Pump Power and Efficiency

P = \frac{γ Q H}{η} = \frac{ρ g Q H}{η}

Water power is γQH. Brake (shaft) power is water power divided by efficiency η. H is the pump head added to the fluid (EGL rise across the pump). Watch units: Q in m³/s, H in m, γ in N/m³ → P in watts.

$P$ (W): Power
$Q$ (m³/s): Discharge
$H$ (m): Pump head
$η$: Efficiency

Step-by-step solved example

Q = 0.050 m³/s, H = 20 m, η = 0.75, γ = 9810 N/m³. Shaft power?

Pump adds head H between suction and discharge grade lines.

1. Water power
γQH = 9810×0.050×20 = 9810 W.
2. Shaft
P = 9810/0.75 = 13 080 W = 13.1 kW.
$P = 13.1 kW$

Answer: 13.1 kW

10 practice questions

0/10 correct

1.Water power equals

2.If η drops, required shaft power

3.H for a pump is the

4.Q = 0.02 m³/s, H = 10 m, η = 1, γ = 9810. P =

5.A turbine formula is the same with

6.1 horsepower is about

7.Specific speed of a pump uses

8.Cavitation risk rises when

9.Series pumps at the same Q

10.Parallel pumps at the same H