Hydraulic Power and Cylinder Force Formulas
Hydraulic formulas: the power from the flow and pressure, the motor power with the efficiency and the force of a cylinder from the pressure and the bore.
The formulas
| To find | Formula |
|---|---|
| Hydraulic power (kW) | P = Q × p / 600, with Q in L/min and p in bar |
| Motor power | Pm = P / η |
| Cylinder area | A = π / 4 × D² |
| Cylinder force (N) | F = p × A, with p in N/mm² (1 bar = 0.1 N/mm²) and A in mm² |
Q is the flow in litres per minute, p the pressure in bar, η the overall efficiency of the pump and drive as a fraction, and D the piston bore in millimetres. The factor 600 comes from the units: 1 L/min at 1 bar is 1/600 kW. The force is for the push stroke on the full piston area, and the pull stroke has a smaller area because of the rod. The efficiency of 0.85 and the other values are examples, so use the data sheets. The formulas ignore the friction of the seals and the pressure drop in the pipes.
Worked example: 60 L/min at 200 bar
- P = 60 × 200 / 600 = 20 kW
- Pm = 20 / 0.85 = 23.53 kW
Worked example: a 100 mm bore at 100 bar
- A = π / 4 × 100² = 7,854 mm²
- F = 10 N/mm² × 7,854 = 78.54 kN
Hydraulic power at 60 L/min
| Pressure | Hydraulic power |
|---|---|
| 50 bar | 5 kW |
| 100 bar | 10 kW |
| 150 bar | 15 kW |
| 200 bar | 20 kW |
Frequently asked questions
Where does the 600 come from?
One litre per minute is 1/60,000 m³/s and one bar is 100,000 Pa, so the product is 1.667 W, which is 1/600 kW.
Is the motor power the same as the hydraulic power?
No. The pump and the drive lose some power, so the motor must be larger by the efficiency.
Why is the pull force smaller than the push force?
The rod takes part of the area on the rod side of the piston, so the pressure acts on a smaller area.
Does the speed of the cylinder come from this?
The speed is the flow divided by the piston area, so a larger flow gives a faster stroke at the same force.
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