmRYTB64lrFYfpeFWpufriuW7dmWeLll+cshTam67JGg2FOvWZxtAqHNddDdf6cm9PRgHJ7elVgg67KIhj/CFGGvwLaLVQ/kCeeQMAv8Qhio1e2GNyWNlq9ueBOC34U5zsgYb6seq/XSD3/GfhQOBeRa5Qeid7cwmDd6RRoD2HOpttOqx1LJhXuTsulHFG3sxUTEbNS7wZLYK9JkfPJEau9bFLGdNlloOmLs88kuAvD8lgRhXjXM0wvSuW2n7z2It8zGFYSbXveCNKG5TshpO61XMMMpn4eF0h59QE8vSNdpO+2cbaXRyLfV93ebdGnbSQa+Klh5hPxJ4Ujd0O6Fp+u0nWT48BDCM3RwvOWKZfbKdei2p60ZyTlRkb1pXML9638cKArzoSQ9SwYOfp2ILHdu22lDIf1IiJU1K2dh41Lp5VR4W8eETNM3Jk8zmdh6dGsAKDVcYStIWHKl2k7faPuAsUYP/ZOSdWREjX3cyCJrQjFPU0f3CZye7ILQQyH0JLIcSGyPIR9LMLaIdfageZPe/6zwXhgrHHPz8bWlqHSlDhyx1cPr4fkU4msF2sLnkffoyWk7w/nYu8yF/gXCVCfAKSt6ZIwZHHtW9WEwV0+VHF57IxSVmCrldd93g3Ru21nX9mL5bpAmsfErQ07bWUykzsBukKbtJBGVfsivwydLttOkS9vOLONLhTpNOvyNqdTOIR3XadIkMUpZqlMbUkI5yjpNOseGrsuMku76kvdown/8EOgoTEGFhgAAAABJRU5ErkJggg==\" alt=\"ft/s2\" style=\"width: 30.5px; height: 19.5px;\" width=\"30.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.8833px 8px; transform-origin: 17.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The geometry of the channel’s cross section will be specified by a structure channelStruct as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58314\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.125px 8px; transform-origin: 87.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSpecific energy for a flow is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL4AAAAnCAYAAACxHfIWAAAIKElEQVR4Xu2d28uvUxDH9/4L5HAlSQ4XckHOiQsuEBJRiAtFTrmhHLJJytmFcuEUd4Rwo4gUhZTDBUWUQ8KlQ/IHMJ/8RrPXXmvNWut51u/9ve+znpr2731/6zjznVkzs+Z59+5d4xkcWCAHdi9wz2PLgwO7BvAHCBbJgQH8RYp9bHoAf2Agx4Fj5ctThfYT+lno5Z3CrgH8nSLJ+ffxpAx5udCnQueshv9c/r1W6MuG6a6XPr8IvdXQd/YuA/izs3RHDHi77OL4FfDZ0IFCbwudKPSO0LkNu/xD+ty0KafGAH6DBBfQ5TPZ42VCP5q94vZ8sfr5IPn39wo+nCdtXxA6oKJP16Ye8NH81gfL0HIkts635H64JIcmGPCX/P6ZyHcp2T4vbU8Rirkk/zQCH7eJB4ufemw8QZuPhT7qJVQP+MzLgl4XOsIs4in5/FOwqMPk57NNO9pbi9FrD2Pc/ziAVX3TMOOHlTxyMkBhXlr1wVBdKZSz5AAfP/+kCqbjJv0mdL5QTJkOl9+jGBpH2KGnxBTZJZYAnwEeELprNVJu4+oLAvqNOdYqhLTdm+Ki4IfzPCi0x9mQui9/rvrllOR0afOh0A1CsRMkNRXKdb/QkZEG4OU7of2FwBVKRztrZFHgS4Rm9R5KgU9goxrpMZQj9CyhlgBouwOvdP2AiOeblbBL+3ntsJw3rhp5cqKZGrQSMDM2lr7G2jMHKVDAG1NCvsNLODMANvx5XEiV+BX5jALN9pQCX307Jj5DKOd7AXzyvp61mW0T23Ag5edxgcCnboWU4dOrQTyXRK0toPTAzMnwfgSg3npxYxg/ts/cd4yr3/OZE+kooZqAOru2EuDrEVe6ABZMQDXbIj3ubsPvewHfygrAEaSm5KCng6d8KMiLQrgrtcEmikjeP6ZYJQaSE4HsEo+3zioYlADf+vepHC4bfG2AvZj3vYCvgaQuJJV2VN++xB0CfFj7Gr9e5yfmeC7RVy/HcnEFyvHIVgHfBkwxX5ANXCQ0qw9WDKF5GnJKHSx0iBBpwUcjw6LcuHCk+6aeZr2Az7K5KCJY5Em5pcRsJwt57gOnAkFlCHoySJ84fFDlmpLdU+Dj6pQkSzjxTlvtHa/jXaGoYnkWP7Qg4XHD9zDgsQhzaiGZy0XXjBUDba6/znudNNJsQph6sy7EHIFWT+DbREQshahpzytkv7naG0AP2EKDBi9ujvw+5DGeAvycYhDV1fFOJozSQ0IoPVj8WuhuIRIyeCk8KMD/9wge8G2el853mN1h/fC/2NwUrdYhrcBqgG7bllqG2Pg2tRZz6dQnbr2yt3P2BL51TUPAqKH6XhaTy7rZIDnGK09p6MMcgG9KYZueXjl8qVzCANgaK+6dPrBr8YBv02NkCV41XKCWA+ATRMVytLXgncPip24pS9diQRNjNsr5nlDtqRLO3xP4FrQI3N6W4jrcKRSmD+36UI5rHIZ5+9cSBc+Vyk2jRhdjm5rPgjtURvvdPiefB3y0Vo//mJbj/6MMHiNKgbfV7Ww9Smy/8KPkMsVTYg3YsMgoa+pp4asVuE1pEsfwM8rQO9VcUqKQk7U9mXK3ySlrz9jWAFQB34KAgWIZAoB/i1BtmmurAZ6bX5U99OX1UsXLeTP2VrptNv9tU5p6WVQSJE6Rj7qMV8kgrSXIAJqLrVw61vI5dmeh8UH0DiBn8UsuQ1jgPUJTsxxTGD1335QVAcxPFAqz1OLHap50P1PcNnvhiME6Wohyg1S9zJw8zJUolMxDf2TAra1X66WyCoFvlT8aGOeAby8Pcn5WyWZK2nhgKRmDNi3ugR3bBvSaxaqx9iXr7OnjhycOYL9PCOs/JcNSsi/a5EoUvDFqQM9Y6tbZWiO9cCOjk8zA5YBfU6agGyJ4ai1H3kr3wArEWgu9t8Clu7fQ2nvC5fvewLdJCeRBzr7EgpasPdfGK0PI9a0FvY5FIM1JDPiJN0lL8zwrlDSCKeDXlikw0dRIfg6LP8U9sEJRP59jkndNLxaas+iuN/DtjSf7WseJzTy4x7cJ1Wb5wNsbjnKiVChwmB4lE0dhHtmrX4X+FnIrOVPAt4wryVtrEROLyr1sYMG1yZ/VYuIe8JRkcmr20xv4Yc1OLRBr9mLb5koUUmMqdnLBsJa7h6eu4rTk3YO95k8B35YphLlgOwBaeKmQpue8ys1Whq67nw3se1jL3sC37tq6ZKJz1lxmKuiRLy+1px4sPZdZoQLbOBRXh5+x9m7dWAh8NAsga2krC2FAwG/zzdzakm7SemnazXWRtW6Qx+ZTi9lrT72Bz56YI2e05uYzLscJQqUuoYJe64q89cQMkLrX9LXjgNmHhYp9fI6O1qfrO5Kti2rspz7nhdK/xx3FOoBPzESR1rpSzbUlCrUxnS0OxEDfKkTlgOb6UYILhPRFHESfrPHxbm4bcbPtu00pxS3ZfK83sErm7tFGT8jav77QuhZccVyqWEkELhdpTLyR5AssA/j7sp5Tz/5NmVbhLKnf1BKFGl7pPUuuYtPGOFFlHMDfm+VTbx1rBLiT2hJ4TilRqOGFZnJywNdy+mRGcunA1+wVQSDZAHLQXn1IjZCW0FYvnnrXACkvtYYsl8LkBGJdyRht6cC3byuV/F2ZJQC5do9TShRq59L2qmzIjxtaEis8vEF3tRAWP/xLcHvNtXTg6z3ETspItYKptR8ZqllfBK9YCEH1MUKk13m+EvpWyCtuG/8xRAWTR9M4B3A93BKBTWPe0i3+psljrGdNHBjAXxOjxzSbxYEB/M2Sx1jNmjjwL4e77DeFMTLgAAAAAElFTkSuQmCC\" alt=\"E = y + V^2/2g\" style=\"width: 95px; height: 19.5px;\" width=\"95\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.7333px 8px; transform-origin: 72.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.908px 8px; transform-origin: 122.908px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"V = Q/A\" style=\"width: 61.5px; height: 18.5px;\" width=\"61.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and differentiating with respect to depth gives\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg 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fpH9/i2WcKIrEd2jO8au2n2CDMyD13set5KBPey+82r35Fs9yECpDGv4DCiwzx5Od7m6Stq+z25OPXhoipZjaVvX3qcez7Ykx2KkqU9aqh26VMs37u+PQA8ysH8t2krA/PAsS95hdKkDe9uXD/7UpZCBHiqqKTZ9v8e4tMh70jBle1jsJlg2cLZUrZdKuoQIkK/IQMte4mWIxdt7ILC1CW2sjtdEBvZo51N8MyUD7z1YqVlMW66tyQBlUjjiUvAYeWRDNKac5hZkoKXVx5+hP3Dk8p7HLrcQAcwAJW9l9YOWw5bwR7imizGVO6XtCHNY67wVZGB6jz1jP/9jq2ZuG+Oh+mpKBnp0zunNO/7G948M+J7fmJuXtqzw/thkrRjZW9h859aj9N4ZzQTURxqZrcMRC0uFOcV2WRrwmA3ebWksxgb3IZE1UsMEeYSJZY0+OJZnTpOHXwNjbu+LfeMsAGe5zqIZoI+flQzQJ/z1bfYHsXr2vjiMi7EUDoQLW0KLZW6xF1nY8hSshdV5yutnJQPyG5himumFnYgA+RHdbOz6cbsBiSyFTGaSbvV9+PpeFThJPkxgRwgacxK4isU8CxmgEmfs52zNPfx1KT4DewHtD7rwdl1UxJ+whJRy1u1W6Vn1a0jZazgQqi9AZLhetmHn8P2h5bMl51ORyRYTQcu34plAIIeAPz+l5byMQPFCEQgysLxhWQAId/mKIStswPyP/asPWjqb9MLk8MOW0u1k2kL2F3ZPoTGXorcmGVDeWy6m/pCuGjY1PxLIDBLF0Q4CqtUr7p8DAcb3nZZ8zHpKjibzAUulAFPnqGGUchICQQYmwRUPd0ZA8e/Jdg0JnngQqBXXyLszFDdlR1z991l6rqWrCYeaAZT+ca9bsJBca0dEr9kukXcgMIYAY/ZnLOkAPmIW7HES4uwWWpMM4MR1bU5NsxsiXlwFAant02O2V/lYp0xlnskdu9rpE6fIBr8PtGtIqewDZ1+4jjtfc94CHL79PEu9NGCnADwKORsBiMC7LBFLhFMF8QdC47JFoDm+/Y+WFmugew4qSWF4PuuMaFRRcQUCeyKgY0LP4ruBeeAhS1MDFO2J8RrfZlsuEeT8Tgtt1e0ddwGTEhO4zo+nPi2RJdeod+R5PgQYs4Qw9guytp739rViTb1hiXkNLUQ3B/WeZIAmhKV8dGjLKaedna/5o8RnQkCxyvHMP3LEPBa7Pw0i8P9diwU63XKpuAtrLdTy+eg2wZ5pkERZZyHA3ELY7nReUayTKYeStRbAn4Y75TTGYv69yYD3TF1rwLYCFs8FAh4BBtDzMwvMUVBCNf2MTmSFvN5giQOEFIsdeztBeo5wvDAT5eOWpmoOeQ/pCylsjUtbabtNsGsUMvLcFIE5fVWmvjUPPNJ20G5Cd28yIObOxIPT1jU7P23aY+NjgcCAAAssGoaxg4X23j4mgWFqOfBBwnlwzXlFE+we8SmiAx8PgTl9FSLw9qEqa5FWL3R32y3VmwxIzXbGQ3mO1xWjRIHANATQCLDIoubGaRJnJk5se7ml17is9pR8ZUulOC32VEyPP2HppUP5qVstIuM01L7wtDdxdptg5xQk3jkMAlP7KoT1jZakjVtrHdSpuV2F7p5kwNsxglkfpj9HQa4IAZwOcYJ7paVUK+cP1wKSPRa89MyNF1k5xkIxp83mNR6tURmnNP0qE+yUAsSzh0Jgbl9V3BntfJnSx1sBWEXo7kkGWmL1t1Y2ngsEAoFpCEgr8BJ7bcxJUt745Lw1YVf5+LZMGFPLIEKzxpYtSYFrSXPTWjOe3hOBHn1V56P0Jq4Ktd59DM8lA9qKI3UITIULVaRsgTzznZYI+qJtELktQWI5Zz3MZ89OG98OBIQAZPzFlkp2yj13+0BEmMiIqvjmodBzxjwOXcwnpTMdSr3CRwxFe4LJATOEdkFpjkIyfIElNC23W8I8kX5TeNaiSUYvPRcCvfoqPihz+rjQkiMw/U6RbTn87P7hAcxst1i6y9Idw/8wp+W+6TVf2bEzlQxoixYfxIvxg0MhUU8qrGVaEEjBhy0hDeSchnwI1xYb4rm6VZQ2EDgOAt7xqPde/VIt9V12GLGj4/3Dw3Mk/CU7CmRqYGFXJMPUfOLnIDmDyd8ixcyTqyWT/nF6SJSkZ1+FDEzVfqkFtHijqfplS+yikbaBZ9K1FOKAL5AiIKZrqfLj3ezYn0IGdD472oC0gt6+krOR+PvplkMRDH6u6Skc3TwQuHYEpkiyil3P5IIKHemYiIC/Zel/BiBb7f0QfhJaC09IpjoDasvWqyyfqdEBSz4B2kWQIyf+wK6c46UwnTvpX3uf7FH/I/ZVCcGMnynRAb3AnZqs/NjJmR/8/dyWQ42BrL9QKxlQFDcyyTFgLfaoy3Lx1L2dI1cJ3r9tmCx6dI7IIxAIBJ6KgJc2xswJ6WQkqcSPYeXcosmTNO4nRS2+5DOWBwSE5ANFob7lequlKduWJVGNqfNVnjH7rve1yM2ZvL+HQ+a19/Ej9FWdUIt2XP1SYdBR6U8NyS8tO8Q0dQT2i/2YY6J8X3LElvd/zVJW6G4lAwrGMbaVoSVYh8wBuUJyj7PfWyWNax8EUf9AYA4CTBTPtFSSVkpjvbZopmWSVP1Ou+GDHfktW2OTml+AmTPwNZhzYqafQHPSe0ugNG8OSMurrY9nOwxrTv852jtH6KuQZPqqtr4izUM6f9/S1GinXqjOOQLrfilCpjcHpOs79z6fjMUn2rSFDPiBMGZnbImG5E0FnkUzGO/LsKCjdbwoTyBwZgS026cUsczbz9Pn/NbhVvs4kw++RGlIVk3i4Lm2et0LIbktly0TLOXUHJeqbqkLh9RMNVucuS8doeyX1le1gwHfurHx1SJ0j5FfafeJSpo1W7SQgVq8br+lsBSCeMx5KQbTEYZWlOGSEZCEzkL2lkJFxwg7r0zdiSCzQm6x999pJRZz2qelzNJS1AIxeSlU3tghyMxplT7vXFpf9RJ9bh31ZrpaCGIRVz+2wIudB6Pjv0YGPPsa239bMyH4pk8LGYOpz8CIXAKBEgKMUa6cZOzf8xNsasuX2r51G52X/ktlm7OjoLW1/S6nnE2/ZkKoYROCTGtL9H/u0vrq5wwi7bjL2fRL5CdFNyWuVa0AGdTIgJf6cwzfM++WYB1pIWHl7PENFVv/wRI5BgIgoD3TNSLAs578+8WzpJLNoax5YUxTuGRHwZRWldQ/5uvktzXXHABTzSZhnm80EKwp5Y1n2xG4pL7qpf7cOupNCC0hiFOixFkJkPiSVrBKBnymqb+A33JDE4os4Ln7iKWcXcI7SOBURFAPCEdcgUAg0B+BKURAX5cGQGpzFsGHLOF4eK+lFu9oFmEmrdLYbtlRsBQRfSMX38TPbZpg+d7dlsZOdvQOlG+y50rRHpeWPd6vI3ApfdUTzZzZzGvZRBZ4B0KaE6TTLYacl1A9SnmKZsBvu1GAA7waFWwIZs1e5Dst3WMpt/XHF7JV3VjvEvFEIBAIpAi0EAEIfTpO+d97LCm+APl+yNInLbV4R2uRrR1hLrUo+a8Rv518pRlItzwjsHzvMF+hmmWCZVsYk25pV5OflNf0dYje3IbApfRVrxnwZjMFvYKIa51F6P6MJbYt8r+xGAaebDcFGKuRgVT6ZwBwEZELKQGHBB3IgCQBISgV0Hsk15wg2rpDPBUIBAIpAkjk77BUkgZQszJ2/ZY47Y+GCNTU5jnUNV8QnKim8dtiR0Eq/X/AykXYVsrJPIUww8VPCENtX7icvEpbu6I3boPApfVVPx5YSz9t6dWWGEsfsaRw2ZAFQmjfsFTaii8TWM0x9onWqpEBHlSgAoU5JPN3DwXhHqGGYfkPWHrQUi0YCIwlF1Bhmy4UXwkELhsBv4XwH0aqeqv9H83Bqyx5NaMPd8oY9QF/WlCT2ramFSCvUgjzlm+1PMOC8TpLCC9oAFjE/TylMvg5rZSvyEWTpNVSwHhmNgKX1lfRDiBsSwOA6YpjyOmjcgBEQ8DfCgRWAg9ygaa+OQJiCxmY3VqZF+UI0VzAnh+PvAKBC0fAO/zWqpqTbhVNTacKKg8fH30sX//tlsiEXhKaGpa4Vre17kN2qo5Ya3088r0Jgeir5Q4x2Tl/SzIgtc7brA6xeyBGdiDQFwG/s6cl59TmLSka88AfWML3R1KK8hsLECSNgJ5Dq/CQJaSY9EK6vs2SDv9peaelPms/A9m5YallV8baZbn2/KOvlnvALNK6JRmggI9ZGvPUvfYOHvUPBPZCQIeQYZ/0cf+ZdPGux3Ne2oIWqX+veqz1XfCpOWyt9e3I92YEoq+WewSkteTEP/r2WmSABiNW86OWcHKACHBNPWAkBkIgEAisjwAqRa4xh0O/p/sa7OXYo7k4oh3/ioct3RjmsvVbI75QQiD66pPoiKx/1v6FFg4i8HpLJSf+UWzXIgOpPTCVOKK7BwKBwDEQ0Hbf3F58X0KN6RbnwGPUbF4p0u3POEcHEZiHZe+3oq/ejKjfLaMdMbOIANmuRQZgKGgDGEgcQpSzHfbuKJFfIBAITEdAe5xxjMNbOXdpy+Cn7Oal28zHjsWdjmy80RuB6Ks3IyqTCeOWIH4tu/lG22QtMtC7E0R+gUAgsB4CPpJbGjBMAcbYMvxaS2NBTtYrXeQcCDyJQPTVlXpDkIGVgI1sA4GTISDHI7b9oiVg8X98qAO7CwgxXoshcrIqR3FPikD01RUaLsjACqBGloFAIBAIBAKBwJkQCDJwptaKsgYCgUAgEAgEAisgEGRgBVAjy0AgEAgEAoFA4EwI/B8+KPSzeM5RIQAAAABJRU5ErkJggg==\" alt=\"dE/dy = 0 = 1+(-2) (Q^2/2gA^3)dA/dy = 1-(Q^2/gA^3)dA/dy\" style=\"width: 257.5px; height: 36.5px;\" width=\"257.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.583px 8px; transform-origin: 127.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen using the definition of the top width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"T = dA/dy\" style=\"width: 70px; height: 18.5px;\" width=\"70\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.6px 8px; transform-origin: 211.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr^2 = Q^2T/gA^3 = 1\" style=\"width: 95.5px; height: 36.5px;\" width=\"95.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.283px 8px; transform-origin: 230.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFlows with depths smaller than critical are supercritical—fast and shallow (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr \u003e 1\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.742px 8px; transform-origin: 114.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), and flows with depths greater than critical are subcritical—deep and slow (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Fr \u003c 1\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 240.533px 8px; transform-origin: 240.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=qsC9FUYpHqU\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003efield\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.9417px 8px; transform-origin: 22.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://youtu.be/5etwhZ0d2GU?t=373\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003elaboratory\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.8417px 8px; transform-origin: 47.