Pump Hydraulic & Shaft Power
Water power from flow and head, and the shaft power once efficiency takes its cut.
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The engineering
Hydraulic power is the physics — lifting ρQ kilograms per second through H meters — and it doesn't negotiate. Efficiency is where the money goes: a mid-size centrifugal pump peaks around 70–85% at its best-efficiency point and falls off fast to either side, so a pump run far from BEP burns power and bearings alike.
Size the motor off *shaft* power at the worst expected operating point, then add service factor; and remember density matters — the same volumetric flow of brine (ρ ≈ 1200) costs 20% more power than water, while hydrocarbons run cheaper.
Where this math comes from
Leonhard Euler wrote the fundamental equation of turbomachinery in 1754 — how a spinning rotor exchanges energy with fluid — a century before anyone could build to it well. James Watt's horsepower (1782) is the other ancestor: defined by horses lifting water from mines, it made pumping power a commercial quantity, which is why this card still prints hp.
The centrifugal pump matured through the 1800s (John Appold's 1851 Great Exhibition demonstration of a curved-vane impeller tripled efficiency over straight blades), and the Hydraulic Institute — founded 1917 — standardized the test codes that make a vendor's η claim mean something.
- 1754Leonhard EulerEuler's turbomachine equation.
- 1782James WattHorsepower defined — pumping becomes a priced commodity.
- 1851John AppoldCurved-vane impeller shows efficiency is design, not luck.
- 1917Hydraulic InstitutePump test standards make efficiency claims comparable.
See the full timeline of the math behind every calculator →
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