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 formula_1 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
formula_2
in which formula_3 is the density of air in the shaft or roadway under consideration and formula_4 is Fanning friction factor (dimensionless). It is related to the Darcy friction factor by 
formula_5
in which formula_6 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.