Empirical implicit correlation for Darcy friction factor f in non-smooth pipelines \epsilon > 0 which works for non-laminar ( {\rm Re} > 2,000) flow:
(1) | \frac{1}{\sqrt{f}} = -2 \, \log \left( \frac{\epsilon}{3.7 \, d} + \frac{2.51}{{\rm Re} \sqrt{f}} \right) |
where
{\rm Re} | Reynolds number of a pipe flow |
d | Inner diameter of a pipe |
\epsilon | inner pipe walls roughness |
There are numerous explicit approximations of Colebrook–White correlation, particularly (Monzon, Romeo, Royo, 2002):
(2) | f = 0.25 \, \left[ \log \left( \frac{\epsilon / d}{3.7065} - \frac{5.0272}{\rm Re} \log \Lambda \right) \right]^{-2} |
where \Lambda – is dimensionless parameter:
(3) | \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
Physics / Fluid Dynamics / Pipe Flow Dynamics / Darcy–Weisbach equation / Darcy friction factor / Darcy friction factor @model