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Serghide's solution

Serghide's solution is used to solve directly for the Darcy-Weisbach friction factor f for a full-flowing circular pipe. It is an approximation of the implicit Colebrook-White equation.

The solution involves calculating three intermediate values and then substituting those values into a final equation.

A = -2\log_{10}\left( {\varepsilon/D\over 3.7} + {12\over \mbox{Re}}\right)
B = -2\log_{10} \left({\varepsilon/D\over 3.7} + {2.51 A \over \mbox{Re}}\right)
C = -2\log_{10} \left({\varepsilon/D\over 3.7} + {2.51 B \over \mbox{Re}}\right)
f = \left(A - \frac{(B - A)^2}{C - 2B + A}\right)^{-2} = \left(\frac {C - 2B + A} {AC - B^2}\right)^2

where f is a function of:

  • roughness height, ε (m, ft)
  • pipe diameter, D (m, ft)
  • Reynolds number, Re (unitless).

The equation was found to match the Colebrook-White equation within 0.0031% for all practical applications.


This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Serghide's_solution". A list of authors is available in Wikipedia.
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