The formula for fan air power expresses how much useful power is carried by the moving air stream, before motor and mechanical losses are considered. In its simplest form, air power is the product of airflow and pressure rise across the fan. In symbols, this is often written as P = Q × ΔP, where P is power, Q is volume flow rate and ΔP is the fan total pressure.
In SI units, if airflow Q is in cubic metres per second (m³/s) and pressure ΔP is in pascals (Pa), then the air power P is obtained in watts (W):
P (W) = Q (m³/s) × ΔP (Pa)
For example, a fan delivering 5 m³/s against a total pressure of 800 Pa has an air power of 5 × 800 = 4,000 W, or 4 kW of useful air power.
In Imperial units, airflow is often given in CFM and pressure in inches of water gauge. In that case, you must apply a conversion factor. A commonly used approximate formula for air power in horsepower (hp) is:
P (hp) = (Q (CFM) × ΔP (in.wg)) / 6,356
This factor combines unit conversions and assumes standard air density. More detailed formulas include explicit density terms, which become important when dealing with high temperatures or high-altitude mines where air density differs significantly from standard conditions.
It is important to distinguish between air power and shaft or motor power. The motor must supply more power than the air power because of losses in the fan and drive system. The ratio of air power to shaft power is the fan efficiency. For instance, if a fan has an air power of 4 kW and a shaft input power of 5 kW, its efficiency at that duty point is 4/5 = 80 %. The electrical input to the motor will be higher again, depending on motor efficiency.
In industrial and mining ventilation design, calculating air power helps you understand how much useful work the fan is doing in moving air through ducts, filters, roadways and mine workings. Comparing air power with motor power reveals whether the fan is operating near its best efficiency or wasting energy due to poor selection, incorrect duty point or system problems such as excessive resistance and leakage.
In summary, the basic formula for fan air power is P = Q × ΔP, with appropriate units and density corrections. This simple relationship underpins more advanced fan engineering calculations used when specifying mining and industrial ventilation fans.
