ColebrookWhite

ColebrookWhite refers to the Colebrook–White equation, an empirical relation used in fluid dynamics to determine the Darcy–Weisbach friction factor for turbulent flow in pipes. The equation was developed by Cyril F. Colebrook and White and introduced in 1937. It expresses the Darcy friction factor f implicitly as a function of the Reynolds number Re and the relative roughness ε/D of the pipe.

The standard form of the equation is 1/√f = -2 log10( (ε/D)/3.7 + 2.51/(Re√f) ). In this expression, f is the Darcy–Weisbach friction factor, Re is the Reynolds number, and ε/D is the pipe roughness ratio. Because f appears on both sides of the equation, it must be solved iteratively for a given Re and ε/D. In practice, engineers use iterative methods or employ explicit approximations such as Haaland, Swamee–Jain, or rely on the Moody chart for quick estimates.

Applications of the ColebrookWhite equation include the design and analysis of pipe systems in water supply, wastewater, and oil and gas industries, where accurate head loss calculations are needed. It is central to predicting pressure drop and confirming pump and piping performance under turbulent conditions.

Limitations include its applicability only to steady, fully developed turbulent flow in circular pipes with constant roughness. It is not valid for laminar flow (low Re), non-circular ducts, non-Newtonian fluids, or highly variable conditions, though variant correlations exist for some of these cases. The equation remains a foundational tool in fluid mechanics and civil/mechanical engineering.