WOLFRAM SYSTEM MODELER
This information is part of the Modelica Standard Library maintained by the Modelica Association.
This function shall be used within the restricted limits according to the referenced literature.
The pressure loss dp for a thick edged orifice is determined by:
dp = zeta_TOT * (rho/2) * (velocity_1)^2
|rho||as density of fluid [kg/m3],|
|velocity_1||as mean velocity in large cross sectional area [m/s],|
|zeta_TOT||as pressure loss coefficient [-].|
The pressure loss coefficient zeta_TOT of a thick edged orifice can be calculated for different cross sectional areas A_0 and relative length of orifice l_bar =L/d_hyd_0 by:
zeta_TOT = (0.5*(1 - A_0/A_1)^0.75 + tau*(1 - A_0/A_1)^1.375 + (1 - A_0/A_1)^2 + lambda_FRI*l_bar)*(A_1/A_0)^2 [Idelchik 2006, p. 222, diag. 4-15]
|A_0||cross sectional area of vena contraction [m2],|
|A_1||large cross sectional area of orifice [m2],|
|d_hyd_0||hydraulic diameter of vena contraction [m],|
|lambda_FRI||as constant Darcy friction factor [-],|
|l_bar||relative length of orifice [-],|
|L||length of vena contraction [m],|
|tau||geometry parameter [-].|
The geometry factor tau is determined by [Idelchik 2006, p. 219, diag. 4-12]:
tau = (2.4 - l_bar)*10^(-phi) phi = 0.25 + 0.535*l_bar^8 / (0.05 + l_bar^8) .
The pressure loss coefficient zeta_TOT of a thick edged orifice in dependence of a relative length (l_bar = L /d_hyd) with different ratios of cross sectional areas A_0/A_1 is shown in the figure below.
Incompressible case [Pressure loss = f(m_flow)]:
The pressure loss DP of an thick edged orifice in dependence of the mass flow rate m_flow of water for different ratios A_0/A_1 (where A_0 = 0.001 m^2) is shown in the figure below.
And for the compressible case [Mass flow rate = f(dp)]: