I am getting unrealistic values using vpasolve

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clc, clear
d = 5/12; % Pipe diameter, ft
L = 1; % Pipe length, ft
h = 2/12; % Height difference of mercury, ft
rho_w = 1.937; % density of water, slug/ft^3
rho_m = 26.3; % density of mercury, slug/ft^3
mu = 2.09*10^-5; % slug/ft*second
g = 32.2; % gravity, ft/s^2
syms Vcl hf f V Re_d
x = vpasolve([(rho_w*Vcl^2)/2 == ((rho_m-rho_w)*g*h)+(rho_w*g*hf), ...
hf == f*(L/d)*((V^2)/(2*g)), V/Vcl == (1+1.3*sqrt(f))^-1, ...
1/sqrt(f) == -2*log10(2.51/(Re_d*sqrt(f))), ...
Re_d == (rho_w*V*d)/mu], ...
[Vcl, hf, f, V, Re_d])
I am getting values with an i in them, and I am unsure how to fix this. I have confirmed that the equations in the solver are correct.
This is the answer I am getting:
x =
struct with fields:
Vcl: - 11.618976698556484163757444664859 - 0.0000000000000000031159299773113211212032247085422i
hf: 0.00000000010691099774793287072143003602414 + 0.0000000000000000011243452733140998420596898170279i
f: 4491158430069173668821.2496305322 + 12026888742356199124.612735277612i
V: 0.00000000000000054448854808565276662309009580122 - 0.00000000000000000072904648955139354037146343208172i
Re_d: 0.000000000021026202504822758976257513492856 - 0.00000000000002815317085847387421157383877638i

Answers (2)

Paul
Paul on 3 May 2022
Edited: Paul on 3 May 2022
I had to rearrange the second and third equations to muliply through by Vcl and sqrt(f) respectively and restrict the range of the solution space in the call to vpasolve()
d = 5/12; % Pipe diameter, ft
L = 1; % Pipe length, ft
h = 2/12; % Height difference of mercury, ft
rho_w = 1.937; % density of water, slug/ft^3
rho_m = 26.3; % density of mercury, slug/ft^3
mu = 2.09*10^-5; % slug/ft*second
g = 32.2; % gravity, ft/s^2
syms Vcl hf f V Re_d
x = vpasolve([(rho_w*Vcl^2)/2 == ((rho_m-rho_w)*g*h)+(rho_w*g*hf), ...
hf == f*(L/d)*((V^2)/(2*g)), ...
V == Vcl*(1+1.3*sqrt(f))^-1, ...
1 == -2*log10(2.51/(Re_d*sqrt(f)))*sqrt(f), ...
Re_d == (rho_w*V*d)/mu], ...
[Vcl, hf, f, V, Re_d], ...
[ -inf inf; ...
-inf inf; ...
0 inf; ...
-inf inf
-inf inf])
x = struct with fields:
Vcl: 11.766003641583686200483461147558 hf: 0.053388543152905222463767286417839 f: 0.013742615972609076804165352881268 V: 10.210021170256005402469178079995 Re_d: 394274.54160258943110540850414583

Walter Roberson
Walter Roberson on 3 May 2022
As a third parameter to vpasolve pass in a 5 x 2 array of constraints, lower bounds and upper bounds. In particular f should be used constrained to lower bound 0.

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