Colebrookyhtälö

Colebrookyhtälö, also known as the Colebrook equation, is an implicit equation used in fluid dynamics to calculate the Darcy friction factor for turbulent flow in pipes. Developed by R. M. Colebrook in 1938, it is considered a highly accurate empirical formula that accounts for both the Reynolds number and the relative roughness of the pipe.

The equation is stated as: 1/√f = -2 log₁₀(2.51/(Re√f) + ε/(3.7D)). Here, f represents the Darcy friction factor, Re is the Reynolds number, ε is the absolute roughness of the pipe's inner surface, and D is the pipe's diameter. The term ε/D represents the relative roughness.

Due to its implicit nature, the Colebrook equation cannot be solved directly for f. Instead, iterative numerical methods or graphical solutions are required to determine the friction factor. Various approximations and explicit equations, such as the Swamee-Jain equation, have been developed to provide direct solutions, although they may offer slightly less accuracy than the Colebrook equation itself.

The Colebrook equation is widely used in engineering practice for designing pipe systems, calculating pressure drop, and estimating flow rates in various industrial applications, including water supply, oil and gas transportation, and HVAC systems. Its accuracy and broad applicability have made it a cornerstone in the study of turbulent pipe flow.