WOLFRAM SYSTEM MODELER

## dp_laminar |

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`SystemModel["Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.PressureLoss.StraightPipe.dp_laminar"]`

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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.

**circular cross sectional area****laminar flow regime (Reynolds number Re ≤ 2000)***[VDI-Wärmeatlas 2002, p. Lab, eq. 3]*

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** 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:

**Laminar flow regime**is restricted to a Reynolds number**Re**≤ 2000- and calculated through:
lambda_FRI = 64/Re

with

**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.

- 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, Prague, 1995.- 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.