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and even in a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://youtu.be/OoA1ASjMfag?t=24\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ekitchen sink\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function yc = criticalDepth(Q,units,channelStruct)\r\n  g = 9.81*(units=='SI') + 32.2*(units=='USCS');\r\n  yc = solve(Q^2*T/(g*A^3)==1,y)\r\nend","test_suite":"%%\r\nQ = 12;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 20;                   %  Width (m)\r\nyc_correct = 0.33;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 10;                   %  Width (m)\r\nyc_correct = 0.74;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 400;                                    %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'rectangular'; \r\nchannelStruct.size1 = 50;                   %  Width (ft)\r\nyc_correct = 1.26;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 0.82;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 20;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 8;                    %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 0.82;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 45;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'trapezoidal'; \r\nchannelStruct.size1 = 1.7;                  %  Bottom width (m)\r\nchannelStruct.size2 = 1.5;                  %  Side slope\r\nyc_correct = 2.34;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%  \r\nQ = 45;                                     %  Discharge (m3/s)\r\nunits = 'SI';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1.5;                  %  Side slope\r\nyc_correct = 2.84;                          %  Critical depth (m)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 14;                                     %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'triangular'; \r\nchannelStruct.size1 = 1;                    %  Side slope\r\nyc_correct = 1.65;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%\r\nQ = 250;                                    %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 10;                   %  Diameter (ft)\r\nyc_correct = 3.72;                          %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)\r\n\r\n%%  \r\nQ = 8;                                      %  Discharge (cfs)\r\nunits = 'USCS';                 \r\nchannelStruct.type = 'circular'; \r\nchannelStruct.size1 = 1.5;                  %  Diameter (ft)\r\nyc_correct = 1.1;                           %  Critical depth (ft)\r\nyc = criticalDepth(Q,units,channelStruct);\r\nassert(abs(yc-yc_correct)\u003c0.01)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-18T13:28:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-18T13:25:33.000Z","updated_at":"2023-05-18T13:28:20.000Z","published_at":"2023-05-18T13:28:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the critical depth of a channel with discharge \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to be either 9.81 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m/s2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or 32.2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ft/s2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm ft/s^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The geometry of the channel’s cross section will be specified by a structure channelStruct as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58314-compute-the-normal-depth-of-a-channel\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58314\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSpecific energy for a flow is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"E = y + V^2/2g\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eE = y + V^2/2g\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the water depth and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and differentiating with respect to depth gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dE/dy = 0 = 1+(-2) (Q^2/2gA^3)dA/dy = 1-(Q^2/gA^3)dA/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dE}{dy} = 0 = 1 + (-2)\\\\frac{Q^2}{2gA^3}\\\\frac{dA}{dy} = 1-\\\\frac{Q^2}{gA^3}\\\\frac{dA}{dy}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen using the definition of the top width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T = dA/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = dA/dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr^2 = Q^2T/gA^3 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr^2 = \\\\frac{Q^2T}{gA^3} = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFlows with depths smaller than critical are supercritical—fast and shallow (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr \u0026gt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr \u0026gt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), and flows with depths greater than critical are subcritical—deep and slow (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fr \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eFr \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=qsC9FUYpHqU\\\"\u003e\u003cw:r\u003e\u003cw:t\u003efield\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/5etwhZ0d2GU?t=373\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elaboratory\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and even in a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/OoA1ASjMfag?t=24\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ekitchen sink\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57969,"title":"Compute flow in a partially full pipe","description":"Problem statement\r\nWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow  equals the diameter  of the pipe. \r\nWrite a function that takes the ratio  and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \r\nSee Test 13 for the answer to the initial question.\r\nBackground\r\nSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow  is\r\n\r\nwhere  is Manning’s roughness coefficient,  is the hydraulic radius,  is the slope of the channel,  is the cross-sectional area of the flow, and  is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient  is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 392.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 196.4px; transform-origin: 407px 196.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.35px 8px; transform-origin: 65.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e equals the diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the pipe. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.933px 8px; transform-origin: 109.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the ratio \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"h/D\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.258px 8px; transform-origin: 251.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.917px 8px; transform-origin: 150.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee Test 13 for the answer to the initial question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.8px 8px; transform-origin: 369.8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7px 8px; transform-origin: 7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANMAAABGCAYAAABWrKEpAAAMkklEQVR4Xu2dV6stSxHH9/0CiuFJQcQAiopiRvRBwYCCKFcxPB1QzAhec3oypzcxoXARI+qLmAV9UMSMonAfDFwE9cXsB9D6cabuqV27Q/XsmbVmza6B4uyzVk9Pd3X9u2LPuuksr+RAcmARDty0SC/ZSXIgOXCWYEohSA4sxIEE00KMzG6SAwmmlIHkwEIcSDAtxMjsJjmQYIrLwH2k6T1M8//K3782/3+8/H2b0N/jXWbLPXEgwdReTQDyQqHnC91F6A9Cv59uear8+0+hnwrdbfrsUXsSjpzLGAcSTGV+PVQ+fp8QgOF6o9CXhf5omqOpvij0yOmzj8q/rxhjf7beEwcSTBdXEy30EaOJbpa/rTln70Aj/UTovhPg3r8n4ci5jHEgwXSeXwDp89NHmHSPEer5QC+VNh8TeobQN8bYn633xIEE043VxD/6gVlctI0162rrjkn4K6G7B4C3J9nJuTgOJJiuMwRz7XdCBBm4Xib08QFpQTuNtB/oetWmGmBJX28BNieYrjMRH+nlEz+J0N11Ad6eQhfM+3NCPzyFwW59jAmm61rpb2ahiNydUiCB8ePbPXiag486tmSQMP/9Cg2ebvr7tvxdC8AcU76/JQ9Ho0ZM8YOMM8F0dqYBBGX4wzYqPCWBwF/7vhDBEkxU/DyuyIZAsOVebuMAmAgpfQE0TQ2Mmr1rCy9pCbTq09Z+0Ej/Caazsy8Iw543Me2UTDwNy1+TsauZZqORTzCfl2SitLMjoLcbgGlwJRrZHJE92xbf7U5C0WjoG6Ttn4RYO3sx3scK3bny/dzxhe5LMJ2d/WPaiWHYz4VOpYoB4DxE6K1upXVzeHfhO9sUMNmdHXDeUriHdmioNaKVaBjGyWbWG68de8k8ZSOAJ1SkqEZlPV8sdBAz9TJgghEPEFJbnclu1b5u7Sz/M19S0cCCHOpiR35c4GG/lTZ+167VArJrU73REk6do9/ZS0P5mXyIZurxxftu9KX+G9+9SOhTQpq3Y/wPEnqi0AiYShFI5vxwM0Y1V6lOQSYvYw7iBvxYqAvIOWCCqa8V0oF+b1qBJ8m/7Agw/tWFxQ/IzFGaWDCN7I5LDRbT5JMTP7VPdtQvCWGuEGXEh8EEpWTJayI/DgVTK4kcdd4R3FuFeslrnvmmaSDfkX9/Of39kmnc6suVoqQR8Ns50v5HQjYCCeABpA1GqInKvXO1quYeQ3IxAia76Cy2HzyDtjb71pzWmvBvwcxTgWKM3m+zuyzf92oAAcqjhWrh/ajzzo78HiHMpnc64bW8fJf85y3TuJ/p2tmx17T+KJi8ecpYiD6W/C3dKOeCCZCiNEIWSxRMtl6t17Ha2AgFKryrHmtSfqDPbQCCTQKToFdCtPTQVCDpt8RfhOXr5qG1iCNAwTJoaaWa827nBJCI9KlWpM+nCPkwtD6Pe2sg17HXIowjYBpNMgOmuX6wjfIy/1IK4ZwcRMA0Wq9m2/eAt7RQzunPjpf7o6FxDUvffwHw4VCrKVTT6NYcfYG0L/k7fIambVU01HJLJd5ZzVJ6puVdyxRi7DWAj4BpJMmsJtocC8lXxMCbrnbrgUkFRstseuFWHmpr3NBOSwjbHJCM3KPqXHfYt3cAwhy/KrSE5rW7O8+v1QRaMJUEE8F+llArUDC6szMeHV8JLNY8bW2cjL0mjCNgGtkIAB6R2TnRWb3X5u66st8Ckz1eoEIWqeHyBaPdQYxI/Upt/VwRHCJPJbPmdZPALgEkpuM1f60iwZp5HnBsel8R6gUKRnZ2y2rAUDLTvPlZW2tkolayFAVTKclcEwdVAnPWSAMXzOVtQhpmr1kDd4yhBSa767R2TD8hD6ZTOZoAoN4hZGv0NDJFVO0RE2PxDXqaawTzti6w5Hf4AITXEBoY8r6ehqqtYz6ys+sctNyqBhRromKJ4LCPlPhEwRSNQDLezwq1giat9eE5/5o2OYuBbkSvBiZvM474Ph6EUR8kmnPpCepIbVqpL8waomE44IT7uX4h9Buh7wotHZyw0US/8fjTvH4dVCNdk3HZnV83BlvE2tvZuec50xwtGFjP5wrVzCW/eY4mSiNgikYgWSv8Rkqs5lTxa6BNNwRrNXTzVTUw+Xq1Ee1io2NMruu4TQLrQdgDTe37KHjn9r/kfTYXQr/sfv8WQhMSPdMj8QgouSgrIN409ePyESg04AeFalrDgoJxfFOIhDLJ0FcKtTYRH8SppU5KvIuAKRKBpG/mSPTYAwlzlBPRrTkoP9mwNJdnedKN6NXApOFtBjgaRJibt1lKM9ks+5KCv0ZfPvz6CXmIJr95HrthrTLaVnaXxuYTm6X8jL/PrgG1b+SYoibbXEBFwBQxTwESuTUfgGFOryp87ufOOEg8+/ycDfw0FUMNTHNLbPxOG6leXkNIT6VPu2lpCNfvhr2gQmSuPRMv0kekjQdUxD1QHtTaYuIR9GkFv7wl5cfaCx5oxLIURrc+YTOYVgLTZQBhnek5zmhkwfbUxm5a1jy1C9gThAg/os57pK9eG5uApm3NRUCAnyyESatXSRuiMbyWtWPQur/WuHrn03BNMKvfW+iEkijNATbXogSmudE4H7ToRj96q7Lz730+zpoX0fxNhEUjznukv0gbq3F75U+9/iImXq+P1ve2/g5/1V/W7G7KdEQzRYMPVgBG/SwmsJTPdNlo3mUWZuTeVglRNJE78rwl27aSsDzHWjdzy3lUJngJaCS/OXd+gJUx1pLd4YhexGeKgInFZ0Ba3ewLHiMTPXQ0j7zRGtdfpNO/Bjq2VRclW73kTwW6Xb2JAr0XpVUT9jJgmptkjjJBfa1WBDgc0auByYa3I0GEnmBEJreUZopE83hn+J8jg5rRBjDds3Off+9EqYTI7oiXEcgZU2jeosLVcsbt/FqmEe3wm8jplU7OLj1225+6JSTmWyVYfq2qm0gNTBaNvYXUoAOmHeo4cuBsTSZF+8axXOMCTF/rdBwpIfI+6FbyZ7qbt5KYdn61cRPa/4zQm4Uwzak+ITFcOtqzxjqpmR3hqw0UVTeRVjmRtelLZog6ttQujWa912DOKfVpo56tzcq220pAx8pFyWqxxdG1im11C7xWwH9hU55TnDqy/urT9RSF9mlzp9Uq9F7VuB4QwxciD6AnKO8tf1PDRlb4A0JzSjdGJr+ntj4nAg9vFiqd+5obWV2TX/hyaE1MezQQgkaymYtqCTRLTy50k/ChZgVqxE+fO0d4SsW//qpJ6ZyW7btULlXUnj0w0anatbyDG9XOMXVCiKFz8XNnvNP7CLLUrprP4O85tG/hx+vfXmvfCETbVk5I+9Kd3ptYah5Gkr1zRASNSP2hv0pjrrXVey/cEwGTqm0YMJKNZ5cpHWOYw4S8Zz8csGF/78yrFujWwW2RHT0wqZOISsS+ZJKYeuyOtQpqrXTGDFgzP7BFfuaY+hywZlMNTPTSC733n3TgFtEARG1YgAsn8vapgWaLt+IsH5id+bgAB64UmPRwFQekPi30n4lBlONzrkWPBZT4hvZ6jVC+CD4gVVe0yZUCU2+NAdsDhXiBoBYp8pLE3nmRXr/5/dXggE2C1sw8/7qzk+BMz2c6iUnkIE+OA1oV7ys/1o7mrcqoBNOq7M3OKxzo5ZnmvJ7r6MxOMB19Ca7kAFoVEDCk+8LHLXItwVRfFfJrWrCqb/ixhZmll+lvcY23OiZ9eQm1eVTQoK2oRqhVg2x1HneMK8F0fonI7j9bSN+Vxrda8mJzbnrXmmUvmxeeBQaob0QikHXym1OCqSwReqREDzlyTID3sF0T4ke59IWQmU9bAFF76SLBVF5JjTZRI/ZhoVuFtJTK5klO4W21e5HVzc8jwXRxiWztGFGl108aSRPReiJ4ztH8zQtEDnA+BxJMF3nnD+75IyZ6Cnmtyub5q5l3HpUDCaaL7LdH9kunSfXU5UnmQo4qbTt/eILp4gLrWZvSj7VZf6n20y87F5mcXo0DCabznLFgKb3vTU+CnuR5m4TBuhxIMJ3nr32/QelFGxoy15A4wYrou7jXXcns/egcSDCdXwIFS0nz2CgfIfHbhPgdIF4qsvXf7T26oF2FASSYbqyyPRpQeuuOfREK/hLRvA8Jncqrza6CPB91jgmmG+y3IfFSMtb/wkNG844qutt7eILpxprYN8rWfjUB7UQd2am8z3x7ErfjESWYdry4ObXDciDBdFh+59N2zIEE044XN6d2WA4kmA7L73zajjmQYNrx4ubUDsuBBNNh+Z1P2zEHEkw7Xtyc2mE5kGA6LL/zaTvmQIJpx4ubUzssB/4P3KP+ZXElbY0AAAAASUVORK5CYII=\" alt=\"Q = (C/n)R^(2/3)S0^(1/2)A\" style=\"width: 105.5px; height: 35px;\" width=\"105.