Fanning friction factor

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The Fanning friction factor (named after American engineer John T. 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:^[1][2]

$${\displaystyle f={\frac {\tau }{q}}}$$

where

f is the local Fanning friction factor (dimensionless);

τ is the local shear stress (units of pascals (Pa) = kg/m², or pounds per square foot (psf) = lbm/ft²);

q is the bulk dynamic pressure (Pa or psf), given by:

$${\displaystyle q={\frac {1}{2}}\rho u^{2}}$$

ρ is the density of the fluid (kg/m³ or lbm/ft³)

u is the bulk flow velocity (m/s or ft/s)

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 ${\displaystyle \Delta P=f{\frac {2L}{R}}q=f{\frac {L}{R}}\rho u^{2}}$