Horsepower (Water) to BTU/hour

Water HP = (Flow in GPM × Total Head in feet) / 3,960. The magic number 3,960 comes from the weight of water (8.33 lb/gal) × 33,000 ft·lbf/min per hp ÷ 8.33 × the appropriate conversions. For example: 200 GPM at 80 feet of head = 200 × 80 / 3,960 = 4.04 water hp. If the pump is 75% efficient, you need 4.04 / 0.75 = 5.39 shaft hp, so you'd select a 7.5 hp motor (next standard NEMA size up).

Because the motor must provide shaft hp, not water hp. If your application needs 3 water hp but the pump is only 65% efficient, you need 3 / 0.65 = 4.6 shaft hp — meaning a 5 hp motor minimum. Underestimating this gap leads to overloaded motors, overheating, and premature failure. Pump efficiency varies from 30% (tiny pumps) to 90% (large, well-designed centrifugal pumps), so the water-hp-to-shaft-hp gap ranges from 10% to 70%.

Water hp is the useful hydraulic output — the power actually delivered to the fluid as pressure and flow. Brake hp (bhp) is the shaft input power measured at the coupling. The ratio is pump efficiency: η = WHP / BHP. A pump rated at 10 bhp with 80% efficiency delivers 8 water hp; the other 2 hp is lost to friction, turbulence, and heat in the pump. When specifying pumps, you calculate the required water hp first, then divide by efficiency to find the necessary brake hp.

Rarely. International pump engineering uses kilowatts for both hydraulic power and shaft power. The formula becomes: Hydraulic Power (kW) = (Flow in m³/h × Head in meters × density × g) / 3,600,000. European pump catalogs list "hydraulic efficiency" as a percentage relating input kW to output kW. The concept is identical — water hp is just the US customary wrapper around it. If you see "water horsepower" in a specification, it's almost certainly an American or Canadian document.

Municipal water supply: 50–500 water hp per pump station. Oil pipeline pumping: 1,000–10,000 water hp per station. Mining dewatering: 100–5,000 water hp. Hydroelectric dam penstocks deliver thousands of water hp to turbines (in reverse — the water does the work). The largest single pump installations, like the pumps protecting New Orleans from flooding, can exceed 10,000 water hp each — moving millions of gallons per minute against levee heights.

The classic rule: 20 BTU/h per square foot. A 300 sq ft bedroom needs about 6,000 BTU/h; a 500 sq ft living room about 10,000 BTU/h. But this varies wildly with sun exposure (+10% for south-facing), ceiling height, insulation quality, number of occupants (+600 BTU per person), and climate zone. A room above a pizza oven in Phoenix needs more than a basement in Seattle. When in doubt, oversize slightly — an undersized unit runs constantly and never reaches setpoint.

Undersizing is obvious — the unit runs constantly and never reaches the thermostat setpoint on hot days. But oversizing is worse in subtle ways. An oversized AC cools the air quickly then shuts off before removing enough humidity, leaving you with a clammy 72°F house. The short cycles also wear the compressor faster (startup is the hardest moment) and waste energy. A 1-ton oversize in a humid climate like Florida can raise indoor humidity from a comfortable 45% to a muggy 60%. Proper Manual J load calculations matter more than most homeowners realize.

Exactly 12,000 BTU/h. One ton of AC is the cooling effect of melting one short ton (2,000 lbs) of ice over 24 hours. The ice absorbs 288,000 BTU of heat as it melts (2,000 lbs × 144 BTU/lb latent heat), divided by 24 hours = 12,000 BTU/h. Residential systems run 1.5–5 tons; commercial buildings 10–500 tons. The "ton" unit persists because HVAC contractors think in tons — "that house needs a 3-ton unit" is faster than "that house needs 10.5 kW of cooling."

Modern units achieve 12–25 BTU/h per watt of electricity (SEER 12–25). A SEER 20 unit removes 20 BTU/h of heat for every watt consumed — effectively a 3:1 heat pump ratio. That 12,000 BTU/h window unit draws 500–1,000 W of electricity depending on efficiency. The best mini-splits achieve SEER 30+, removing 30 BTU/h per watt, making them cheaper to run than resistive electric heaters even in heating mode.

A gas furnace's BTU/h rating is its thermal output after combustion efficiency losses (typically 80–96% of fuel input). A heat pump's BTU/h rating is the heat delivered including energy moved from outside — at COP 3, a heat pump delivering 36,000 BTU/h uses only 12,000 BTU/h worth of electricity. This makes direct BTU/h comparisons misleading: a 60,000 BTU/h furnace and a 60,000 BTU/h heat pump deliver the same heat, but the heat pump uses one-third the energy.