ColebrookWhitevergelijking

The Colebrook-White equation, named for Colebrook and White, is an implicit relationship used to determine the Darcy-Weisbach friction factor f for steady, fully developed turbulent flow in a circular pipe. It is widely used in engineering to estimate pressure losses and flow behavior in piping systems.

The equation is typically written as 1/√f = -2 log10( ε/(3.7D) + 2.51/(Re √f) ), where Re is the Reynolds number, ε is the absolute roughness of the pipe inner surface, and D is the pipe diameter. Because f appears inside the square root and inside the logarithm, the equation is implicit in f and usually requires an iterative method or numerical solving to obtain a value of f for given Re and ε/D.

Applications of the Colebrook-White equation include its use in the Moody diagram, which provides friction factor values across a range of Reynolds numbers and relative roughness. It is applicable to turbulent flow in circular pipes and bridges smooth and rough regimes, though it is most reliable for fully developed flow in ducts with conventional conditions. The equation is not explicit in f, which can necessitate repeated computation, especially in design optimization.

Several explicit approximations exist to avoid iteration, such as the Swamee-Jain formula: f = 0.25 / [ log10( ε/(3.7D) + 5.74/Re^0.9 ) ]^2. Despite its implicit form, the Colebrook-White equation remains a standard reference for predicting head loss in turbulent pipe flow.