Pump Efficiency Calculator

Pump Efficiency

Pump efficiency measures how effectively a pump converts input power to hydraulic output power. Higher efficiency means less energy waste and lower operating costs.

How to use this calculator

1. Enter the fluid density \(\rho\), flow rate \(Q\), head \(H\), and input power \(P_{in}\).
2. Make sure the units are consistent, especially for \(Q\) and \(P_{in}\).
3. Check the calculated hydraulic power, which is \(\rho g Q H\).
4. Read the efficiency \(\eta\) as a percent, which shows how much input power becomes useful output power.

The formula explained

This formula computes pump efficiency, \(\eta\), as the ratio of hydraulic output power to input power, then multiplies by \(100\%\) to express it as a percentage. The hydraulic power is found from \(\rho g Q H\).

• \(\eta\) = pump efficiency, as a percentage
• \(\rho\) = fluid density
• \(g\) = acceleration due to gravity, usually \(9.81\,\text{m/s}^2\)
• \(Q\) = volumetric flow rate
• \(H\) = pump head
• \(P_{in}\) = input power to the pump

Step by step method

1. Find the hydraulic output power using \(P_{out} = \rho g Q H\).
2. Divide \(P_{out}\) by \(P_{in}\) to get the efficiency as a decimal.
3. Multiply by \(100\%\) to convert the decimal into a percentage.

Worked example

Problem. A pump moves water with density \(\rho = 1000\,\text{kg/m}^3\) at a flow rate \(Q = 0.02\,\text{m}^3/\text{s}\) and head \(H = 15\,\text{m}\). If the input power is \(P_{in} = 4000\,\text{W}\), find the pump efficiency.

1. Compute hydraulic power: \(P_{out} = \rho g Q H = 1000 \times 9.81 \times 0.02 \times 15\).
2. So \(P_{out} = 2943\,\text{W}\).
3. Now find efficiency: \(\eta = \frac{2943}{4000} \times 100\% = 73.575\%\).

Tips and common mistakes

• Use consistent units, because mismatched units can give a wrong efficiency.
• Efficiency should usually be less than \(100\%\), so a value above that often means a unit or input error.

Frequently asked questions