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) — 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 0.60–0.85 for centrifugal pumps). 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. 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. Low Ns (< 100): radial flow pumps — high head, low flow. Medium Ns (100–300): mixed flow pumps. High Ns (> 300): axial flow pumps — low head, high flow.

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 > NPSH_required by at least 0.5–1.0 m to prevent cavitation. Cavitation: vapor bubbles form and collapse — causes noise, vibration, impeller damage.

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.