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LaTeX Math Inline
body{\rm Re}

Reynolds number of a pipe 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):

LaTeX Math Block
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f = 0.25 \, \left[ \log \left( \frac{\epsilon / d}{3.7065} - \frac{5.0272}{\rm Re} \log \Lambda \right)   \right]^{-2}

where 

LaTeX Math Inline
body\Lambda
 –  is dimensionless parameter:

LaTeX Math Block
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\Lambda = \frac{(\epsilon/d)}{3.827} - \frac{4.657}{\rm Re} \log \Bigg[  \bigg( \frac{\epsilon/d}{7.7918} \bigg)^{0.9924} + \bigg( \frac{5.3326}{208.815+Re} \bigg)^{0.9345} \Bigg]

See also

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