Centrifugal Pump Power Calculator

Hydraulic Power The power delivered to the fluid by the pump: P_hydraulic = ρ × g × Q × H Where: ρ = fluid density (kg/m³), water = 1000 kg/m³ g = gravitational acceleration (9.81 m/s²) Q = volumetric flow rate (m³/s) H = total head (m), the sum of static head, friction head, and velocity head

Shaft Power and Efficiency P_shaft = P_hydraulic / η_pump Where η_pump = pump efficiency, typically 60 to 85% for centrifugal pumps. Enter it as a percentage. Motor P_input = P_shaft / η_motor Overall efficiency η_total = η_pump × η_motor × η_transmission

Total Head Components Static head: elevation difference between source and discharge (m). Friction head: losses in pipes, fittings, valves (use Darcy-Weisbach). Velocity head: (v₂² − v₁²) / (2g), usually small enough to ignore. Pressure head: (P₂ − P₁) / (ρg), for pressurized systems.

Specific Speed (Ns) Ns = N × √Q / H^(3/4) Where N = rotational speed (rpm), Q in m³/s, H in meters. Specific speed is a shape number, not a size: it tells you what kind of impeller suits the duty, and two pumps with the same Ns have geometrically similar impellers no matter how big they are.

Watch the units here, because there are two conventions in circulation and they differ by a factor of about 51.6. The metric nq above uses Q in m³/s and H in metres. American pump curves usually print Ns with Q in US gallons per minute and H in feet, which turns an nq of 30 into an Ns of roughly 1550. If your catalogue number looks about fifty times bigger than the one here, that is why. The calculator reports both.

NPSH (Net Positive Suction Head) NPSH_available = (P_atm − P_vapor) / ρg + z_s − h_f,s Where z_s = suction lift (negative if below pump), h_f,s = suction friction losses. NPSH_available must beat NPSH_required by at least 0.5 to 1.0 m, or the pump cavitates. Cavitation is vapour bubbles forming at the impeller eye and collapsing further along the vane. It sounds like the pump is passing gravel, and over months it eats pits into the impeller.

Affinity Laws When pump speed changes from N₁ to N₂: Q₂/Q₁ = N₂/N₁ | H₂/H₁ = (N₂/N₁)² | P₂/P₁ = (N₂/N₁)³ This is why VFD (variable frequency drive) speed control saves enormous power.