Calculating the brake horsepower (BHP) of a fan means determining how much mechanical power the fan needs at its shaft to deliver a certain airflow and pressure. This is essential for sizing motors and estimating energy consumption in industrial plants and mines.
The starting point is the concept of air power, which is the rate at which useful work is done on the air. In any unit system, air power is proportional to flow multiplied by pressure. In imperial units, a common approximate relationship for total air power in horsepower is:
Air power (HP) ≈ (Q × ΔP) / 6356
where Q is airflow in CFM and ΔP is fan total pressure in inches of water gauge. The constant 6356 comes from combining unit conversions.
However, not all shaft power is converted into useful air power. Some is lost due to aerodynamic losses, mechanical friction and turbulence. The ratio of air power to shaft power is the fan efficiency (ηfan). Therefore, the brake horsepower required at the shaft is:
BHP = Air power / ηfan
Substituting the earlier expression, one widely used formula in imperial units is:
BHP ≈ (Q × ΔP) / (6356 × ηfan)
For example, suppose an industrial or mining ventilation fan must deliver 20,000 CFM at a total pressure of 4 in.wg, and the fan efficiency at this duty is 75% (0.75). The estimated BHP is:
BHP ≈ (20,000 × 4) / (6356 × 0.75) ≈ 16.8 HP
In practice, you would then select the next larger standard motor size (for example 20 HP) to provide margin.
In metric units, airflow might be in m3/s, pressure in Pa and power in kW. A similar relationship applies:
Pair (kW) ≈ (Q × ΔP) / 1000 (with density and unit corrections as required)
and then:
Pshaft (kW) = Pair / ηfan
It is important to remember that fan efficiency depends on the operating point. Using an efficiency value from the peak of the curve when the fan is actually running far away from that point will give misleading results. The most accurate BHP calculations use the manufacturer’s data for the specific airflow and pressure of interest.
In summary, to calculate fan BHP you first compute air power from airflow and pressure, and then divide by fan efficiency to obtain shaft power. This approach, using appropriate unit constants, provides a practical way to size motors and evaluate energy use for industrial and mining ventilation fans.
