Centrifugal Pump Power Calculator
Calculate centrifugal pump hydraulic power, shaft power, efficiency, and NPSH.
Find flow rate, head, specific speed, and motor sizing for pump selection.
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.