Darcy friction factor

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The Darcy-Weisbach friction factor is a dimensionless number used in internal flow calculations. It expresses the linear relationship between mean flow velocity and pressure gradient.

It is defined as:

$f = \frac{(\frac{-d p*}{d x}) D_h}{\frac{1}{2} \rho V^2}$

where:

$\frac{-d p*}{d x}$ is the pressure drop per unit length

$D h$ is the hydraulic diameter

ρ is the fluid density

V is the bulk velocity

The factor is named after French engineer Henry Darcy and German engineer Julies Weisbach.

It may be evaluated for given conditions by the use of various empirical or theoretical correlations, or it may be obtained from published charts. These charts are often referred to as Moody diagrams, after L. F. Moody, and hence the factor itself is sometimes called the Moody friction factor. Also sometimes called a Blasius friction factor, after the approximate equation he proposed.

The Darcy-Weisbach friction factor is 4 times larger than the Fanning friction factor, so attention must be paid to note which one of these is meant in the "friction factor" chart or equation consulted. Of the two, the Darcy-Weisbach factor is more commonly used by those following American usage.