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LaTeX Math Block
anchorf_CW
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\frac{1}{\sqrt{f}} = -2 \, \log \left( \frac{\epsilon}{3.7 \, d}  + \frac{2.51}{{\rm Re} \sqrt{f}} \right)

where

LaTeX Math Inline
body{\rm Re}

Reynolds number of a pipe fluid flow

LaTeX Math Inline
bodyd

Inner diameter of a pipe

LaTeX Math Inline
body\epsilon

inner pipe walls roughness


There are numerous explicit approximations of Colebrook–White correlation, particularly (Monzon, Romeo, Royo, 2002):

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Physics / Fluid Dynamics / Pipe Flow Dynamics / Darcy–Weisbach equation / Darcy friction factor / Darcy friction factor @model

Surface roughness ]

References

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Colebrook, C. F. 1939. “Turbulent flow in pipes, with particular reference to the transition between the smooth and rough pipe laws.” J. Inst. Civ. Eng. 11 (4): 133–156, doi.org/10.1680/ijoti.1939.13150