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:

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

where:

• ${\displaystyle f}$ is the local Fanning friction factor (dimensionless)
• ${\displaystyle \tau }$ is the local shear stress (unit in ${\displaystyle {\frac {lb_{m}}{ft\cdot s^{2}}}}$ or ${\displaystyle {\frac {kg}{m\cdot s^{2}}}}$ or Pa)
• ${\displaystyle q}$ is the bulk dynamic pressure (unit in ${\displaystyle {\frac {lb_{m}}{ft\cdot s^{2}}}}$ or ${\displaystyle Pa}$)

where the dynamic pressure is given by:

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

where:

• ${\displaystyle \rho }$ is the density of the fluid (unit in ${\displaystyle {\frac {lb_{m}}{ft^{3}}}}$ or ${\displaystyle {\frac {kg}{m^{3}}}}$)
• ${\displaystyle u}$ is the bulk flow velocity (unit in ${\displaystyle {\frac {ft}{s}}}$ or ${\displaystyle {\frac {m}{s}}}$)

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