Atkinson friction factor

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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 {\displaystyle 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

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

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

k = 1 2 ρ λ 4 , {\displaystyle k={\frac {1}{2}}\rho {\frac {\lambda }{4}},}

in which  λ {\displaystyle \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

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* Atkinson resistance

## References

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

## Further reading

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* 1999 paper giving the derivation of  k {\displaystyle 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