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Pipe, White-Colebrook

This is a straight pipe with constant section and head losses $ \Delta_1^2 F$ defined by the formula:

$\displaystyle \Delta_1^2 F = \frac{f \dot{m}^2 L}{2 g \rho^2 A^2 D},$ (15)

where f is the White-Colebrook coefficient (dimensionless), $ \dot{m}$ is the mass flux, L is the length of the pipe, g is the gravity acceleration ( $ 9.81$   m$ /$s$ ^2$), A is the cross section of the pipe and D is the diameter. The White-Colebrook coefficient satisfies the following implicit equation:

$\displaystyle \frac{1}{\sqrt{f}} = -2.03 \log \left( \frac{2.51}{\text{Re}\sqrt{f}} + \frac{k_s}{3.7 D} \right).$ (16)

Here, $ k_s$ is the diameter of the material grains at the surface of the pipe and Re is the Reynolds number defined by

Re$\displaystyle = \frac{U D}{\nu},$ (17)

where $ U$ is the liquid velocity and $ \nu$ is the kinematic viscosity. It satisfies $ \nu=\mu/\rho$ where $ \mu$ is the dynamic viscosity.

The following constants have to be specified on the line beneath the *FLUID SECTION, TYPE=PIPE WHITE-COLEBROOK card):

The length of the pipe is determined from the coordinates of its end nodes, the gravity acceleration must be specified by a gravity type *DLOAD card defined for the elements at stake. The material characteristics $ \rho$ and $ \mu$ can be defined by a *DENSITY and *FLUID CONSTANTS card. Typical values for $ k_s$ are 0.25 mm for cast iron, 0.1 mm for welded steel, 1.2 mm for concrete, 0.006 mm for copper and 0.003 mm for glass.


next up previous contents
Next: Pipe, Sudden Enlargement Up: Fluid Section Types: Liquids Previous: Pipe, Manning   Contents
guido dhondt 2007-02-18