Colebrook-White Equation

[1] 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.

[2] 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;

$i_F = ( \frac{u^2}{8gd_1} )$

i_"F " =(u^2/(8gd_1 )) {log_10⁡[k_p/(3710d_1 )+1.775"v" /√(gi_"F" d_i^( 3) )] }^(-2)

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