Pump Power Calculation
Two power levels matter: hydraulic power (what the fluid receives) and shaft power (what the motor must deliver). The ratio is pump efficiency.
Formulas
Hydraulic Power:
P_hyd = ρ × g × Q × H
ρ = fluid density (kg/m³) — water ≈ 1000
g = 9.81 m/s²
Q = flow rate (m³/s)
H = total head (m)
Shaft Power (motor input):
P_shaft = P_hyd / η_pump
η = pump efficiency (0.5–0.85 typical)Worked Example
Water supply: Q=0.05 m³/s, H=40m, η=0.75
P_hyd = 1000 × 9.81 × 0.05 × 40 = 19,620 W ≈ 19.6 kW
P_shaft = 19.6 / 0.75 = 26.2 kW → select 30 kW motorHead Loss Sources
- Elevation head: H = Δz (m height difference)
- Pressure head: H = ΔP / (ρg)
- Friction (Darcy-Weisbach): H_f = f(L/D)(v²/2g)
- Fittings: add 10-30% extra head for bends/valves
Calculate pump power: Free Pump Power Calculator
Pump Power Formula
Hydraulic power: P_hydraulic = ρgQH, where ρ = fluid density (kg/m³), g = 9.81 m/s², Q = flow rate (m³/s), H = total head (m). Shaft power (accounting for pump efficiency η_pump): P_shaft = P_hydraulic / η_pump. Motor input power: P_motor = P_shaft / η_motor. Example: pump delivering water at Q = 0.05 m³/s against H = 30 m total head, η_pump = 0.75, η_motor = 0.92. Hydraulic power = 1000 × 9.81 × 0.05 × 30 = 14,715 W = 14.7 kW. Shaft power = 14.7/0.75 = 19.6 kW. Motor input = 19.6/0.92 = 21.3 kW.
Total Head Calculation
- Static head: Elevation difference between source and discharge (m)
- Friction head: Pressure loss due to pipe friction (calculated using Darcy-Weisbach)
- Velocity head: ½V²/g — usually small, often negligible
- Pressure head: (P_outlet - P_inlet)/ρg — if discharge pressure differs from suction
- Total head H: Sum of all above components
Frequently Asked Questions
What is pump affinity laws?
The affinity laws relate pump performance to impeller speed and diameter. For speed change: Q ∝ N, H ∝ N², P ∝ N³. Halving pump speed reduces flow by half, head by 75%, and power by 87.5%. This is why variable speed drives (VSDs) on pumps save enormous energy in systems where full flow is not always needed — reducing speed from 100% to 75% cuts power consumption to about 42% of full speed.
What is NPSH and why does it matter?
Net Positive Suction Head (NPSH) is the margin between the pressure at the pump inlet and the fluid's vapour pressure. NPSH_required (NPSHR) is a pump characteristic. NPSH_available (NPSHA) = atmospheric head + static head - friction losses - vapour pressure head. NPSHA must exceed NPSHR (usually by at least 0.5–1 m safety margin) to prevent cavitation. NPSHA decreases with: higher fluid temperature, greater suction lift, longer suction pipework.
How do I select a pump for a given application?
Plot the system curve (H vs Q, showing how required head increases with flow due to friction) and the pump curve (manufacturer's H-Q characteristic) on the same graph. The intersection is the operating point. The optimal pump operates near its Best Efficiency Point (BEP) — typically the peak of its efficiency curve. Oversized pumps operate away from BEP, consume excess energy, and suffer accelerated wear.