WOLFRAM SYSTEM MODELER

# Wolfram Language

In[1]:=
`SystemModel["Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.PressureLoss.StraightPipe.dp_turbulent"]`
Out[1]:=

# Information

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

Calculation of pressure loss in a straight pipe for turbulent flow regime of single-phase fluid flow only considering surface roughness.

#### Restriction

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

• circular cross sectional area
• turbulent flow regime (Reynolds number Re ≥ 4e3) [VDI-Wärmeatlas 2002, p. Lab 3, fig. 1]

#### Calculation

The pressure loss dp for straight pipes is determined by:

```dp = lambda_FRI * (L/d_hyd) * (rho/2) * velocity^2
```

with

 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 for a straight pipe in the turbulent regime can be calculated for a smooth surface (Blasius law) or a rough surface (Colebrook-White law).

Smooth surface (roughness = Modelica.Fluid.Dissipation.Utilities.Types.Roughness.Neglected) w.r.t. Blasius law in the turbulent regime according to [Idelchik 2006, p. 77, sec. 15]:

```lambda_FRI = 0.3164*Re^(-0.25)
```

with

 lambda_FRI as Darcy friction factor [-]. Re as Reynolds number [-].

Note that the Darcy friction factor lambda_FRI for smooth straight pipes in the turbulent regime is independent of the surface roughness K .

Rough surface (roughness = Modelica.Fluid.Dissipation.Utilities.Types.Roughness.Considered) w.r.t. Colebrook-White law in the turbulent regime according to [Miller 1984, p. 191, eq. 8.4]:

```lambda_FRI = 0.25/{lg[k/(3.7*d_hyd) + 5.74/(Re)^0.9]}^2
```

with

 d_hyd as hydraulic diameter [-], k= K/d_hyd as relative roughness [-], K as roughness (average height of surface asperities [m]. lambda_FRI as Darcy friction factor [-], Re as Reynolds number [-].

#### Verification

The Darcy friction factor lambda_FRI in dependence of Reynolds number for different values of relative roughness k is shown in the figure below.

Note that this pressure loss function shall not be used for the modelling outside of the turbulent flow regime at Re < 4e3 even though it could be used for that.

If the overall flow regime shall be modelled, the pressure loss function dp_overall can be used.

#### References

Idelchik,I.E.:
Handbook of hydraulic resistance. Jaico Publishing House, Mumbai, 3rd edition, 2006.
VDI:
VDI - Wärmeatlas: Berechnungsblätter für den Wärmeübergang. Springer Verlag, 9th edition, 2002.