Fan Brake Horsepower

Air power is flow times pressure rise, exactly as hydraulic power is flow times head — and the fan's efficiency turns that into shaft power. The trade constant 6356 converts cfm × inches of water gauge into horsepower (1 in w.g. is 5.202 lbf/ft², and 33 000 ft·lbf/min is 1 hp). Move 2 m³/s against 500 Pa through a 65%-efficient fan and you need 2 × 500 / 0.65 ≈ 1.54 kW at the shaft. This page evaluates Q·Δp/η in SI, so any pressure and flow units work.

Two subtleties bite. First, use fan total pressure, not static, if you want honest total efficiency — static-pressure numbers paired with total-efficiency values overstate the fan. Second, the constant assumes standard air at 1.2 kg/m³; at 5000 ft of altitude air is about 17% thinner, so a fan moving the same cfm develops proportionally less pressure and needs proportionally less power, which is why altitude derating tables exist for every rooftop unit sold.