Hydraulic Efficiency Calculator

Hydraulic and overall pump efficiency from measured head, flow, and shaft power. Hydraulic efficiency compares actual to Euler head; overall efficiency compares hydraulic power to shaft input.

Turbomachinery · Efficiency

Fluid presets — click to fill ρ

Inputs

Actual pump head Ha (m)

Measured head across the pump (outlet − inlet)

Euler (theoretical) head He (m)

From velocity triangle calculation (Euler equation) — must be > H_a

Volume flow rate Q (L/s)

Shaft (input) power Ps (kW)

Fluid density ρ (kg/m³)

Theory

Efficiency definitions:

η_h = H_a / H_E [hydraulic efficiency]

η = ρgQH_a / P_shaft [overall efficiency]

η = η_h × η_v × η_m [efficiency components]

Efficiency components:

Component	Symbol	Formula	Typical range
Hydraulic	η_h	Hₐ / Hₑ	0.85–0.95
Volumetric	η_v	Q(net) / Q(total)	0.95–0.99
Mechanical	η_m	Pₕ / Pₛ	0.95–0.99
Overall	η	ρgQHₐ / Pₛ	0.70–0.90

Where:

H_a = measured pump head (outlet − inlet pressure head) [m]
H_E = Euler head from blade kinematics — U₂Vu₂/g [m]
ΔH = H_E − H_a = hydraulic head loss inside the impeller [m]
P_h = ρgQH_a = useful hydraulic power delivered to fluid [W]
η_v accounts for internal recirculation (leakage back through wear rings)
η_m accounts for bearing friction, seal drag, disk friction

The product η_h × η_v × η_m = η defines the overall pump efficiency. A typical centrifugal pump has η = 0.75–0.88 at the BEP. Hydraulic losses dominate at off-BEP conditions (recirculation, shock losses).