WOLFRAM SYSTEM MODELER

# dp_thickEdgedOverall # Wolfram Language

In:= `SystemModel["Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.PressureLoss.Orifice.dp_thickEdgedOverall"]`
Out:= # Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

#### Restriction

This function shall be used within the restricted limits according to the referenced literature.

• Reynolds number (for vena contraction) Re > 1e3 [Idelchik 2006, p. 222, diag. 4-15]
• Relative length of vena contraction (L/d_hyd_0) > 0.015 [Idelchik 2006, p. 222, diag. 4-15]
• Darcy friction factor lambda_FRI = 0.02 [Idelchik 2006, p. 222, sec. 4-15]

#### Geometry #### Calculation

The pressure loss dp for a thick edged orifice is determined by:

```    dp = zeta_TOT * (rho/2) * (velocity_1)^2
```

with

 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]
```

with

 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) .
```

#### Verification

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)]: #### References

Elmqvist,H., M.Otter and S.E. Cellier:
Inline integration: A new mixed symbolic / numeric approach for solving differential-algebraic equation systems.. In Proceedings of European Simulation MultiConference, Praque, 1995.
Idelchik,I.E.:
Handbook of hydraulic resistance. Jaico Publishing House,Mumbai, 3rd edition, 2006.