# Fanning friction factor

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Fanning friction factor

The Fanning friction factor is a dimensionless number used in fluid flow calculations. It is related to the Shear stress at the wall as:

:$au = frac\left\{ f ho v^2\right\}\left\{2\right\}$

where:

*$au$ is the shear stress at the wall
*$f$ is the Fanning friction factor of the pipe
*$v$ is the fluid velocity in the pipe
*$ho$ is the density of the fluid

The wall shear stress can, in turn, be related to the pressure loss by multiplying the wall shear stress by the wall area ($2 pi R L$ for a pipe) and dividing by the cross-sectional flow area ($pi R^2$ for a pipe).

The friction head can be related to the pressure loss due to friction by dividing the pressure loss by the product of the acceleration due to gravity and the density of the fluid. Accordingly, the relationship between the friction head and the Fanning friction factor is:

:$h_f = frac\left\{ 2fv^2L\right\}\left\{g D\right\}$

where:

*$h_f$ is the friction loss (in head) of the pipe.
*$f$ is the Fanning friction factor of the pipe.
*$v$ is the fluid velocity in the pipe.
*$L$ is the length of pipe.
*$g$ is the local acceleration of gravity.
*$D$ is the pipe diameter.

Fanning friction factor formulæ

This friction factor is one-fourth of the Darcy 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 Fanning friction factor is the more commonly used by Chemical Engineers and those following the British convention.

Special cases of the Fanning friction factor are given below. Other values may be derived from the Darcy friction factor formulæ article.

f=16/Re is the friction factor for laminar flow in round tubes.

For a square channel this becomes 14.227/Re.

References

*Shah R.K. and A.L. London, 1978, 'Laminar Flow Forced Convection in Ducts', Supplement 1 in Advances in Heat Transfer, Academic, NY, 1978.
*Rohsenhow, W.M., J.P. Hartnett and E.N. Ganic, 1985, 'Handbook of Heat Transfer Fundamentals, 2nd Ed., McGraw-Hill Book Company.

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