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.55px 8px; transform-origin: 112.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is Manning’s roughness coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 8px; transform-origin: 73.5167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAACaklEQVRYR+1WOy9EQRTe/QEKj1KFnsKjQaJB+AGIRodohYRCgwSdQkK1HRKtZ6Og8kgoRINC7ZHwA/g+mbM59+7ce+fuzmYj2Zt82dl7Z853zjfnnJlspoJPtoLcmSp5RdT/V7J3K4keMX43/1vx+w28pJHQJfImGJwFpo3hU/Pbgt8zM+a3HuDSJzkjOgdqgX1gVBmvx/gEaDfvXAIJ+Ja0gMYHgE+gzhIVVXkGboCONFFzbhw5I3szBuOMXxv5F32SM7kuFPkgxpJgmofq5IA9n+QiqdgcxuDIQsA8uAJSZXqS7Pwue84x970PuE8bYdT8pIRjtt+pxdz7kWKitDmQRM41lHVXLWZ29/twwIXc5oAXBVzJbQ6w6cwAtgpwSos05DQ4B6wpy1MYb0cwMV9qAH0GBKamJedi1jOTjo+t+bA/5IAd4BVYBjZsTtrIVzDxGIg6JHTnowMNSnqpjlW8k44nzWrMOJ6P3kbOdrkE2BqKLNT1r8nlfRsm6n7wZBZ2KUetvf0HE+L2knaEhGXHo5WP7ojhoGSrAtGHJ4kBntnj2su8VpmMll3LO4Q5h4AtDyRR9fyCyPVhMg9D64pUhlsY8PLAqLWMQhBHHvgWjlwM0HAzQAU2gS+gEZgAeL6HielYyeSTMPIAMNO5BZ1ArxmT4BaIqoSSyS0qO7+SMyBOdirJe8HfU0yTifJGatxGzt6xAATyyCc5nfoAeNnUtc/3UpqBG65vctl3Xc9SmgWK+CZnlOyQfOTSwdJkPvCKHbhqlYOcxCRjlfDqxcPlACg4estFHpWUgfdVcieZfE+qyu5bUSd7v7RmiilK8yatAAAAAElFTkSuQmCC\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.125px 8px; transform-origin: 87.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.6667px 8px; transform-origin: 39.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the cross-sectional area of the flow, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 278.1px 8px; transform-origin: 278.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182.383px 8px; transform-origin: 182.383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function f = pipeFlow(hoverD)\r\n  f = hoverD.^2;\r\nend","test_suite":"%%\r\nhoverD = 1;\r\nf_correct = 1;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.9;\r\nf_correct = 1.06580;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.8;\r\nf_correct = 0.97747;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.75;\r\nf_correct = 0.91188;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.6;\r\nf_correct = 0.67184;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.5;\r\nf_correct = 0.5;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.4;\r\nf_correct = 0.33699;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.3;\r\nf_correct = 0.19583;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.2;\r\nf_correct = 0.08757;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.1;\r\nf_correct = 0.02088;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0;\r\nf_correct = 0;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = (1:6)/7;\r\nf_correct = [0.04395 0.17812 0.38187 0.62268 0.85931 1.03672];\r\nassert(all(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4))\r\n\r\n%%\r\ng = @(x) -pipeFlow(x); \r\nhoverD_max = fminsearch(g,0.9);\r\nhoverD_max_correct = 0.93817;\r\nassert(abs(hoverD_max-hoverD_max_correct)\u003c1e-4)\r\n\r\n%%\r\nfiletext = fileread('pipeFlow.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":9,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-08T16:02:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-08T12:50:01.000Z","updated_at":"2023-04-08T16:02:01.000Z","published_at":"2023-04-08T12:50:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equals the diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the pipe. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the ratio \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h/D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh/D\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee Test 13 for the answer to the initial question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = (C/n)R^(2/3)S0^(1/2)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = \\\\frac{C}{n}R^{2/3}S_0^{1/2}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is Manning’s roughness coefficient, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR=A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the slope of the channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the cross-sectional area of the flow, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57879,"title":"Route a hydrograph through a river section with the Muskingum method","description":"Problem statement \r\nWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph , the times  at which the hydrograph is reported, the routing parameters  and , and the desired time step . If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph , and a Boolean flag that says whether the time step is within the guidelines .\r\nBonus points to anyone who can solve this problem using the FILTER command. \r\nBackground\r\nHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow  and outflow  are connected to the storage  in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\r\n\r\nThis equation is written in discretized form as \r\n\r\nwhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow  and the current storage . \r\nIn the Muskingum method, the storage, inflow, and outflow are further related by \r\n\r\nwhere  is a time scale related to travel time in the river section and  is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\r\n\r\nwhere\r\n\r\n\r\n\r\nNotice that . With the assumption that the first value of the outflow equals the first value of the inflow, this equation for  can be used to compute the outflow hydrograph. The guideline for  above ensures that the coefficients , , and  are positive.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 882.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 441.35px; transform-origin: 407px 441.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.95px 8px; transform-origin: 64.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.783px 8px; transform-origin: 383.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"I(t)\" style=\"width: 26.5px; height: 18.5px;\" width=\"26.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2167px 8px; transform-origin: 34.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 187.875px 8px; transform-origin: 187.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at which the hydrograph is reported, the routing parameters \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eX\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 8px; transform-origin: 29.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the desired time step \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dt\" style=\"width: 18.5px; height: 18px;\" width=\"18.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 284.583px 8px; transform-origin: 284.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O(t)\" style=\"width: 30px; height: 18.5px;\" width=\"30\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 234.942px 8px; transform-origin: 234.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a Boolean flag that says whether the time step is within the guidelines \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"2KX \u003c= dt \u003c 2K(1-X)\" style=\"width: 149px; height: 18.5px;\" width=\"149\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.925px 8px; transform-origin: 251.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBonus points to anyone who can solve this problem using the FILTER command. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.742px 8px; transform-origin: 368.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eI\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and outflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eO\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are connected to the storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.25px 8px; transform-origin: 97.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJEAAABGCAYAAADM43a0AAAHtklEQVR4Xu1dS8h1Uxj+/zkJIwYMGPijSG6RAeVXYiDlNjKQy0CSKAbCwC+STNwy+JOBS5RIoUykXCdSDBj8BozcYs77aL/1nPes61n7nL3XPu+ut/N939lr7bWe9ex3vZe11nfwgF+OQCMCBxvLe3FH4ICTyEnQjICTqBlCr8BJ5BxoRsBJ1AyhVzAmiR4SOI84pPuHQAuJXhK4zhU5TeQUkY9Erg5AeJf87TaRi+m7L+Tno8PvT8vn7SJv7B/8y+hxC4mAwE0irw9QPGw00Uny+2ciZ4n8IHLvQDTcfljkbZHjhrIny+fvy4B0/3rRSiKQ4cMBtovk8yuCEJrlRpF/RM4T+cnAq2VBsEP7B/1yetxKoqcEigcGTXOZ0Sb/DjClSPKL3POpCDSaX50i0Eqi76XfmK7eNERgDZUi0edS7l0RN8g7JRCa3UIi2Dy/DX2/Wz5fJBwulJ+/pN/tVKdfwTiHbQSj3K9OEWghEbyuF4Z+nymf1ubBVAWvDdevIueIuPHcKVFSzS4lEaan+0XgzuP6dviE4Rybrthzw+2xEMACYd2vLuVIhCnrAxHEeODCY/qBNoFHBmLhelnkzghs6qHp14gPXbJfEC+/tykSwa6B0Yspydo86pUBIQQYUzaNJZJrpIXxKkYiaKDvBgKFNI2SCDGg0wftlILGEimlvRYG8fK7EyMRXG9MYbB3bPwHqOj3NVqFp0DUcbNIr6kOOBVXiMAm5AsOxGsiTxa8WHNj1xnSoAdFkMriFFW2TyESsUEcG2gNJNpURwoYToPgviXYR7AR7xg6HYvMz40stj0YF3jZeCFAmMdFEPeD7QtiPS+i9m/QdAmRSAOIMbecXXsb/8F3H4tYd18bbuNHOcN+7gPAJKrRynPpFxTGKyLIYYI4sH1DYRieRdZifnYQeZBtFFo7nprq8N2zIqlpSkmK+npPvHJfarTyHEjEyiBFILSVebE2g1gSccXWI0NlPNWFSIZpLlSOQVMS9h6AhKr/kToWi8rPgTC2DTzOIMU1EQ3E5dSEwd9WgsuWROy6W3sIc+exQfWhIiULFqOBUH+IIA2SU+t/D3Xk7psj+NwmHoiYAzLHPkCrfELjWEp+JtEKN1KaCIvFYK3jwlv3vsjPImpkgY1XiVwvcovIBSK6LCRmkINwT4jACL1ShJeOzBHwVJs4bBGb+ufYJ50J0LaaUAuTaKWcJZHVNrgZ163D4J8on1j6gQuaBGmQa0VgSCtBFDiQUF1dkBBRbZQFgW4Yys8R5NI2cW4wN4WX1rnt+1h71niTdupOkgidgKZ5TgRLPJQszwyDrisSMSXZeAg8lb9E8AkNhTjK5SKahIXKf0/kLZEWDcRv0qagA8DjNy0s5SyovTgITPwac8LmQVeciB5d7DmQiLVuLyszLRFqtCeHMvDurcSLeiRRgwIZrSjHTdh2HO0BW6jIBkZL0lXaDA5lrKW6nESbjZZ6mGtvZWV1bKxWFv3/9pppmTV4jfa0AeK1adBJVD90DGppAjr2lF2SiIlf45XZ5Hk2Yl0P6f6VYHuoxjidGqmoi55omPXWg6GMHjXR1IY1P7+nVAfbNaWaiO0oTIEazlnhnSXR+RO+LkiDQHLX1CTiN7o02pvr0y6+rw2O8o6dZGzPkqh1jm4B41Ep/FhLBTsoa7dChdZa7aAZGz2C246X9dRELZwayQaHLYl0bcxGrWws9I2Uh8z56n3pB4cmYqkpEOhVEQSbkZy9RyQZHO7RJpqKZLxkGG0otSumam/oubzxAt9zwJFTU3ZxWrIPTqKyIYYGuk5EUzhaCkTqcfMlcmhInF8qoodqwHDGVrB3RLCwsHiPoJOojER+VwKBbZEIahNrdnlrtQ/EQhEYi0SYT7FOCPmYswcV2VMMZaHDu5tujUUibS17Lz3FUHaD9kKfMjaJdHlt7+unFzrc2+nW2CTSaHJquSjWtXwtEttWtJ2eeq1bQ2BMEqXOK9IOaAY8t39/ax32isdHYEwS8cq50HlFGkrHkgQ/q2j8sZysxjFJpAm+0PYZ3orU0/KJyQampwdvSiI9m/oE6SwE+7cfEUFEl9MBvE3X4tLTXq2exnTnba0lkZ5ZhJ0SeoC5zSmFEnu8kCs01e284/7A8RCoIRG0Dxal47IbD9Uriy0X1eyxa5/xxm42NZWSiNcVhzSNkih2XIyu7+1pp+hsBmnuDSkhEa+zjZEgdV4RL4bq+WCruY/lZO0rIZGmMnL/XgGdCKU62DPrZafoZAPS44NzJOIAYsw1V9c+lurITXU94uZtJgRyJGKvKrTtNjfVMQl72SnqBKlEIEci3iEQcs05a587FMtTHZWD08vtORLx9hxrz7DBjP4qyUAsPRyd7SmsNcLRNPhOzz3qBSdvZwKBHIlYE7EmAYGOiuDQKz6qGKeQHiOS6IY52FM4CAun82d3D/iI9YVAjkR2AxtIAo2CM/5wUBXSHXrmMYjypwifQMr/8wzI4NwjXzLbF0eyrc2RCBXAuIb2QF4Mbj60CZa+8uloiESHCMLHGd8n9/R6+HkWyH2+oYRE+4yP970AASdRAUh+SxoBJ5EzpBkBJ1EzhF6Bk8g50IyAk6gZQq/ASeQcaEbASdQMoVfgJHIONCPgJGqG0Cv4D/j3tFaAuAMDAAAAAElFTkSuQmCC\" alt=\"dS/dt = I - O\" style=\"width: 72.5px; height: 35px;\" width=\"72.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.583px 8px; transform-origin: 141.