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 [math]\displaystyle{ k }[/math] 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

[math]\displaystyle{ k = \frac{1}{2}\rho f, }[/math]

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

[math]\displaystyle{ k = \frac{1}{2}\rho \frac{\lambda}{4}, }[/math]

in which [math]\displaystyle{ \lambda }[/math] 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

References

• 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 [math]\displaystyle{ k }[/math]
• 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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