Colebrook-White equation

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The Colebrook-White equation is used to iteratively solve for the Darcy-Weisbach friction factor f.

For Free Surface Flow:
\frac{1}{\sqrt{f}} = -2 \log (\frac{e}{12R} + \frac{2.51}{Re\sqrt{f}})
For Full Flow (Closed Conduit):
\frac{1}{\sqrt{f}} = -2 \log (\frac{e}{14.8R} + \frac{2.51}{Re\sqrt{f}})

Where f is a function of:

  • roughness height, e (m, ft)
  • hydraulic radius, R (m, ft)
  • Reynolds number Re (unitless)

Because the iterative search for the correct f value can be quite time-consuming, the Swamee-Jain equation can be used to solve directly for f.

[edit] Reference

  • 2002, Computer Applications In Hydraulic Engineering, 5th Ed., Haestad Press, pg. 16
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