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis equation is written in discretized form as \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.95px; text-align: left; transform-origin: 384px 18.95px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATkAAABMCAYAAAAWecA3AAAOqklEQVR4Xu1dTeh+RRXWRQshSXOViwR1oSTlphI/AsUUwpAQ+nTxo6SPhYiEYgXxRyRFEQkXaZiIRJ9IRCCYoqAYpQZGRS1UsEWtVMRom+eR98hx/nPvnPmeufdcOPze9/fOzD3zzJnnnpk5d+bEE+wyBAwBQ2DDCJy44bpZ1QwBQ8AQOMFIzozAEDAENo2Akdymm9cqZwgYAkZyZgOGgCGwaQSM5DbdvFY5Q8AQMJIzGzAEDIFNI6AluW8SCkcknxRo/Ik+P3T4fhf9vY7kl53QGl2/0rCgvpeSfN4p+D/0/ackd5C8XvqmDcrbar2WoLuCfvgayUdJzhGJ/kmff0hyXwPMe9/ig6TAN0iuJvkIyfsPCv2X/j5K8l2Sl3OUDJEcFHj20AAA/gaS3x9uiAZ6RCh1WoeONbp+OW2jyXs/Jfq6MIrzcw1Cc9MGabZaL4bu4/ThXhI4DXAW7iFhBwH9CgQH0sND65KNtKnPbO6kf37r8MOP6C/aHYSGfn0LyU2H3+BE3ZxqdyGSA/DwFsCqvg6EBnmMBAR4bqoSGflG1y+jaqqskgzw8LlSlWv8RFutF5BHx+bOCy/ldk9zoJP/jeRDJCC680hm9MyXLA0k/zAJiBzccRWJz1v7Dv3/B4dClrAKWnOI5P5/KGGNxP5NaZ4h+ULwbuUTjK5f+Rq/t8R/HAwF/002ggQlQUIfI5EeSEIxi1l61atkHXxl8UNZ016yg2d5MpGV4qmfpylfsve0ck8Q3JMkGJauERwX8dYhLb6H+Mp727VM7KUh4xrJ/ZF+/y2J74kUiW9U8tH1i6pMQuKzKM9LIt8n6PPzCeWkZEGbY6hVg1h71isFC20eSXA/pkyYh1q7pH3Dmztde6PMdOxp1hgZSIJbGh266rOt4f8Y2kbPU66RHBR6TtGJ8FTH3BzP1WVirM4+un7qiiQmxBMX8xi48BC6iKTVkKYmyfWsV2JTBLPJOmmHn5LkcINWc961SE7On6M+2gekJDnNw+G4xgi5fxiKYl4Al7Zxgi1eMMHo+hWs6nFFSc/gV/Rry+mCmiTXs1412gud+1USXjX8In3WRCG4JKfNl1uHWiQn5yKx2PIZ5UNZklzS3H+I5NBxfiFQq+HC5jTK6Prl1C2UVxJ8khsfusHK7zVJrme9MiBZzCpJO6ZzS+8Phc9Mcu4URExdpD1UITmAKxsJ39FQF9SwhsQyR9cvsVqr2VyjaTWUYaVqkVzvepVuK7c+2iEa9JArzPjeas61hicn+2jMiBBe8Gu5TlbIk+PyXSIZzaMbXb/SnUeuvCU93TIVqkVyveuVCctx2V2iOptSaANb5QozJunPIGkx51qa5FyiiplacUdqSavMWpLzeXRJk4ClrUiU5xLdaPqVrDpiEzFngyup4TOVqUVyveuVCctx2SVRxYyAXGKIyZtbh9Ik5xIVYjm1i5TuQyIm77s4xJAcMkkjxPeYsXUu+Jr8o+unqYMmjYwdSmr4wE3kJLFGn6U0sUOs2vXKqUtKXo7jRN6Yh670aJE3Zpgb0tNd0AilX/pdq5NrSzFTK9IeYoa579E5luTcZWDfEwbMfSMJv+eKNNeTcAwXKp16/VqU4ytDox/ng54IZoWumtWuVJ1L55OhM6FhDL8+9BdSIhSXJfXsQXKaeiHNbSQXkmC1EoY/avu5IU4xDoE2aoBfi4oZyrYmOel4xEytuAsvLqmqbcFHcij8cZKluQO38WQZyIv3W/Hu3RskXyXhYRU8jhdI5ERiLAHAUE7N0A/3gz7XkPA7nzHGF6tvjfTyKb80N4oJb5AaVl1BBjFehEbnGsPVUL1gdwg6xzuff3basMeQPYRTagiIm8+3co5+9jnRt2K8o5DepYerqSEgbj4ZBxplCz6SQ+Gh13XkXIMEGE8g94ViZvJSixU5+qGBARC8SgZxNpKTjb80ZADJ4SHDLznPQHKhesGOHiSRXjcTIzzak0O9t/Hv7rya1s5k38IkPUjOXXBgG+bh8MgkJ+fVtJ6cnMdD28IpkfN4UbbgIzkAF4q7YoOU42T2kNxhESusrWDIFlP1c8udleTkPE9ozoufyjOQXKheaC83gFQSScmOHrJB7e+xMX9ymkDzXucMJOe+7RF6Pc0NnvY9yKNswSU5NpqQ18UTgqF0MAZ2vzVpQ8ZTUr8ZSc59Xzf0KtcsJBdbL2kn6OjJk9Ihg8v8XZJWKHTCfZ1taWcOt+74XpLgSw9XXdJaC6NJffWLMfHagkty0tiW3Gs5RLjsMPRbswVuPO1qzFpZJfWbkeRityCaheRi68U2wsG2JR6gmXzmzS63TFojI4x2HiDh+VO0myaebgZPDvWW861Lowpg9fODU5SyoLRoCy7JuUvXmNC9gwRzAjyZjb2wfOPkJSPBHAp2Pg15HRojK6nfbCTndhjNEHQGkkupF9sKHqCwUc3DVmNfNdLwJDnvDXdEN+H5JV4hxMMbUQihuXBXv1lIDnrLBxlsF30ZvIL2x56VaEdccvPMmPZYtAWX5KDImweFPk1/scU2FhL4JX3ME/yOJBTKwcoxu5aK5Sqp30wkh3p/VrQD4wtjWdsBZnSSS60X1x9zXtjuvca+ZzEdLJRWbvHtHiGA8J7UXXxmIjlgBDLHdu+SU+C1/ZXkNyRrUR0hjBdtITZOLnQj93cQSY+95jR6zkRymvr40tQiOZATNs18iCR6f6/Uyjj5UDfEh/lWHwvdYvhiapAcPKIjktjYyp5grdpCTZJDR8AVE4TaEigjuZZol70XB5xrt+spe/dxSqtBcuPUTqdJ0BZqkRyeBhjqjvyUNZLTGdFoqfgtjq+QYprJ+dH0L6nP3klOZQs1SI7dXV9MEyYVW27uuGZQRnIlu1ubsngS33eCFRa4Rn6o1kBozySntoXSJMeBv4gJwm6o8rqWvoz0niFHlmsj0WsYae0yeUVLsxJbW5fc8rGI9SLJ30lwyIq8PkVfZppDysUC+UcPhC5Rx6UyomyhJMnJQyp8yo0SsAk9cRA2v7uKFeNjJFjZabFfV83G57JhBFiWR2wiYq8Q8oPQn5zVqxZ6L93DDRL1pQu9/dFT/9L3hjMh3wtHSMrdJNotjErr07K8aFsoSXItK2r3MgQMAUNAhYCRnAomS2QIGAKzImAkl9ZyrffkStPSchkChkDaidSG27ubDuRCUeJ93lwdLL8hsGkEzJPbdPNa5QwBQ8BIzmxgTwiUmGYYdceTPbVjVF2N5KLgssSTI2AkN3kDpqjvkpzcnTWlvC3kGZH4nyFgL94CuJXrgPjAVyrfQ1P8/yjRSZqElqYaAthF6QmU7nboY9VuOU/BGgxKeARARLvwgMDPD88DYTdN+QClbgocbvw9+vu+3krs/P4P8wNvRK9lhrZpTXIzYGI6GgJDImAkN2SzmFKGgCFQCgEjuVJIWjmGgCEwJAJGckM2iyllCBgCpRAwkiuFpJVjCBgCQyLQk+Rw8MS9JLcPiYwp5SKALW5uIcGBOuccfsT2WQhv2dtmlVu0DiymfZvkQhJsz4Ur5QSx4bDpRXK8Ool9zk4eDhVTyEVAHqvnQwfteD7J3rcjn9Vy5HGBvjpMvelqL5LjrccB6JZ35p3V6F29sYvyB0hw/N87AZZ0XUPyZfHUtwfWnK3Nu3njdbUHSd4gOZPkiEQen6iN6RwOhR4kx2exMhjYmffcDGTQSC+YF5GB4HpWHAJ8PcnVJM87Sd2DoTFs7XVEYTUANl7wW1S/n5H4TtWTh7ljauL0GbHoQXI4cASH3ODisX+qN4dh1HMkpQ6vnrENa+uMudNbV8gLBxfhgCJcONtjlIOKauOyhfLRdjeQXESytPU/2p8Plz+bPk83JdGa5PjwDYzx3yTBuQO4MMF5QaTV8JkSeBKdt9JIkcVacoEAvG4sLKw9weWBKrZDx1zmA4fjKZI171vO1015jkZrksNJ1xjSYJIa10vCJmIA5JPhkd06Vv+OxRs7TD1B3R/GITXgvjbt4lJLksMTH8cU/oEEw0tceJLgVCktWWEo9AAJD3OlVWBub83tHtKCNqCU9ORSpx02AMNmq8CeXO7ceTeAWpIcxv93kWBVjo9O4zk1BkA75pcToto83UDe+I15dW7aiemNt09u9fh84mkXlVqSHCYwMQ/nrqTKcBLtcOcxKgexdua95Zpwfn72xs2Ly8dytBI4EmJaLw6AtiI5ftr7OgL/xg18Gn0IHfKMxQYMWW01r2+34E5g86J926HW3TkSQo6+at2rWrmtSA7eGoJJl+Lh5DJ1yJuTe7mZ91DNNFQFo11xISQo9GBSFWiJhkEA/ewREkRATB372ILkeN5tLWJaxlqFIuflyqrG6xvGajamCNrhWhJfkPDGqrq76vAi4VKQ8FSAtCA5uLyXkIRi2XgICgDXCJHn8FJi66ZqnIGVxUPp+0ZwA7dQumoguGdJnibxvQWRXnKnnLVJjudsQkNQVF96aEvenAxXwErtzZ1w2/NtjeC22/qbIzg0VW2SQ4wNXuLW7FAhCQy6hRYp7FWu9p1NQ3BoR5ufa982uXfUEtx07VuT5FLG9TI42LdszYGJ8PTOIDn14FKbR5dr4uH8vN3SESXlOEc3F3cUC8oO4zlaCvS9U0g4UN+nH+JT0eem6m81SY4DdhEk+i9li2IFljdk9HlzHJiITvYlkkdJsEOGuzuG8naWTIkAvycMvH+ykAfGf4xkM3M5Smy2kIxDRa6jymCrJd91Of2TX8mc6iX9miQnw0JSDcFdXOB3JOHl4cI5m1Mvb6cC0zAfE5zvVTpXDXjYU8dUNcR1lFvJ0VNIpynjIWuRnAwJCQEX+l2+uM+eHLzDG0nQQHbVQwALRy+SaAgOWkwdGV8PxmFLDu0I7Co+ZVxqLZIbtlVNMUPAENgXAkZy+2pvq60hsDsEjOR21+RWYUNgXwgYye2rva22hsDuEDCS212TW4UNgX0hYCS3r/a22hoCu0PASG53TW4VNgT2hYCR3L7a22prCOwOASO53TW5VdgQ2BcCbwOyEbR6h9JHagAAAABJRU5ErkJggg==\" alt=\"(S2-S1)/dt = (I1+I2)/2-(O1+O2)/2\" style=\"width: 156.5px; height: 38px;\" width=\"156.5\" height=\"38\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O2\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.2333px 8px; transform-origin: 76.2333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the current storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S2\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 249.317px 8px; transform-origin: 249.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the Muskingum method, the storage, inflow, and outflow are further related by \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S = K[XI + (1-X)O]\" style=\"width: 143px; height: 18.5px;\" width=\"143\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185.917px 8px; transform-origin: 185.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a time scale related to travel time in the river section and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eX\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.75px 8px; transform-origin: 156.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O2 = C0 I2 + C1 I1 + C2 O1\" style=\"width: 152px; height: 20px;\" width=\"152\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.0667px 8px; transform-origin: 19.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.2px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.6px; text-align: left; transform-origin: 384px 17.6px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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V0zomSCVtlRSbyAfhtJDCEP7PXSWtcYrBU73mDJbLIEPjIW4gS8VVhCaB/xuSuEKMHiATcs2rGfQjiaOlsmsVD69dNIaB7ACFucsUZhZEIen2defBoSAQV/zYF1/TY5XwjkxZCAf1G7kEuhoaAVxHA364R/2BB0a/tEdZQitDb452rC9o+qNrUoQx1g8j50b1Et4T9Zijx67nGv7fuDW2CJBHI2AbSA5NI+sNXwD5V+6iIFXB+JBHB2gbeAVGOMeEmmJfLWBas1SRGhnMDbG04BAEEcDWJE0EAgE/odAEEf0hEAgEGhGIIijGbJ4IRAIBII4og8EAoFAMwJBHM2QxQuBQCDwBBqkyHR7zIhNAAAAAElFTkSuQmCC\" alt=\"C0 = (dt - 2KX)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35px;\" width=\"135\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.2px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.6px; text-align: left; transform-origin: 384px 17.6px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ4AAABGCAYAAAA9zXoQAAAPSklEQVR4Xu1dbei2yRT/73fy9ok2Ch9oWSQvYdVqUVoJ5S3pCXnZkqQVPsgnxAfJBy9Jm7QWISlCUbTyWtgtEkqJT0viO+dn71/P2fPMzDkz91zXfV33/1w1Pffzv+aal9/M/ObMmTNnrrvIJxFIBBKBTgSu64yf0ROBRCARuEjiyE6QCCQC3QgkcXRDlh8kAolAEkf2gUQgEehGIImjG7L8IBFIBJI4sg8kAolANwJJHN2Q7eaDt0lJPybhwbsp8XhBHyeffkjCTRIeeUjm9/LvtyS8J5DsRyXOUyS8yMT9u/z/ixK+KuEXh/evlH9fJ+FBKu5X5PfdEq6X8HpVBkb5mfz4kYSPSPjH4Y/I08ZFfu+S8OVAmU8aJYnjpPAvmvlPJfVnSXi/hA8vmtNpEydB6oGsSwQCeWKwiL+TeE84xMV3t0r4U+FbxvuPvHuzGegPl//fq8gD6TxXEYZODkT13cMf0E6fqcQLFn+9aEkc62G9Zk66Q/YMnDXLOCMvSBq/lvBXCZ+Q8GcJD5PwCgmvUhl8T36/OJChJo4a4UIaQNotYgGZfUrlVxtnIA201e7IPYkj0Jt2GIWdm0V/jfwYFX8xg2KgfHoCDhhQVyRAbI8sIbwsMfAeIuElErgE4DfPkB8/Vwk8Xn6XpAdGAQn90YlPXD8r8d5XyJOfA7O/SKAU9PYCfvgeyyuk9Vavolt7n8SxtRY5vjwcAFgv6/V+VFy3JeDgfPbxRbvAuv52CVEJoJUlpY0XSCToH0qPJtDS4NXfaCnBLi9ABNRhYLBHln46b+g4NH6vlv/fJQG6EZTLkt4EqJdNIoljWXxPkTrWyVDeYUD9QAJnPYjqGLA9Dzv/LFF6JnFgoN8sAYOw9nCA4r1XBz3QMaCZLv79nAQsh97ZgaGVeJ4p34Lg8He0C9Kr6VB62ugkcZM4TgL7YplSRL5TcoD4qwdDzyyPzv0FCVQUstMfW/CZxBEpi9b1eMu1f0uCdmkBEn7LgSxuk39bS51SebTOBDtc2FXBEgZ5YQeoN71InVeJk8SxCsyrZYKBCdEXW4YgCrtujxAAd2NKhfbEfa+iaxMHJQ7sfjy1MVBL0gGJ85jdDuoxgAvKACkDW7ZsHw+vzb5P4ths0wwV7G/y1T0S9A4CNfdIUIvgXgacgXu+8dJcmzgoMXh1sAMc9YD04S1vvPpCArzPRDqWfL08V3mfxLEKzKtkQuWeFcm1uI6CPEKCp4zTM/DMjr42cYBIYQDXkjaAiSZX3VgztrJbStJVOsYSmSRxLIHqadLEehpPafdEr7Uj2396Bva2MXtquyZxkEgjUsN/VSVAlNBHUN/h6Ua8+rPOjDcTTy/vxd6PEAf39V8upXqyBG75oZBYx/1Ewm8kYH/9+RJqVnOLVeoSJkypotbJrUGSJ3VQz9E741rpZrQpIoO9lbZVErfi6jKj/z5GwnslYNsYD7a1HzVYEe6gaKvWY+s2WJS5n/UQBxoDgIKRAQT2pu+Q8H0J1A5b898eTf7cml2u1CBqg8SfJKG2DIHYTpL3Oi9n4Ih0opHeCnGA+PCUDMNsz6AeBH+nvYU14PLwKvU2pgGFKAzesDuD5xgi2kyvjhKH3p4DK7eMYDTL9na8zQCzo4Jw58Tr3FYBWDv8pgf/iO1HC7o1lirQKUBqiJAGymq3TGnRqqU0SiKeboh11wZjsKfBxKqVpLNxXb27RohDEwEAjGwlkcWPXR+uDsgOM8RAwSDxFIDRWZRt1ztYItAtTRy9pGF3Pex2tZbSeiZBtokeKzUDswhum4vjEQfNensVRZy1zkIRtLlWu1ogdvxop9ZieU1/wRnYmknPgGFJ4oiQBvDSUoOWKrCEsEs9u/SK9GfW0UqANi1v7M3Ae7E0vML3auN1QbHufq1pqMUqckkTpsGXJ20QHmsQZiVCPQNjZwFiO/IA4cywclyKOEAAHygMfN0tIDl/UoI+MxKxrNUGcZ7OjkRE7Gy37NEzbbpLt4hDbyN5lnebruQZF45GWpAOos8NEpESpJU69NkOiO1Pl+CdB4nmi3hLEIfedv1VpTCPlb9jMFvfGZGBbCWFmn6C5UBb1PQrEYmvB8+TxW0Rh7bd9yzvTlaBS5yx3WIdhUIPBD1ZoM1vlDBzO302cfRgYJcilhBahm7azqO0K6J3E1vpaGJGe+1WB1gjDtsgW9ACb2Wrb3SAzv5Oz5bHpK3Fb92xoTfBQJ+xRGH5ZhKHHYQeBtQDYbmGJRhOEGv7CkjVcL7DZRni4aAgbJHgSU0/jPsd+SOO2Ov3Nh18h757i4SSW0Hg/w0JM/ydeBhMe18jDr32W0K7PlKBJI4R1Lb1DR35wEBwd85rtgXlaUtTIw49m/VaD562Rpl7IpAILI5AjTj0mm6JbbnFK5YZJAKJwHIIRIgjaiMQKSXWpR+XsAsX8JEKZZxE4DIiECGOGRIH9BOwoqO9/m61yZexk2SdEwGLQI04tNHLDB0HjG/gb5HpjhBHKkez/yYCG0GgRhz6QBSKGjG1RTxYHn5JQs1idE/E8TSpB1wD5JMIJAIXF9gw+QOBqBGHPRBVM6HVgPJEIHw11tzHH0McazfejyXD562daeaXCGwUgQfoOluWo9aBa8sijpZzreP2wGNPxPFGKe+jN9qIWaxEYG0EYM6Pu3j//3iH3EAe35SgL/aBRIFEcNUezjLAGu5fEiJ3TuyJONZumMwvEdgNAh5xsCK8/AYOUmheC6XpbyV8XQK8gEWcnCRxrNM1oKPazQXG60BSzQVYRW5mO3Ext5V9lDhmlTqJYxaS9XRwXOCHEnZ19mF5WKo5wLYIdkVRj2EnLOp2sk7i2E5bzCgJSAO3t+cM2ocmJGostWeeBO4rwc5iJ3HEGwx2JO+W8BwJPFUJ4zhYwmLAth6etHypROK1ioyPNODMFtcDYrnHZSFuiOeDg4Z3SsAdprULlnHyFCc5ey6HpgOclzXSjSO0TkwaE9rTrcgdrgA0cdZOwgLzd5g6Az8sxVt30a5Tw+NzocOmyM19Q7klccRg0w5YSl9EzfKtj0t0dOxWWf2Qjgdd0hucgd3rqpGEQaX3Yh0sBu9QLLvr1/IZw+P8IGDrzIeZA/N7JZzDcYiZ7guKjbM2cdAV4Yjl6FDvmvAR/T7Ab8LnJfxTAjxKXZGg/TB4XsZRFM85LuPcLT8gmdSIxVYLuiNcZuzNlhhsGDh49Iy9R+JAHSK3pJEQ4NXdc7RNswJIHhFl/4TuNT0Ja4Pl3aEzVIC1iIMdlmdVMIt+UEJ0N2aocpM+gic0LBNK/iO0hW3kvgztIAkY2DW1dqvv2cSwej3SBkRYOubR3r72ShwRZ8K83jEyWXHQRbGPdjH6O4XZgr7XN/p9TzzrhCsqDZfy4OVr1yja1yKOnopvKW5EaaZ9l3im+S0X+byGAkR1RQIknMiDgQFDtdLVj63vz4E4UD+Nv7Vw5hIzIg0SK7TRTRJGb28rYU6Cw1Kpdp9NpK0jcYAHHn3D4qjUgb6FYxfX6M2SONpNEdna1PoPb+bWnVxb4uo16W1SpKi7vt7rEXRtz4U4ahdNceaNLveIDb/z2jIyiBlnLeLgshrSFXQ1XEpHjozY+nCSK5JuEkdP85fjasVb65oCq8yDdAJ9ybcPDYzG5c5KtFS6o3g7OzbNcyEOqzfiUgCzJaS23is62E49UorXXmsRB3RdkBAgfeolS4+ko29tRL2KBJrE4TW5/54Sh+d+QM+MiAu7ga8dkq9p+r3cOfhHnEmfC3EAI+ox8BvYXi8Bd7beKiEqvWms4QFvpmf/NYiDeWjCi1z/oOut3WnYvveAs2pJHN7Q9N9zp6h1CNB2bihSZ2yFcsCMtOM5EYf1eI4ZFne21mxevFYFccxwYMV81iAO6mb0bXS9ynuWl1ejVMlzpMN5oF+m9zS08aQNYKLvqdEYHaP15gwx0o7nRBzAs6Uk7e2TwBUK51kK0qWJg/3Q9iW7NRvZWdJL6upkONLhehvhnOOD5XHGwbMP0NuGmA1vl4A7PPiMar2TOK5iqMXsyNZ4q18eg2sp3aWJA8tl2OWUdGy9t8dpKaW6S5jEMU5r6AzQUYAEvANlenanCKw7+uh6+pgOPkPi0GmMIjlDCWltF1CWY3ZFRnDVNwOMYuHdTVtKl1JFzdbIuy/Ypsm6N6XoJI6xJvYay6aqL+/m1pg1Xhrp6CMdnGU7F+IgjiBf7fZhlIyBD9oLT49tzKmIAxICyLcl9Wr7IY+cWI/mEjqJo584aN2Jg2mR28hK24U07oqYTLdKyO9H2nEGcfSjN/cLGs1hBwVWuC+UcJfKYgQXfL4n5Sh0O/dIaFmkWlOA2iSlJ7PmTt0osHObfz+p9ZIGaqY1/vbi414x0iJ1mbdj2RbARG+71ozsenoZiOMYpbXNaykdB5doEaWnXhrXpA7qQ9xrX5M44t0pShqIpw9IeWKinvl7lXrskN5WcKmWe5c4MBBuKIjoJX1SvJXvvyAa29wjmNbyWYo4epZUdsu6pJDnktrdik7iiHcpEMBDHZEQ6034YsVt6Hw8Ixy7ZdarLGwdwmvVbs/EQTIuidNWiuvVHXFXwTt3FO85V8mox4LTS59kFJE2Sn2xtHV73yEi9XDoI5BCrjGiS+Lwmuf+99x2hYUnzMRLzy2HWUpviUU7sR7ErphoMh89lLVX4iBptJYSWhndu+SAJIOnxyGS14uWkDho/IfdD5y6jTywTakdftMSCcgWjshvllB01ZDE4cOtlxpebLt2tNuVtVnM7rD07Ajw216zc73m7Zm1PAyWfK9tEloSgXW8FLWTIdHPXKYAj9nEYSekUcz14TfdV9H/bpRQdaWYxNGG3PP8Zb/mAERHeZME7f4PcTE74G4KLmUQD5IKrpjQM0EpbqukUUc+dKUHF4Y2P3SWrforBU53mDJbLIEPlIW4ga/kVhCSB+xuWu4KMHiATc82bGTQziaOnsmsVT69dNISB7ACFtVzPkkckWbffhwQAga9Z8G6/ZqcroRLYkhHPqjdzCXQydBK4jgZ9NMzjjgdmp7pGSUIqQ22OVqxfUbVm1uVJI65eJ46NYiX5+Kpe00sE7dOtJM4OgHbQXRIHlVt+A7Kv3YRE68BxJM4BkDbwSdQxv1Swl49da8JMZSCvd7T1izfJvNK4thks2ShEoFtI5DEse32ydIlAptEIIljk82ShUoEto1AEse22ydLlwhsEoEkjk02SxYqEdg2Av8D+CrNdJVBoswAAAAASUVORK5CYII=\" alt=\"C1 = (dt + 2KX)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35px;\" width=\"135\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.8px; text-align: left; transform-origin: 384px 17.