Method
Hydraulic power from density, gravity, flow and total dynamic head, adjusted by pump and motor efficiencies.
Equations
Ph = ρ · g · V̇ · H1000
Ps = Phηp
Pin = Psηm
Symbols and units
| Symbol | Quantity | Unit |
|---|---|---|
| Inputs | ||
| V̇ | Flow | m³/s |
| H | Total dynamic head | m |
| ρ | Fluid density | kg/m³ |
| g | Gravity (blank = 9.80665) | m/s² |
| ηp | Pump efficiency | 0–1 |
| ηm | Motor efficiency | 0–1 |
| Results | ||
| Ph | Hydraulic power | kW |
| Ps | Pump shaft power | kW |
| Pin | Motor input power | kW |
Assumptions and limits
- Gravity defaults only to physical constant 9.80665 m/s².
- Density and efficiencies are explicit inputs.
In practice
- Take the pump efficiency at the duty point from the pump curve. The total head comes from the pump-head note.
Worked example
The input values are the calculator's own verification test, run through the calculator. They show the working; they are not design values.
Inputs
| V̇ | Flow | 0.01 m³/s |
| H | Total dynamic head | 30 m |
| ρ | Fluid density | 1,000 kg/m³ |
| g | Gravity (blank = 9.80665) | 9.80665 m/s² |
| ηp | Pump efficiency | 0.75 0–1 |
| ηm | Motor efficiency | 0.9 0–1 |
Results
| Ph | Hydraulic power | 2.942 kW |
| Ps | Pump shaft power | 3.92266 kW |
| Pin | Motor input power | 4.35851 kW |
A preliminary check for engineer review, not an engineering approval. The project calculation to the applicable codes, authority requirements and specification governs.