Pump Power Calculator Formula
Understand the math behind the pump power calculator. Each variable explained with a worked example.
Formulas Used
Hydraulic Power
hydraulic_power = density * 9.81 * q_m3s * total_head / 1000Required Shaft Power
shaft_power = density * 9.81 * q_m3s * total_head / (1000 * eta)Variables
| Variable | Description | Default |
|---|---|---|
flow_rate | Flow Rate (Q)(L/s) | 20 |
total_head | Total Dynamic Head (H)(m) | 30 |
density | Fluid Density (rho)(kg/m^3) | 1000 |
efficiency | Pump Efficiency(%) | 75 |
q_m3s | Derived value= flow_rate / 1000 | calculated |
eta | Derived value= efficiency / 100 | calculated |
How It Works
Pump Power Calculation
The power a pump must supply depends on the flow rate, the head it must overcome, and pump efficiency.
Formulas
Hydraulic power = rho g Q H (useful work on the fluid)
Shaft power = rho g Q H / eta (actual input from motor)
where rho is fluid density, g = 9.81 m/s^2, Q is volumetric flow rate, H is total dynamic head, and eta is pump efficiency.
Worked Example
A pump delivers 20 L/s of water against 30 m total head at 75% efficiency.
- 01Q = 20 L/s = 0.020 m^3/s
- 02Hydraulic power = 1000 x 9.81 x 0.020 x 30 = 5886 W = 5.89 kW
- 03Shaft power = 5.89 / 0.75 = 7.85 kW
- 04Select a motor of at least 7.5 kW (next standard size up).
Frequently Asked Questions
What does total dynamic head include?
Total dynamic head = static lift (elevation difference) + friction head loss in pipes and fittings + velocity head at discharge + pressure head required at the outlet. It is the total energy per unit weight the pump must add.
What is a typical pump efficiency?
Centrifugal pumps typically operate at 60-85% efficiency at their best efficiency point (BEP). Small pumps tend toward 50-65%, large pumps 80-90%. Operating far from BEP reduces efficiency significantly.
How do I account for motor efficiency?
The electric motor also has losses. Total electrical input = shaft power / motor efficiency. Motors are typically 85-95% efficient. Specify the motor based on shaft power, and the electrical supply based on motor efficiency.
Learn More
Guide
How to Size a Pump: Flow Rate, Head, and Efficiency Calculations
Learn the step-by-step process for sizing centrifugal and positive displacement pumps. Covers flow rate requirements, total dynamic head, system curves, pump curves, NPSH, and efficiency considerations.
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