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C2 = (2K(1-X)-dt)/(2K(1-X)+dt)\" style=\"width: 135px; height: 35.5px;\" width=\"135\" height=\"35.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 66px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 33px; text-align: left; transform-origin: 384px 33px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.3917px 8px; transform-origin: 35.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNotice that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C0+C1+C2 = 1\" style=\"width: 108px; height: 20px;\" width=\"108\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 289.742px 8px; transform-origin: 289.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. With the assumption that the first value of the outflow equals the first value of the inflow, this equation for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"O2\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 207.717px 8px; transform-origin: 207.717px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be used to compute the outflow hydrograph. The guideline for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dt\" style=\"width: 18.5px; height: 18px;\" width=\"18.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.892px 8px; transform-origin: 111.892px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e above ensures that the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C0\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C1\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C2\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are positive.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t2,O,dtOK] = Muskingum(t,I,K,X,dt)\r\n  y = x;\r\nend","test_suite":"%%  Chin example 5.38\r\nK = 40;         %  Time parameter (min)\r\nX = 0.2;        %  Weighting parameter \r\ndt = 30;        %  Time step (min)\r\nt = 0:30:600;   %  Time (min)\r\nI = [10 10 25 45 31.3 27.5 25 23.8 21.3 19.4 17.5 16.3 13.5 12.1 10 10 10 10 10 10 10];   %  Inflow (m3/s)\r\nt_correct = 0:dt:600;   %  Correct time (min)\r\nO_correct = [10 10.000 12.234 23.361 35.133 32.120 28.799 26.195 24.294 22.100 20.094 18.259 16.592 14.410 12.623 10.949 10.343 10.124 10.045 10.016 10.006];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Chin example 5.39\r\nK = 0.604;      %  Time parameter (h)\r\nX = 0.102;      %  Weighting parameter \r\ndt = 0.5;       %  Time step (h)\r\nt = 0:0.5:8;    %  Time (h)\r\nI = [42.4 46.3 51.8 56.2 57.6 65.1 80.3 90.6 103.2 81.5 78.3 65.8 59.6 56.3 50.8 53.1 50.7];   %  Inflow (m3/s)\r\nt_correct = 0:dt:8;   %  Correct time (min)\r\nO_correct = [42.400 43.327 46.510 50.893 54.574 58.266 66.191 77.540 88.774 92.714 84.880 77.757 68.741 62.190 57.167 53.698 52.750];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c5e-3))\r\n\r\n%%  Gupta example 12.7\r\nK = 3.07;       %  Time parameter (h)\r\nX = 0.39;       %  Weighting parameter \r\ndt = 12;        %  Time step (h)\r\nt = 12:12:120;  %  Time (h)\r\nI = [100 300 680 500 400 310 230 180 100 50];   %  Inflow (cfs)\r\nt_correct = 12:dt:120;   %  Correct time (h)\r\nO_correct = [100 222 573 626 373 359 235 197 123 58];  %  Outflow (cfs)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c0.6))\r\n\r\n%%  Homework problem 44a\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 30;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5.000 6.424 15.930 23.650 20.977 19.035 17.713 16.841 15.948 14.981 13.746 13.187 12.289 9.465 6.074 5.258 5.062 5.015 5.004];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44b1\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 35;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5 7.350 18.103 22.845 19.774 17.965 16.839 15.781 14.614 13.436 12.489 9.898 6.283 5.214 5.036 5.006];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44b2\r\nK = 35;         %  Time parameter (min)\r\nX = 0.3;        %  Weighting parameter \r\ndt = 10;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5.000 4.223 5.122 7.129 10.048\t13.062 16.139 20.271 22.245 22.793 22.094 21.428 20.785 20.119 19.543 19.027 18.519 18.104 17.751 17.450 17.150 16.850 16.550 16.250 15.950 15.687 15.344 14.948 14.442 14.073 13.796 13.597 13.398 13.199 13.167 12.773 12.140 11.404 10.444 9.334 7.865 6.894 6.252 5.827 5.547 5.362 5.239 5.158 5.104 5.069 5.046 5.030 5.020 5.013 5.009];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n\r\n%%  Homework problem 44c\r\nK = 35;         %  Time parameter (min)\r\nX = 0.6;        %  Weighting parameter \r\ndt = 45;        %  Time step (min)\r\nt = 0:30:540;   %  Time (min)\r\nI = [5 17.5 27.1 20.4 18.6 17.4 16.7 15.8 14.9 13.4 13.1 12.5 9.2 5 5 5 5 5 5];   %  Inflow (m3/s)\r\nt_correct = 0:dt:540;   %  Correct time (min)\r\nO_correct = [5 5.711 26.085 18.977 17.719 16.407 15.024 12.997 12.606 8.234 4.247 5.175 4.959];  %  Outflow (m3/s)\r\n[t2,O,dtOK] = Muskingum(t,I,K,X,dt);\r\nassert(~dtOK)\r\nassert(all(abs(t2-t_correct)\u003c1e-3))\r\nassert(all(abs(O-O_correct)\u003c1e-3))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-02T23:02:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-02T16:23:33.000Z","updated_at":"2024-11-11T12:36:59.000Z","published_at":"2023-04-02T16:31:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that routes a hydrograph through a river section using the Muskingum method. The input to the function will be the inflow hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I(t)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI(t)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at which the hydrograph is reported, the routing parameters \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"X\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the desired time step \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If the desired time step differs from the time step in the given inflow hydrograph, use linear interpolation to get the inflow hydrograph onto the new time base. Return the time base of the outflow hydrograph, the outflow hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O(t)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO(t)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a Boolean flag that says whether the time step is within the guidelines \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2KX \u0026lt;= dt \u0026lt; 2K(1-X)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2KX \\\\le \\\\Delta t \\\\le 2K(1-X)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBonus points to anyone who can solve this problem using the FILTER command. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHydrologic routing is used to predict the movement of a flood wave in a river. The Muskingum method is an example of hydrologic routing, in which the inflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and outflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are connected to the storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a channel section through a conservation of mass (or volume), which states that the rate of change of storage is the difference between the inflow and outflow:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dS/dt = I - O\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dS}{dt} = I-O\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis equation is written in discretized form as \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(S2-S1)/dt = (I1+I2)/2-(O1+O2)/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{S_2 – S_1}{\\\\Delta t} = \\\\frac{I_1+I_2}{2} - \\\\frac{O_1+O_2}{2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere subscripts 1 and 2 denote the previous and current time steps, respectively. In applications, the inflow hydrograph (or flow as a function of time) is known, and we assume that everything at the previous time step is known. That assumption leaves two unknowns, the current outflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the current storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the Muskingum method, the storage, inflow, and outflow are further related by \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S = K[XI + (1-X)O]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS = K[XI+(1-X)O]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a time scale related to travel time in the river section and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"X\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a weighting factor. Substituting this relation into the discretized form of conservation of mass and rearranging gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2 = C0 I2 + C1 I1 + C2 O1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2 = C_0 I_2 + C_1 I_1 + C_2 O_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0 = (dt - 2KX)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0 = \\\\frac{\\\\Delta t – 2KX}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C1 = (dt + 2KX)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_1 = \\\\frac{\\\\Delta t + 2KX}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C2 = (2K(1-X)-dt)/(2K(1-X)+dt)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_2 = \\\\frac{2K(1-X)-\\\\Delta t}{2K(1-X)+\\\\Delta t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNotice that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0+C1+C2 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0+C_1+C_2 = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. With the assumption that the first value of the outflow equals the first value of the inflow, this equation for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"O2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eO_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be used to compute the outflow hydrograph. The guideline for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dt\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e above ensures that the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are positive.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57605,"title":"Determine flows of given probability using empirical frequency analysis","description":"Write a function that takes as input  observations of peak streamflow  and exceedance probabilities  expressed as percentages and returns the flows  corresponding to the probabilities. \r\nUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank  (e.g., the highest flow has ). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with . Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return NaN for any probabilities that fall outside the range. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 158px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 79px; transform-origin: 407px 79px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.158px 8px; transform-origin: 109.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes as input \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.242px 8px; transform-origin: 104.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e observations of peak streamflow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Qo\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5417px 8px; transform-origin: 94.5417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and exceedance probabilities \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p1\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5083px 8px; transform-origin: 45.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e expressed as percentages and returns the flows \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q1\" style=\"width: 19px; height: 20px;\" width=\"19\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.925px 8px; transform-origin: 108.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to the probabilities. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 345.033px 8px; transform-origin: 345.033px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.4917px 8px; transform-origin: 31.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (e.g., the highest flow has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m = 1\" style=\"width: 40px; height: 18px;\" width=\"40\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.142px 8px; transform-origin: 311.142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 100m/(n+1)\" style=\"width: 115px; height: 18.5px;\" width=\"115\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7833px 8px; transform-origin: 63.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.2833px 8px; transform-origin: 87.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for any probabilities that fall outside the range. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Q1 = floodFreq1(Qo,p1)\r\n%  Qo = observed flows\r\n%  p1 = exceedance probabilities at which the flows are to be reported\r\n%  Q1 = flows corresponding to the probabilities p1\r\n\r\n  Q1 = Qo*log(normcdf(p1));\r\nend","test_suite":"%%  Small sample from lognormal distribution\r\nQo = [27 360 71 8798 58 122 468 638 19 114 3542 781 356 635 6093 748 8305 8 6253 875];\r\np1 = [5 10 20 50];\r\nQ1_correct = [8773 8100 5583 552];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Larger sample from lognormal distribution\r\nrng(1)\r\nQo = 10.^(randn(1,500)+1.7);\r\np1 = [0.2 1 2 4 5 10 20 50];\r\nQ1_correct = [106602 21248 6176 2975 2432 1062 326 58];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Yellowstone River at Livingston, MT\r\n%  Flows from here down are in cubic feet per second\r\nQo = [18300 15400 13100 10600 18500 30600 13500 20400 15800 20600 26800 17500 21400 20000 22800 21200 20400 14900 25800 21900 17100 24200 15700 15600 20400 20200 20200 27900 16000 24900 24600 21200 24400 29200 26700 21100 36300 25700 21400 14200 26000 20100 15000 23800 27900 18600 17900 15200 24000 7450 16200 16200 17200 23000 13800 24000 16900 23700 37100 38000 18800 23400 19300 14800 25900 27200 13300 17900 22600 15200 26300 23500 28100 40600 23500 17900 32700 15600 12800 26300 33600 22800 30600 18500];\r\np1 = [9.58 13.53 50];\r\nQ1_correct = [30000 27900 20850];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct))\r\n\r\n%%  Mullica River near Batsto, NJ\r\nQo = [1190 407 815 360 382 350 384 245 287 1170 645 990 1050 435 430 630 489 1380 499 240 857 1840 380 204 420 705 946 143 419 666 269 579 490 565 401 488 578 149 401 473 747 364 335 343 201 509 452 420 449 1320 258 312 867 1860 303 332 537 387 222 342 517 676 249 285];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 1854 1564 1365 1110 747 433];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%  Charles River near Waltham, MA\r\nQo = [690 1520 1020 1370 2540 1020 2180 1020 1600 555 1470 1180 1000 1240 1360 692 1730 575 869 933 1250 1360 1550 2490 1990 957 1940 1460 1510 1850 1540 1340 890 904 637 1250 2670 1800 1790 1110 1670 1630 1090 895 4150 1610 1740 3480 1140 1220 2960 1970 2410 811 1110 2710 837 779 1240 1030 637 2180 1430 757 1430 2990 2180 1080 1090 2190 721 1170 1510 1510 1590 1250 1390 1390 4270 1770 1080 1570 1460 1640 634 1150 1250 1180 806 1520];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 4172 3166 2974 2482 1840 1367];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%  Merced River at Happy Isles Bridge near Yosemite, CA\r\nQo = [2500 3320 3180 3800 2720 2720 3240 2620 1240 2620 2240 2820 2050 2520 1870 1350 2570 2520 935 2820 2380 3020 8400 1210 2620 3220 2800 3480 1980 3040 3690 2450 3080 2480 2520 9260 3580 2180 2500 2800 9860 2910 3640 1520 1710 1080 2230 5200 1720 9240 1640 4640 1480 4980 2330 2170 2690 4240 3260 4650 1440 1800 4190 3500 4040 2100 4880 5450 2860 1600 4040 1750 1640 1910 1090 2310 1490 3140 1870 5220 5900 10100 4150 2810 2920 2330 2290 4550 1830 5680 4350 1180 2760 2750 4470 4610 2250 1750 1190 882 2490 5210 8060 4240 2160 1410];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [10083 9776 9005 8281 5213 4247 2700];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isequal(round(Q1),Q1_correct));\r\n\r\n%%  Quashnet River near Waquoit, MA\r\nQo = [41 36 33 41 40 35 28 34 39 42 32 27 39 26 33 40 36 61 83 32 39.2 52 44 42 58 30 32 30.1 50.1 48.4 53.2 40.8];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN NaN 76.0 68.7 56.6 49.1 39.1];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(all(isnan(Q1(1:2))) \u0026\u0026 isequal(round(Q1(3:end),1),Q1_correct(3:end)));\r\n\r\n%%  Illinois River at Henry, IL\r\nQo = [104000 108000 53700 106000 95200 46300 45100 45000 40200 53700 30900 67000 47000 58900 78000 117000 88900 55000 40400 71800 88500 38400 52100 84600 32400 90300 128000 92400 58300 64000 49000 161000 65400 98500 107000 93100 111000 108000 120000 64200 51600];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN NaN 138560 127200 115800 106600 67000];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(all(isnan(Q1(1:2))) \u0026\u0026 isequal(round(Q1(3:end)),Q1_correct(3:end)));\r\n\r\n%%  South Skunk River near Ames, IA\r\nQo = [1990 600 3490 2580 3000 2890 3230 2320 3050 2530 4500 8060 4010 2270 6550 2620 3000 3820 5320 1630 980 8630 1340 376 3540 3150 1720 6210 1990 4300 1820 2170 5260 2900 2790 4890 4380 1330 3660 3030 3340 5780 5230 3580 5300 2240 4980 2720 1880 3490 5150 5020 1980 4040 3040 565 370 6600 4700 2350 11200 2340 1640 14000 2080 4760 3630 906 1990 1070 2030 2520 2310 3330 6510 11000 4560 14800 1620 730 6740 9250 11200 6420 1890 4380 6740 3260 455 4210];\r\np1 = [1 2 4 5 10 20 50];\r\nQ1_correct = [NaN 14144 11181 11060 7092 5292 3190];\r\nQ1 = floodFreq1(Qo,p1);\r\nassert(isnan(Q1(1)) \u0026\u0026 isequal(round(Q1(2:end)),Q1_correct(2:end)));\r\n\r\n%%\r\nfiletext = fileread('floodFreq1.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-21T19:33:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-01-21T19:33:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-21T19:29:29.000Z","updated_at":"2023-01-21T19:33:03.000Z","published_at":"2023-01-21T19:29:55.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes as input \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e observations of peak streamflow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Qo\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and exceedance probabilities \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e expressed as percentages and returns the flows \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to the probabilities. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse the empirical method of frequency analysis. Sort the observed flows in decreasing order and assign a rank \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (e.g., the highest flow has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). If a flow occurs multiple times, assign to that flow the average of the ranks attached to the multiple occurrences. Then compute the exceedance probabilities (in percent) with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 100m/(n+1)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 100 m /(n+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Compute the flows corresponding to the requested exceedance probabilities with linear interpolation and return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for any probabilities that fall outside the range. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57800,"title":"Compute infiltration and runoff under constant precipitation with the Green-Ampt method","description":"Problem statement\r\nWrite a function that computes infiltration, depression storage, and runoff using the Green-Ampt method. It should take as input the rainfall intensity , saturated hydraulic conductivity , initial moisture content , saturated moisture content , average suction head , maximum available depression storage , and a vector of times . If ponding occurs, the function should insert the ponding time  into the time vector. It should then compute the cumulative infiltration  and depression storage  at each of the times, as well as the runoff  during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths.  \r\nBackground\r\nTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate  is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) , and the cumulative infiltration  is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \r\nThe infiltration capacity predicted by the Green-Ampt method is\r\n\r\nThe cumulative infiltration  at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\r\n\r\nwhere\r\n\r\nis the time to infiltrate  from the start of the storm under immediate ponding.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 286.3px; transform-origin: 407px 286.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 64.5px; text-align: left; transform-origin: 384px 64.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 257.242px 8px; transform-origin: 257.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eGreen-Ampt method\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.775px 8px; transform-origin: 56.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. It should take as input the rainfall intensity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.467px 8px; transform-origin: 103.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ks\" style=\"width: 17px; height: 20px;\" width=\"17\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.4583px 8px; transform-origin: 75.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, initial moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"thetai\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.675px 8px; transform-origin: 88.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, saturated moisture content \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"thetas\" style=\"width: 14px; height: 20px;\" width=\"14\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, average suction head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Psi_av\" style=\"width: 23.5px; height: 20px;\" width=\"23.