Horsepower (British) to Horsepower (Water)

A horse can sustain about 0.7 hp over a working day, and briefly peak at 10–15 hp during a gallop or heavy pull. Watt's definition was deliberately generous — he wanted his steam engines to look good compared to the horses they replaced. A fit human can sustain about 0.1 hp and peak at ~1–2 hp briefly. So a horse is roughly 7× a human in sustained output, which aligns well with historical accounts of animal labor replacing human workers.

Because American engineering inherited the British unit directly — the US was a British colony when Watt defined horsepower in the 1780s. Both equal 550 ft·lbf/s = 33,000 ft·lbf/min = 745.7 W. The "international" horsepower adopted in 1956 formalised this same value. The only reason it's sometimes called "British" is to distinguish it from the metric horsepower (PS) used in continental Europe, which is 1.4% smaller.

Watt's own improved steam engines: 10–20 hp. Brunel's SS Great Eastern ship engines: 8,000 hp. The Rolls-Royce Merlin (WW2 Spitfire): 1,030–1,760 hp depending on variant. Concorde's Olympus 593 engines: 38,000 hp each (with reheat). The Rolls-Royce Trent XWB (A350 engine): about 97,000 hp. In 240 years, British engines went from 20 hp to 97,000 hp — a 5,000-fold increase.

Almost. "bhp" stands for "brake horsepower" — power measured at the engine output shaft using a dynamometer (historically a brake). "hp" can technically mean the gross figure including power consumed by accessories. Since 2005, European regulations require "net" power (engine with all standard accessories), so bhp and hp are effectively identical for modern cars. The "b" in bhp is mostly a British tradition to emphasize that the number is a real dynamometer measurement, not a theoretical calculation.

From 1910 to 1947, Britain taxed cars by "RAC horsepower" — a formula based on cylinder bore and number of cylinders, not actual power. This incentivised narrow-bore, long-stroke engines with terrible performance. A car rated at "10 RAC hp" might actually produce 30–40 real hp. The tax warped British car design for decades, producing underpowered engines that only made sense as tax dodges. The system was scrapped in 1947, but its legacy shaped British car culture for years after.

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.