What is the Colebrook–White equation used for?

• A. 1/√f = −2 log10( ε/(3.7D) + 2.51/(Re √f) )
• B. 1/√f = −2 log10( ε/(3.7D) + 3.16/(Re √f) )
• C. 1/√f = −3 log10( ε/(3.7D) + 2.51/(Re √f) )
• D. 1/√f = −2 log10( ε/(4.0D) + 2.51/(Re √f) )

Answer: (A)

This equation gives the friction factor for turbulent pipe flow as a function of the Reynolds number and the pipe’s roughness. The left-hand side, 1 over the square root of f, is matched to the right-hand side, which is minus two times the base-10 log of the sum of two terms: the relative roughness ε/(3.7D) and the inertial term 2.51/(Re √f). The first term, ε/(3.7D), accounts for the roughness of the pipe surface, while the second term, 2.51/(Re √f), captures the influence of viscous effects at a given Reynolds number. The constants 3.7 and 2.51 come from experimental data and define the standard Colebrook–White form.

Because f appears inside the logarithm and also under the square root on the left, the equation is implicit in f. It’s typically solved iteratively (or with a suitable explicit approximation) to obtain the Darcy friction factor, which is then used in the Darcy–Weisbach head loss calculation. This form is the conventional expression for turbulent flow in pipes, distinguishing it from forms that alter those constants or exponents.