Horsepower (Water) to Terawatt

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 Sun delivers about 173,000 TW to Earth's surface. Human civilisation uses roughly 18 TW total. So we'd only need to capture 0.01% of incoming solar energy to power everything — an area of solar panels roughly 400 km × 400 km, about the size of Montana. The challenge isn't total energy availability; it's cost, storage, transmission, and the fact that sunlight is spread thin and intermittent.

Imagine 18 trillion light bulbs burning continuously, or 9 billion people each running a 2 kW heater non-stop. That 18 TW figure includes everything — electricity, transport fuel, industrial heat, cooking, heating. About 40% comes from oil, 27% from coal, 24% from gas, and the rest from nuclear and renewables. The US alone accounts for about 3 TW despite having only 4% of world population.

Replacing all 18 TW of human energy with clean sources would require roughly 60–75 TW of installed solar capacity (accounting for ~25% average capacity factor). That's about 40 times current installed solar. At 2023 installation rates of ~0.4 TW/year, it would take 150 years — but installation rates are doubling every 2–3 years. If that exponential trend holds, we could theoretically reach 60 TW of solar within 15–20 years.

Earth radiates about 47 TW of geothermal heat from its interior, driven by radioactive decay and residual primordial heat. That's 2.5× human energy consumption, but it's spread across the entire surface at extremely low density (~0.09 W/m²). Iceland, sitting atop a mantle plume, exploits geothermal for 90% of its heating. Globally, geothermal electricity capacity is only about 16 GW — a tiny fraction of what's theoretically available.

No — the terawatt scale is a very recent phenomenon. In 1800, global human power consumption was about 0.5 TW (mostly biomass burning). By 1900 it reached 1 TW with coal industrialisation. We crossed 10 TW around 1985. The jump from 1 to 18 TW in just 120 years tracks almost perfectly with global population growth times rising per-capita energy use. Pre-industrial humans used about 0.1 kW each; Americans now average 10 kW per person.