Atkinson friction factor is a measure of the resistance to airflow of a duct. It is widely used in the mine ventilation industry but is rarely referred to outside of it.

Atkinson friction factor is represented by the symbol k and has the same units as air density (kilograms per cubic metre in SI units, lbfmin^2/ft^4 in Imperial units). It is related to the more widespread Fanning friction factor by

\( {\displaystyle k={\frac {1}{2}}\rho f,} \)

in which \( \rho \) is the density of air in the shaft or roadway under consideration and f is Fanning friction factor (dimensionless). It is related to the Darcy friction factor by

\( {\displaystyle k={\frac {1}{2}}\rho {\frac {\lambda }{4}},} \)

in which \( \lambda \) is the Darcy friction factor (dimensionless).

It was introduced by John J Atkinson in an early mathematical treatment of mine ventilation (1862) and has been known under his name ever since.
See also

Atkinson resistance


NCB Mining Dept., Ventilation in coal mines: a handbook for colliery ventilation officers, National Coal Board 1979.

Further reading

1999 paper giving the derivation of k
Atkinson, J J, Gases met with in Coal Mines, and the general principles of Ventilation Transactions of the Manchester Geological Society, Vol. III, p.218, 1862

Physics Encyclopedia



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