Darcy Weisbach Equation

The Darcy Weisbach Equation for calculating the pipe losses is as below;

h_f=(f*l*V^2)/(2*g*D)

In the Darcy–Weisbach Equation, the friction factor f  can be calculated from the equation of Colebrook–White.

1/sqrt{lambda}=-2*log(2.51/(R_e*sqrt{lambda})+k/(2.7*D))

 where k is the absolute roughness of the pipe wall (mm), D the inner diameter of the pipe (mm) and Re the Reynolds number .

To avoid iterative calculation, Barr (1975) suggests the following acceptable approximation, which deviates from the results obtained by the Colebrook–White Equation for  1%:

 1/sqrt{lambda}=-2*log(5.1286/R^0.89_e+k/(2.7*D))

 The Reynolds number describes the flow regime. It can be calculated as:

 R_e=vD/nu

where ν (m2/s) stands for the kinematic viscosity. This parameter depends on the water temperature and can be determined from the following equation:

nu=497*10^-6/(T+42.5)^1.5

Where, T is temperature in Degree Centigrade.

Moody’s Diagram