Hydraulic resistance in pipe bend
Local Hydraulic Resistances
The Pipe Bend block represents a pipe bend as a local hydraulic resistance. The pressure loss in the bend is assumed to consist of
Loss in the straight pipe
Loss due to curvature
The loss in a straight pipe is simulated with the Hydraulic Resistive Tube block. The loss due to curvature is simulated with the Local Resistance block, and the pressure loss coefficient is determined in accordance with the Crane Co. recommendations (see [1], p. A-29). The flow regime is checked in the underlying Local Resistance block by comparing the Reynolds number to the specified critical Reynolds number value.
The pressure loss due to curvature for turbulent flow regime is determined according to the following formula:
$$p=K\frac{\rho}{2{A}^{2}}q\left|q\right|$$
where
q | Flow rate |
p | Pressure loss |
K | Pressure loss coefficient |
A | Bend cross-sectional area |
ρ | Fluid density |
For laminar flow regime, the formula for pressure loss computation is modified, as described in the reference documentation for the Local Resistance block.
The pressure loss coefficient is determined according to recommendation provided in [1]:
$$K={K}_{d}\xb7{K}_{r}\xb7{K}_{\alpha}$$
where
K_{d} | Base friction factor coefficient |
K_{r} | Correction coefficient accounting for the bend curvature |
K _{α} | Correction coefficient accounting for the bend angle |
The base friction factor coefficient is determined according to the following table.
Note Friction factors for pipes with diameters greater than 525 mm are determined by extrapolation. |
The correction coefficient accounting for the bend curvature is determined according to the next table.
The bend curvature relative radius is calculated as
r
= bend radius
/ pipe
diameter
Note
For pipes with the bend curvature relative radius value outside
the range of 1 > |
Correction for non-90^{o} bends is performed with the empirical formula (see [2], Fig. 4.6):
$${K}_{\alpha}=\alpha (0.0142-3.703\xb7{10}^{-5}\alpha )$$
where
α | Bend angle in degrees (0 ≤ α ≤ 180) |
Connections A and B are conserving hydraulic ports associated with the block inlet and outlet, respectively.
The block positive direction is from port A to port B. This means that the flow rate is positive if fluid flows from A to B, and the pressure differential is determined as $$p={p}_{A}-{p}_{B}$$.
Warning
The formulas used in the Pipe Bend block are
very approximate, especially in the laminar and transient flow regions.
For more accurate results, use a combination of the Local Resistance block
with a table-specified |
Fluid inertia, fluid compressibility, and wall compliance are not taken into account.
The transition between laminar and turbulent regimes
is assumed to be sharp and taking place exactly at Re
=Re_{cr}
.
The bend is assumed to be made of a clean commercial steel pipe.
The internal diameter of the pipe. The default value is 0.01
m.
The radius of the bend. The default value is 0.04
m.
The angle of the bend. The value must be in the range between
0 and 180 degrees. The default value is 90
deg.
Roughness height on the pipe internal surface. The parameter
is typically provided in data sheets or manufacturer's catalogs. The
default value is 1.5e-5
m, which corresponds to
drawn tubing.
The maximum Reynolds number for laminar flow. The transition
from laminar to turbulent regime is assumed to take place when the
Reynolds number reaches this value. The value of the parameter depends
on the geometrical profile. You can find recommendations on the parameter
value in hydraulics textbooks. The default value is 350
.
Parameters determined by the type of working fluid:
Fluid density
Fluid kinematic viscosity
Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.
The block has the following ports:
A
Hydraulic conserving port associated with the bend inlet.
B
Hydraulic conserving port associated with the bend outlet.
[1] Flow of Fluids Through Valves, Fittings, and Pipe, Crane Valves North America, Technical Paper No. 410M
[2] George R. Keller, Hydraulic System Analysis, Published by the Editors of Hydraulics & Pneumatics Magazine, 1970
Elbow | Gradual Area Change | Hydraulic Resistive Tube | Local Resistance | Sudden Area Change | T-junction