Mine Air Power

Pressure times volume flow is power, in any fluid. $P = pQ$ is the useful output of a mine fan: the rate at which work is being done on the air. It is a floor under the electricity bill and never the bill itself, because three efficiencies stand between it and the motor terminals.

Take them in order. The FAN converts shaft power to air power at 75 to 85 % for a well-selected axial main fan at its design point, and considerably less away from it — a fan run far off its curve can fall below 50 %, and an auxiliary fan pushing a long run of poorly hung vent bag is often worse than that. The DRIVE, if there is a belt or a gearbox, takes a few per cent. The MOTOR takes another 4 to 8 %. Multiplying air power by about 1.5 is a fair first pass for the electrical draw of a main fan installation.

The number worth carrying away is that this power goes as the cube of the airflow. Combine $P = pQ$ with $p = RQ^{2}$ and you get $P = RQ^{3}$ directly. Twenty per cent more air costs 73 % more power. Twenty per cent less air saves 49 %. That exponent is why a small, permanent improvement in ventilation efficiency is worth so much more than it looks, and why oversizing a shaft at the planning stage — a one-time capital decision — is one of the few genuinely free lunches in mine design.

Air power is also the honest way to compare two ventilation designs that deliver the same air, because it strips out the fan selection. If design A needs 400 kW of air power and design B needs 250 kW to put the same quantity in the same places, design B is better and no fan procurement decision will change that. Choosing the fan comes afterwards, and it is a separate problem with its own arithmetic.

One last distinction that trips people up. TOTAL pressure and STATIC pressure are not the same, and neither are the powers computed from them. Total pressure includes the velocity pressure the air leaves with, which in a mine exhausting up a shaft is genuinely lost to the atmosphere and in a booster arrangement is not. Fan manufacturers quote both. Use total pressure for the work the fan does on the air, static pressure for the work available to the circuit, and say which you are using.