dp_laminar

Information

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.

Restriction

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]

Geometry

pic_straightPipe

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 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.

Verification

The Darcy friction factor lambda_FRI in dependence of Reynolds number is shown in the figure below.

fig_straightPipe_laminar_lambdavsRe_ver

The pressure loss dp for the laminar regime in dependence of the mass flow rate of water is shown in the figure below.

fig_straightPipe_dp_laminar_DPvsMFLOW

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.

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.
VDI:
VDI - Wärmeatlas: Berechnungsblätter für den Wärmeübergang. Springer Verlag, 9th edition, 2002.