- Atkinson friction factor
**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, pounds per cubic foot in

Imperial unit s). It is related to the more widespreadFanning friction factor by$k\; =\; frac\{1\}\{2\}\; ho\; f,$

in which $ho$ 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$k\; =\; frac\{1\}\{2\}\; ho\; frac\{lambda\}\{4\},$

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.

**ee also***

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

**Further reading*** [

*http://www.mvsengineering.com/admin/images/pdfs/Practical_Values_of_Friction_Factors.pdf 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

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