Fanning friction factor

The Fanning friction factor, named after John Thomas Fanning, is a dimensionless number used as a local parameter in continuum mechanics calculations. It is defined as the ratio between the local shear stress and the local flow kinetic energy density:

where:

In particular the shear stress at the wall can, in turn, be related to the pressure loss by multiplying the wall shear stress by the wall area ( ${\displaystyle 2\pi RL}$ for a pipe with circular cross section) and dividing by the cross-sectional flow area ( ${\displaystyle \pi R^{2}}$ for a pipe with circular cross section). Thus ${\displaystyle \Delta P=f{\frac {L}{R}}\rho u^{2}}$

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