Colebrook-White Equation

• The governing equation used to calculate the expected friction loss factor (f) used in the Darcy-Weisbach Equation. The equation is a function of pipe surface roughness, pipe diameter, fluid viscosity and fluid velocity.

• The loss of energy head, $\Delta h_F$, due to wall friction in a length of pipe between points 1 and 2 in a system is given by:

$\Delta h_F = i_FL_p$ 

The frictional head loss gradient, $i_F$, can be determined from the Colebrook-White equation, which for pipes flowing 100% full of water may be written in the form;

$i_F = ( \frac{u^2}{8gd_1} ) { \Big\{ {log_{10}} [ \frac{k_p}{3710d_1} + \frac{1.775v} {\sqrt{(gi_F {d_i}^3})} ]} \Big\}^{-2}$

NOTE: An iterative method of solution is required to find the head loss gradient, $i_F$, from equation above because this quantity also appears on the right-hand side of the equation.

References

1. ASPE Standard 45 Siphonic Roof Drainage 2007
2. BS EN 8490:2007 Guide to siphonic roof drainage systems