Fan Motor Heat Gain

When a fan motor is located within the airstream it serves, the full electrical input to the motor is added to the air as heat. The heat gain is calculated as Q = 2545 × (BHP / η), where BHP is the fan brake horsepower, η is the motor and drive efficiency as a decimal fraction of 1.0 or less, and 2545 is the conversion factor of BTU/h per horsepower (1 hp = 2,545 BTU/h). That heat gain is then converted to an air temperature rise using the sensible-heat relationship Q = 1.08 × DF × CFM × ΔT, solved for ΔT = Q / (1.08 × DF × CFM). CFM is the airflow in cubic feet per minute and DF is the altitude density factor, DF = (1 − 0.00000687 × Elevation)^5.256, which corrects the standard sea-level constant of 1.08 for reduced air density at higher elevations. Because thinner air carries less heat per unit volume, the same heat gain produces a larger temperature rise at altitude. For example, a fan requiring 10 BHP through a 90% efficient motor at sea level adds Q = 2545 × (10 / 0.9) ≈ 28,278 BTU/hr; across 8,000 CFM that is ΔT = 28,278 / (1.08 × 1.0 × 8,000) ≈ 3.3 °F of supply-air temperature rise.