Colebrook equation

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The Colebrook Equation is an implicit equation which combines experimental results of studies of laminar and turbulent flow in pipes. It was developed in 1939 by C. F. Colebrook.

It is defined as:

$\frac{1}{\sqrt{f}}=-2.0 \log \left( \frac { \varepsilon/D} {3.7} + \frac {2.51} {\mathrm{Re} \sqrt{f}} \right)$

where:

$f$ is the Darcy friction factor
$\varepsilon/D$ is the relative roughness
$Re$ is the Reynold's Number

Due to the implicit nature of the Colebrook equation, determination of a friction factor requires some iteration or a numerical solving method. Therefore, an approximate explicit relation for $f$ was determined by S. E. Haaland in 1983.

This equation is known as the Haaland equation, and is defined as:

$\frac{1}{\sqrt {f}} = -1.8 \log \left[ \frac{6.9}{\mathrm{Re}} + \left( \frac{\varepsilon/D}{3.7} \right)^{1.11} \right]$