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.208px 8px; transform-origin: 127.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, maximum available depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Smax\" style=\"width: 27px; height: 20px;\" width=\"27\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.775px 8px; transform-origin: 70.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a vector of times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.725px 8px; transform-origin: 72.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If ponding occurs, the function should insert the ponding time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 216.25px 8px; transform-origin: 216.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e into the time vector. It should then compute the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and depression storage \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.933px 8px; transform-origin: 130.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at each of the times, as well as the runoff \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.983px 8px; transform-origin: 169.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.5px; text-align: left; transform-origin: 384px 42.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.342px 8px; transform-origin: 378.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.025px 8px; transform-origin: 140.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAAoCAYAAADg+OpoAAACQElEQVRYR+1WuS6FQRS+HkDE8gSWmgTRUNofAIlCZ+k0JJRCUIulkOjQaQhaOhQqheUJLPEEfJ+cI3N/M/+cOzdExCRf5r93zsx39pmKwg+Nih/iKfwTJXv6V7quFuYsAO1i1j3mNeDcYqbVonocdioHdmDuBnYBkvH3U4zMSnSBg9qAFuAaGAc2gRegJkbCdQvRsGh/grnPObQT3zcWa6xEdxBsACaALYv2PpmYRdT6TDaq25K4YkTrOHWylFiEtPARNUO4UjbsiNsuMU87h5hjo3t8RMeyyLphpnEwjRkrjitgvlT/5blOU5hnDgJHpR7uyucRaXwoXwdEizJPkTwiTWvGR9tOslEhIsbnUU5dSolJVqMQkVs/I9i0l2yKbAwRzWB9RWTYFR6+i4gp3itp3VguCfeHLHrGWjWwD7Cplj18RLx7WKAcZTVSVzsfkV4LlMtrpEyYfqAHYByngDGAruYdNQp8FrmPaBECc4DlUtPspOwysA1UiUf4XxPwUeihXsdEsMRH21RW9k3c9pmxPiIV6oJw7OHB+hoCXFkt9qL3RJZoAJsOjW6j0lQq+0DRGBdZSSL6WTXXRmrpBhqfDUkE8VZBa7Co0EnEmmHQOG5FQ0sT1aRxldKYzeKcVWXWZGCXZorSGqam6Z0GOX2CqebqMm/t0SJtmAfOt6uM71sDzhTmfs6vAJ9kfPd9GbHHSYhQtc/GJ6hgKpEmjfmKTyXS29d8haQQMdtaxUd8EbHtRO+rFKJYonjX/x7RO1S6din/Er4mAAAAAElFTkSuQmCC\" alt=\"fp\" style=\"width: 13px; height: 20px;\" width=\"13\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.4667px 8px; transform-origin: 96.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.408px 8px; transform-origin: 126.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.65px 8px; transform-origin: 195.65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.9px; text-align: left; transform-origin: 384px 19.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"fp = Ks(1+Psi_av(thetas-thetai)/F)\" style=\"width: 162.5px; height: 40px;\" width=\"162.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.3px 8px; transform-origin: 81.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe cumulative infiltration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 290.558px 8px; transform-origin: 290.558px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.5px; text-align: left; transform-origin: 384px 19.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" alt=\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\" style=\"width: 264px; height: 41px;\" width=\"264\" height=\"41\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.0583px 8px; transform-origin: 68.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the time to infiltrate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAoCAYAAACWwljjAAACdklEQVRYR+2XOUsEMRTH3U/gWYlYeICdglejjeCFjZ0KInYeX0DQWhF7r0KwU7+AaK2NeKCFlUdl6YkfQP9/yVuycTKZzG6WLXbgMZmZ5OW378xmKkrsypQYT0UZyOWRsoXytVATFNS7lFi+f+P9ne9al8sI1AaZgUwYyk+N51o8d2nvljDeKDSQ6OvD4ExT3mH59YTaVPBjuB+HApqD4h2l/AP3mpiNBL4Oc95CAW1B8YJSvo37ogNoH99bfGE43xVDovMdg2r1MIX7YcxmdNugY451eRKgdqy+1TQ0Y/xsaOSclzQuMsmSAOnxcwUF3YYSWuQBwgwzQb29lgSI7pGUX8N4xdiF8cXyMOK9e8SCJEA/2rp5jO8hDZBGyABkGML3u8UAMuuPXgx7ACCBHhVXqfhcFlqF1mWlmTCmWy7VNzOuUsFwkQuIG0o7iGoFjK8biHeLsBHHATF7XrWFUe3iBN8J6t1E0wBNYtGBWmhrF8yuvFNdh4uzkN4ujrCIgMGvOKBH7M7s4eVqFwUDtQHRFU/aLgVLaxe5DUhvFwRL1bnV5qxlo5AhZXGeFGaVTh5jpiHZc1MUELPrQnMX+xfrj/fZRrOGFFgmxzpkD1KpvMB3raLfBGLgjkOqDNN+4jmfeiMWN5ND2lI2JFyF0eXypN+lQfdjwblaJHWOIdFrs1DSDXzn0RI5G+NZ6lyO1YphIYkf8+jLKs+TQk4GFwNIGrReyySm/vXHYgBJgxZLiKsiz1ChgSRwmdoMbN6/IDzKRDbk0EBiDddfp2yShAaSBp34X2xoIGnQiXthSCBmV6fyxbVqF86zU0gg3+L5N78M5DLbL6F9cynpLQaQAAAAAElFTkSuQmCC\" alt=\"Fp\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 166.85px 8px; transform-origin: 166.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the start of the storm under immediate ponding. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax)\r\n%  See tests for definitions and units of variables\r\n  F = i*t; S = min(F,Smax); Q = i*t-F-S;\r\nend","test_suite":"%%  Gupta ex. 4.2\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = zeros(size(F_correct));                     %  Depression storage (mm)\r\nQ_correct = [0 0.1680 1.4553 2.2120];                   %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, with depression storage\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = 6;                          %  Intensity (mm/h)\r\ntp_correct = 1.6282;            %  Ponding time (h)\r\nF_correct = [0 9.7689 11.8320 16.3767 20.1648];         %  Cum. infiltration (mm)\r\nS_correct = [0 0 0.1680 1.6233 3.8352];                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta ex. 4.2, i \u003c Ks\r\nPsi_av = 150;                   %  Average suction head (mm)\r\nthetaS = 0.48;                  %  Saturated moisture content\r\nthetaI = 0.23;                  %  Initial moisture content\r\nKs = 1.24;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 10;                      %  Maximum depression storage (mm)\r\nt = [0 2 3 4];                  %  Time (h)\r\ni = rand;                       %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5 \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 0.4375;                     %  Intensity (mm/h)\r\nF_correct = i*t;                                        %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                 %  Depression storage (mm)\r\nQ_correct = zeros(1,length(F_correct)-1);               %  Runoff (mm)\r\n[~,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 0;                       %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 10.5;                       %  Intensity (mm/h)\r\ntp_correct = 0.5609;            %  Ponding time (h)\r\nF_correct = [0 5.8896 9.4982 14.9421 19.0537 22.5444];     %  Cum. infiltration (mm)\r\nS_correct = zeros(1,length(F_correct));                    %  Depression storage (mm)\r\nQ_correct = [0 1.0018 5.0561 6.3884 7.0093];               %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%  Gupta problem 4.5, higher intensity + depression storage \r\nPsi_av = 250;                   %  Average suction head (mm)\r\nthetaS = 0.52;                  %  Saturated moisture content\r\nthetaI = 0.2;                   %  Initial moisture content\r\nKs = 0.72;                      %  Saturated hydraulic conductivity (mm/h)\r\nSmax = 75;                      %  Maximum depression storage (mm)\r\nt = 0:4;                        %  Time (h)\r\ni = 65;                         %  Intensity (mm/h)\r\ntp_correct = 0.0138;            %  Ponding time (h)\r\nF_correct = [0 0.8961 11.1781 16.1243 20.0327 23.4058];     %  Cum. infiltration (mm)\r\nS_correct = [0 0 53.8219 75 75 75];                         %  Depression storage (mm)\r\nQ_correct = [0 0 38.8757 61.0916 61.6268];                  %  Runoff (mm)\r\n[t1,F,S,Q] = GreenAmptConst(t,i,Ks,Psi_av,thetaS,thetaI,Smax);\r\nassert(abs(setdiff(t1,t)-tp_correct)\u003c1e-3)\r\nassert(all(abs(F-F_correct)\u003c1e-3))\r\nassert(all(abs(S-S_correct)\u003c1e-3))\r\nassert(all(abs(Q-Q_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('GreenAmptConst.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-18T02:19:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-18T02:01:12.000Z","updated_at":"2023-03-18T02:19:29.000Z","published_at":"2023-03-18T02:19:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes infiltration, depression storage, and runoff using the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGreen-Ampt method\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. It should take as input the rainfall intensity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ks\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, initial moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetai\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, saturated moisture content \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"thetas\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, average suction head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Psi_av\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Psi_{av}\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, maximum available depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Smax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a vector of times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If ponding occurs, the function should insert the ponding time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e into the time vector. It should then compute the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and depression storage \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at each of the times, as well as the runoff \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"F\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe infiltration capacity predicted by the Green-Ampt method is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fp = Ks(1+Psi_av(thetas-thetai)/F)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_p  = K_s\\\\left(1+\\\\frac{\\\\Psi_{av}(\\\\theta_s - \\\\theta_i)}{F}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe cumulative infiltration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = (1/Ks)[F-Psi_av(thetas-thetai) ln(1+F/Psi_av(thetas-thetai)]+tp-t'p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = \\\\frac{1}{K_s}\\\\left[F-\\\\Psi_{av}(\\\\theta_s - \\\\theta_i) \\\\ln\\\\left(1+\\\\frac{F}{\\\\Psi_{av}(\\\\theta_s-\\\\theta_i)}\\\\right)\\\\right]+t_p-t^\\\\prime_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et^\\\\prime_p = \\\\frac{F_p}{K_s} – (\\\\theta_s - \\\\theta_i)\\\\frac{\\\\Psi_{av}}{K_s} \\\\ln\\\\left(1+\\\\frac{F_p}{\\\\Psi\\n_{av} (\\\\theta_s - \\\\theta_i)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis the time to infiltrate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Fp\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the start of the storm under immediate ponding. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57765,"title":"Determine whether a hydrograph is a unit hydrograph","description":"A hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate  (or flow or discharge) as a function of time  resulting from a given excess rainfall (expressed as a depth ) for a storm of a specified duration. A unit hydrograph results from unit excess rainfall (e.g.,  = 1 cm). \r\nWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time  in minutes, the flow rate  in , and the catchment area  in . Allow for a tolerance of 0.01 cm in the excess rainfall depth.