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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.

References

• http://www.cheresources.com/colebrook2.shtml