Horsepower (Water) to Petawatt

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.

It's a time trick. A petawatt laser concentrates a modest amount of energy (maybe 100–500 joules) into a pulse lasting 10–100 femtoseconds. Dividing a few hundred joules by 10⁻¹⁴ seconds gives you 10¹⁵–10¹⁶ watts — surpassing the Sun's 3.8 × 10²⁶ W is still far off, but these lasers do exceed total human power consumption by 100,000×. The catch: the total energy delivered is only enough to heat a cup of coffee.

Primarily for nuclear fusion research (compressing fuel pellets), particle acceleration (laser wakefield acceleration can produce electron beams rivalling billion-dollar synchrotrons), medical isotope production, and probing extreme states of matter found in stellar cores. The ELI (Extreme Light Infrastructure) project in Europe uses petawatt lasers to recreate conditions found in supernovae, helping astrophysicists study cosmic explosions in a lab.

Solar flares can briefly release 10–100 PW of electromagnetic radiation. The Chicxulub asteroid impact (the one that killed the dinosaurs) delivered roughly 4 × 10²³ watts during the few seconds of impact — about 100 million petawatts. Gamma-ray bursts top everything at 10²⁵–10²⁶ PW, briefly outshining the entire observable universe. Even supernovae "only" sustain about 10³⁶ PW for a few seconds at peak.

Building one costs $50–500 million. Operating costs are surprisingly modest per shot — each pulse uses only a few hundred joules (less than lifting an apple one meter), but the capacitor banks and cooling systems draw megawatts of continuous power. The NIF facility costs about $350 million per year to operate. Individual shots are "cheap" in energy terms but the infrastructure to achieve them is staggering.

In theory yes, but in practice current petawatt lasers are terrible weapons. They fire one pulse every few minutes to hours, require warehouse-sized buildings of equipment, and deliver total energy equivalent to a firecracker. Military-grade laser weapons focus on sustained power (100–300 kW continuous beams), not ultrashort pulses. A petawatt laser is a precision scientific scalpel, not a blunt instrument — brilliant for physics, useless for destruction.