Horsepower (Water) to BTU (IT)/second

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.

In US combustion engineering and power plant heat rate analysis, fuel energy content is natively specified in BTU (natural gas is sold per therm = 100,000 BTU). Expressing burner output in BTU/s keeps the calculation in one unit system, avoiding constant conversions. When your fuel flow is in BTU/min and your efficiency calculations use BTU, switching to watts mid-calculation just creates errors.

One BTU/s ≈ 1,055 watts — roughly a single-bar electric fire or a small hair dryer. It's a surprisingly human-scale unit. A typical US home gas furnace running at full blast produces about 28 BTU/s (100,000 BTU/h ÷ 3,600). A gas stovetop burner on high delivers about 3–5 BTU/s. So BTU/s lands right in the range where you can feel the heat on your face.

Power plant thermal engineering (heat rate analysis), industrial furnace and kiln design, jet engine combustion analysis, and rocket propulsion engineering. NASA specifications for rocket engines often include BTU/s figures. The Space Shuttle Main Engine produced about 12 million BTU/s of thermal power. Steelmaking blast furnaces operate at 50,000–200,000 BTU/s of heat input.

One BTU/s = 1.415 mechanical horsepower, or roughly 1.4 hp. This is useful in automotive and engine testing where dynamometers may report in BTU/s for thermal measurements but engineers think in horsepower. A 400 hp engine rejects about 280 BTU/s through its cooling system at full power (assuming 60% of fuel energy becomes waste heat). The conversion factor is easy to remember: multiply BTU/s by 1.4 to get hp.

The BTU originated as a water-heating energy unit, with several temperature-dependent variants. This converter uses the fixed International Table variant: 1 BTU(IT) = exactly 1,055.05585262 J. BTU-based energy and power units remain common in U.S. thermal engineering, equipment ratings and fuel-energy quantities. BTU alone measures energy; BTU per second, minute or hour measures power.