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 ${\displaystyle k}$ 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

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

in which ${\displaystyle \rho }$ is the density of air in the shaft or roadway under consideration and ${\displaystyle f}$ 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 ${\displaystyle \lambda }$ 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

• 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 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