Fanning friction factor information

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:

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

^[1]^[2]

where:

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

where the dynamic pressure is given by:

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

where:

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

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 ( $2\pi RL$ for a pipe with circular cross section) and dividing by the cross-sectional flow area ( $\pi R^{2}$ for a pipe with circular cross section). Thus $\Delta P=f{\frac {2L}{R}}q=f{\frac {L}{R}}\rho u^{2}$

^ Khan, Kaleem (2015). Fluid Mechanics and Machinery. Oxford University Press India. ISBN 9780199456772. OCLC 961849291.
^ Lightfoot, Edwin N.; Stewart, Warren E. (2007). Transport phenomena. Wiley. ISBN 9780470115398. OCLC 288965242.

[1] Khan, Kaleem (2015). Fluid Mechanics and Machinery. Oxford University Press India. ISBN 9780199456772. OCLC 961849291.

[:1-2] Lightfoot, Edwin N.; Stewart, Warren E. (2007). Transport phenomena. Wiley. ISBN 9780470115398. OCLC 288965242.

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