WOLFRAM SYSTEM MODELER
This information is part of the Modelica Standard Library maintained by the Modelica Association.
Calculation of pressure loss in a straight pipe for laminar flow regime of single-phase fluid flow only.
This function shall be used inside of the restricted limits according to the referenced literature.
The pressure loss dp for straight pipes is determined by:
dp = lambda_FRI * (L/d_hyd) * (rho/2) * velocity^2
|lambda_FRI||as Darcy friction factor [-].|
|L||as length of straight pipe [m],|
|d_hyd||as hydraulic diameter of straight pipe [m],|
|rho||as density of fluid [kg/m3],|
|velocity||as mean velocity [m/s].|
The Darcy friction factor lambda_FRI of straight pipes for the laminar flow regime is calculated by Hagen-Poiseuilles law according to [Idelchik 2006, p. 77, eq. 2-3] as follows:
lambda_FRI = 64/Re
|lambda_FRI||as Darcy friction factor [-],|
|Re||as Reynolds number [-].|
The Darcy friction factor lambda_FRI in the laminar regime is independent of the surface roughness K as long as the relative roughness k = surface roughness/hydraulic diameter is smaller than 0.007. A higher relative roughness k than 0.007 leads to an earlier leaving of the laminar regime to the transition regime at some value of Reynolds number Re_lam_leave . This earlier leaving is not modelled here because only laminar fluid flow is considered.
The Darcy friction factor lambda_FRI in dependence of Reynolds number is shown in the figure below.
The pressure loss dp for the laminar regime in dependence of the mass flow rate of water is shown in the figure below.
Note that this pressure loss function shall not be used for the modelling outside of the laminar flow regime at Re > 2000 even though it could be used for that.
If the whole flow regime shall be modelled, the pressure loss function dp_overall can be used.