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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]

Geometry

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.