| Symbol | Variable | SI | Imperial |
|---|---|---|---|
| P_hyd | Hydraulic (Water) Power | kW | HP |
| P_shaft | Pump Shaft Power | kW | HP |
| P_motor | Motor Input Power | kW | HP |
| Q | Volumetric Flow Rate | m³/s | GPM |
| H | Total Differential Head | m | ft |
| ρ | Fluid Density | kg/m³ | lb/ft³ |
| η_p | Pump Efficiency | % | % |
| η_m | Motor Efficiency | % | % |
| g | Gravitational Acceleration | 9.81 m/s² | 32.174 ft/s² |
- Calculates steady-state power at the specified flow rate and head — does not account for system curve variations or part-load operation
- Total head H must include all losses: static head + friction losses (pipe, fittings, valves) + velocity head differences
- Pump efficiency varies across the operating range — use the efficiency at your design operating point from the pump curve
- Motor sizing should include a service factor — select the next standard motor size above calculated shaft power × 1.15 service factor
- Does not calculate NPSH (Net Positive Suction Head) — verify NPSH available > NPSH required to prevent cavitation
- For variable speed drives (VSD), power scales approximately with the cube of speed ratio
Understanding Pump Power
Pump power calculations involve three distinct power quantities that engineers must clearly distinguish: hydraulic (water) power, pump shaft power, and motor input power. Hydraulic power is the ideal power delivered to the fluid. Shaft power accounts for pump inefficiency. Motor power accounts for both pump and motor losses. Getting this wrong leads to undersized motors, overloaded electrical circuits, or wasted energy in oversized systems.
Worked Examples
Example 1 — Municipal Water Pump Sizing
A water treatment plant pump must deliver 250 L/s against a total head of 45m (including friction and static head). Pump efficiency = 78%, motor efficiency = 93%. Size the motor.
Example 2 — Fire Pump (Imperial)
A fire protection pump must supply 750 GPM at 100 ft total head (residual pressure requirement). Pump efficiency = 70%, motor efficiency = 90%. What motor HP is required?
Example 3 — Variable Speed Drive Energy Savings
A pump currently runs at full speed (1,750 RPM) consuming 75 kW. A VSD is installed and the speed is reduced to 1,400 RPM to match actual system demand. What is the new power consumption?
Real World Applications
Common Mistakes Engineers Make
Frequently Asked Questions
Net Positive Suction Head (NPSH) is the absolute pressure at the pump suction above the vapor pressure of the liquid. NPSH Available (NPSHa) depends on your system suction piping; NPSH Required (NPSHr) comes from the pump manufacturer’s curve. If NPSHa < NPSHr, the liquid flashes to vapor at the pump impeller inlet, causing cavitation — violent bubble collapse that erodes impeller blades and reduces performance. Always maintain NPSHa at least 1.0m (3 ft) above NPSHr, with 2–3m margin for critical applications.
The pump affinity laws relate performance at different speeds (or impeller diameters): Flow scales linearly with speed (Q₂/Q₁ = N₂/N₁), head scales with the square (H₂/H₁ = (N₂/N₁)²), and power scales with the cube (P₂/P₁ = (N₂/N₁)³). The cubic power relationship is why variable speed drives are so energy-efficient — a modest speed reduction produces a large power saving. These laws are approximate and less accurate at speeds far from the rated speed.
Centrifugal pumps use a rotating impeller to add velocity to the fluid, which converts to pressure. They are best for high flow, low-to-medium head applications and have a variable flow-pressure relationship (pump curve). Positive displacement pumps (gear, piston, diaphragm) trap and displace a fixed volume per revolution — flow is nearly constant regardless of pressure. PD pumps are best for high-viscosity fluids, metering/dosing, and high-pressure low-flow applications.