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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:
where the dynamic pressure is given by:
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 ( for a pipe with circular cross section) and dividing by the cross-sectional flow area ( for a pipe with circular cross section). Thus
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