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.467px 8px; transform-origin: 333.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or flow or discharge) as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.267px 8px; transform-origin: 188.267px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e resulting from a given excess rainfall (expressed as a depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.8333px 8px; transform-origin: 82.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) for a storm of a specified duration. A \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eunit hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.9px 8px; transform-origin: 115.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eresults from unit excess rainfall (e.g., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.3583px 8px; transform-origin: 29.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 1 cm). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 330.108px 8px; transform-origin: 330.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in minutes, the flow rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAAnCAYAAAC7bZ4BAAADs0lEQVRoQ+2Zt6sVQRTGfX+AiKESsTB0goIJxEowlyoGxEowlIIBtTSgoK8ygXZiAEERFbWxUMRUKFgIhkJbA/oP6Pd7znnMm507d3b3ce8u3IGP+9yZ3TnnmxPHoQmDMcLA0ICH/wwMiHCWMCCiz0TM0v4rhUnCb+FSv120HxaxRUpfFx4Jc4TZwhths/ClAiG79M434UGFd0df6TURWMJjYZWn9A1Hwu6KlvFT7+0V+E7l0WsiOL0XwjtP4uX6+6lwQjhSUpN1Wn9VmFLyvcLyXhMRkxdl7gsLAoJydDvvFmERtUYTiHgoDW5XcIupeue7sF6oFR9gsJ9EEC840SXChQpuQdA9JhBwa49+ETFfkq8WVrhfFDkonC6hEcHxcwUCo1v0iwhfGEunKJV7ulgT66vElcYSgWC4yB5hmvAjwyrIPjuFxRlrs5akLMKqP6v6+Df+PNN9+ZZ+/QKI4LVUmOfmKZj8NJkS6IAmDwlzM4l4rXWXhVRFGsrzVetfCRNjcoVEoOxGYZOwSPglkKMR9FREE4vYnNBJYXKwJjeiH9d7C4U1GcdHfHkrUJF2qkRZ80Qgjlxz31yr38OeTmO2ihExXSuGPSLwRU6ADz4TbBOUZo5KEbIgAgugQLrrSAn9nrkZTkAThJP7KGwXctIgpEECsaXT+OQUDl3HLK9QgHVyDd8CtgaCsznCwC7jZkQoLOSim/cDGjUD2YLe4ozwR9gh3InskVLyaGK9WQyuGVoYpL8UCkE5h4hYZLayGGFjPYI/7xOJILgeXSfjuYCV5Q4rqVOxxN875pocciFN94KIqs1UjJzckppGzOIV+xPYk9moTUSUiSXWvxiZBP1kh9omIsqW1OZGfiYjblDBFtJ6m4ioUlJjRfsEC+xYCJlsQ0hGW4goU1KzlhLAD8I8476DWzBGIaO0hQjS8X4hpxcha2xzMSEMuHYbZoXi6HxbiMgpqU0pK+hiKdZSK3XMmGKrDUSYW6RKav/kU1d/VigWUnqMCLtgZWMGvnVWsDxMADrn+Vt4Ax36Y50bavYv04ew3i+ouPC5J1DBLhPol6L3HiERfIQXYuOKHlIRUhnGxns9/JCYL9ON+t+nb0iV1KEsHBRy0pD5+lj3GW3UmnAx04HXkcd2urn3FKlvJeeaTkRuSV2ZAHux6UTQM+S257XIaDIRlNRYRO3/vMlhqMlEVCmpc3SOrmkyEX8l8bjdUndjqMlEcNOUe/nbTc+u800moqvw47lgQIRjc0CEI+IfjbbsKMTiRisAAAAASUVORK5CYII=\" alt=\"m^3/s\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 8px; transform-origin: 79.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the catchment area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^2\" style=\"width: 19.5px; height: 19px;\" width=\"19.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.642px 8px; transform-origin: 188.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isUnitHydrograph(t,Q,A)\r\n  tf = isequal(Q*t/A,1);\r\nend","test_suite":"%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:40:520;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2520000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 753601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 735601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 3.2 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 2.3 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-11T12:56:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-11T01:14:20.000Z","updated_at":"2023-03-11T12:56:36.000Z","published_at":"2023-03-11T01:14:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or flow or discharge) as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e resulting from a given excess rainfall (expressed as a depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) for a storm of a specified duration. A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunit hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eresults from unit excess rainfall (e.g., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 1 cm). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in minutes, the flow rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^3/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^3/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the catchment area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57635,"title":"Compute the average precipitation for a watershed using the Thiessen polygon method","description":"Several methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \r\nThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \r\nWrite a function that takes the precipitation amounts and the (, ) coordinates of the boundary and the gauges and compute the average precipitation for the watershed. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93px; transform-origin: 407px 93px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.425px 8px; transform-origin: 366.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSeveral methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190.458px 8px; transform-origin: 190.458px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the precipitation amounts and the (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.767px 8px; transform-origin: 156.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) coordinates of the boundary and the gauges and compute the average precipitation for the watershed. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Pavg = spatial_average(xd,yd,P,xb,yb)\r\n%  (xd, yd) = coordinates of the precipitation gauges\r\n%  P = precipitation values\r\n%  (xb,yb) = coordinates of the boundary of the watershed\r\n\r\n   Pavg = integral(P*dx*dy)/integral(dx*dy);","test_suite":"%% Rectangular catchment with simple gauge placement and values\r\nxb = [0 5 5 0 0];    % km\r\nyb = [0 0 10 10 0];  % km\r\nxd = [-1 6 6 -1];\r\nyd = [-1 -1 11 11];\r\nP  = [20 20 40 40];  % cm\r\nPavg_correct = 30;   % cm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.05);\r\n\r\n%% Example 3 from dreamcivil.com\r\nxb = [0 10 10 0 0]; % km\r\nyb = [0 0 5 5 0];   % km\r\nxd = xb(1:end-1);\r\nyd = yb(1:end-1);\r\nP  = [11 15 12 10]; % cm\r\nPavg_correct = 12;  % cm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01);\r\n\r\n%% Rectangular catchment with more complicated gauge locations \r\nxb = [0 10 10 0 0];\r\nyb = [0 0 30 30 0];\r\nxd = [-3 8  4 13  1 9];\r\nyd = [-2 2 12 21 25 33];\r\nP  = 132+3*(yd-33);\r\nPavg_correct = 77.65;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)/Pavg_correct\u003c0.01)\r\n\r\n%% More complicated boundary\r\nxb = 10*[0.5497 0.4705 0.3840 0.3214 0.2937 0.2882 0.3379 0.4632 0.6271 0.7284 0.7947 0.8241 0.8039 0.8039 0.7689 0.7302 0.6452 0.5497];   % km\r\nyb = 10*[0.1857 0.2512 0.3867 0.5152 0.6717 0.7909 0.9007 0.9591 0.9498 0.8797 0.7605 0.6320 0.4708 0.4708 0.3914 0.2745 0.2194 0.1857];   % km\r\nxd = 10*[0.4 0.63 0.5 0.7 0.8];\r\nyd = 10*[0.9 0.6 0.35 0.8 0.32];\r\nP  = [113 166 140 183 125]; % mm\r\nPavg_correct = 148.271; % mm\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n\r\n%% Example 5.5 from Chin\r\nxb = [2.0084 2.4293 2.8156 3.0028 3.2368 3.4126 3.6713 3.8467 4.0235 4.2117 4.3540 4.5197 4.7338 4.9362 5.0688 5.2611 5.4307 5.5418 5.6399 5.7033 5.7094 5.6167 5.4566 5.3269 5.2170 5.1962 5.2033 5.2325 5.2838 5.3351 5.3630 5.3672 5.3594 5.2956 5.1854 5.0638 4.9172 4.7914 4.5239 4.2432 4.0206 3.9153 3.7154 3.4805 3.3047 3.1412 2.9657 2.6980 2.4305 2.1494 1.9034 1.6444 1.3955 1.1317 0.9849 0.8611 0.7998 0.7605 0.6858 0.5893 0.4919 0.3519 0.2515 0.1265 0.0875 0.0801 0.1796 0.3474 0.5154 0.6832 0.7618 0.8867 1.0592 1.2773 1.4249 1.5055 1.5835 1.5910 1.5914 1.6825 1.8099 1.9151 2.0084];\r\nyb = [6.4122 6.4364 6.4348 6.4401 6.4466 6.4391 6.3966 6.4015 6.3566 6.3246 6.2539 6.1839 6.0530 5.9218 5.7761 5.5824 5.3632 5.1423 4.9708 4.7859 4.5496 4.0617 3.4599 3.0456 2.7688 2.6686 2.3950 2.1719 1.9991 1.8263 1.6529 1.4912 1.3416 1.0910 0.8266 0.5494 0.3337 0.2182 0.1485 0.1406 0.1468 0.1439 0.1756 0.2064 0.2139 0.1969 0.1920 0.1347 0.0650 0.0695 0.0751 0.1301 0.2475 0.4890 0.7338 0.9917 1.5500 1.7106 1.8828 1.9921 2.1387 2.5703 2.8288 3.1364 3.2847 3.5707 3.7975 4.1008 4.3918 4.6951 4.8218 4.9746 5.0914 5.2593 5.4377 5.4897 5.6412 5.8032 6.2388 6.3409 6.3942 6.3972 6.4122];\r\nxd = [1.3 1.0 4.2 3.5 2.1];\r\nyd = [7.0 3.7 4.9 1.4 -1.0];\r\nP  = [60 90 65 35 20];\r\nPavg_correct = 59.301;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n\r\n%% C E 372 problem 11\r\nxb = [33.6241 31.3609 26.3820 25.3635 24.0062 22.8754 21.4057 19.4844 18.2414 17.5648 15.1930 15.1935 15.5336 15.8735 15.8742 15.3089 13.6128 12.9347 12.0319 11.4673 10.2237 8.8694 8.0782 7.7400 7.4023 7.4049 7.7466 8.2004 9.6732 11.4838 14.6517 15.7834 16.4627 16.8027 16.8037 15.5614 14.0926 13.0759 12.3981 12.5118 14.5502 15.4557 16.7001 19.1891 22.2439 24.2812 26.3185 27.5654 27.9054 29.1500 30.9595 32.7690 34.5782 36.2742 38.0830 39.1005 40.6836 41.9275 46.9026 47.6937 49.5021 49.8399 49.8383 49.1574 48.2507 46.8905 45.1911 44.5108 44.0567 43.4877 43.0343 42.5763 42.4619 41.2167 39.1791 38.8389 38.8379 38.3850 37.2537 36.0095 35.5567 34.6511 35.2149 35.4394 35.5514 35.5496 35.3221 35.2082 33.7370]; % mi\r\nyb = [5.2159 3.9673 1.3564 0.6755 0.5609 0.7865 1.4650 2.9363 4.1815 6.2206 9.7311 10.2976 11.2045 11.7714 12.5646 12.7907 13.1290 13.6949 15.8471 16.7530 17.3184 20.3766 20.9425 22.0753 23.7747 26.6075 29.1008 30.5743 33.2952 34.3168 35.4529 36.1339 36.9277 37.6079 38.7411 40.6662 42.2512 43.4967 44.4026 44.9693 47.6908 48.4848 48.8259 49.6215 50.7575 52.3458 53.9342 56.8815 57.5617 58.1295 58.0179 57.9063 57.4547 56.8898 56.0983 55.6460 55.3075 55.0821 53.6137 53.0479 51.6898 50.1037 48.4040 46.0238 43.9832 40.8092 37.7481 35.9344 34.1209 30.4943 29.3608 23.4680 22.1081 20.9738 19.0455 18.1387 17.0055 16.5518 16.2108 16.0963 15.6427 14.8486 13.0361 11.2233 10.0903 8.1639 6.8039 5.8973 4.9894]; % mi\r\nxd = [15.9758 6.0340 4.0115 15.4546 38.1999 50.7358 40.6553 33.7370 31.4005 19.7352 28.4331]; % mi\r\nyd = [0.3267 12.1020 26.1511 47.3517 60.0644 40.6995 25.2792 4.9894 45.8937 28.9988 17.5623]; % mi\r\nP  = [29.79 34.97 25.60 24.27 24.60 42.61 42.35 15.51 39.99 43.04 28.41]; % in\r\nPavg_correct = 35.011;\r\nPavg = spatial_average(xd,yd,P,xb,yb);\r\nassert(abs(Pavg-Pavg_correct)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2023-02-04T01:17:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2023-02-04T01:17:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-01T17:01:04.000Z","updated_at":"2023-02-04T01:17:57.000Z","published_at":"2023-02-01T17:03:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSeveral methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. The Thiessen polygon method involves forming polygons around the gauges, assigning the gauge’s observed precipitation to each point in the polygon, and computing the weighted average precipitation using the areas of the polygons as weights. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe polygons can be determined by connecting the gauges with lines, drawing the perpendicular bisectors of the connecting lines, and finding the intersections of the bisectors to form the polygons. An example is shown below. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the precipitation amounts and the (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" 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