How pump flow and power are calculated
A positive displacement pump pushes a fixed volume of oil per revolution. Some oil leaks back inside the pump, which the volumetric efficiency accounts for:
Q (l/min) = Vg (cm³) · n (rpm) · ηv ÷ 1,000
Phyd (kW) = p (bar) · Q (l/min) ÷ 600
Pin = Phyd ÷ ηt
M (Nm) = Pin (kW) · 9,549 ÷ n
Worked example
A gear pump with 28 cm³/rev runs at 1,500 rpm with 95 % volumetric efficiency and delivers 39.9 l/min. At 180 bar that is 12.0 kW of hydraulic power. With 85 % overall efficiency the drive must deliver 14.1 kW, so a 15 kW motor fits. The torque at the shaft is 90 Nm.
Typical efficiencies
| Pump type | Volumetric | Overall | Typical pressure |
|---|---|---|---|
| External gear pump | 85 – 95 % | 80 – 90 % | up to 250 bar |
| Vane pump | 85 – 95 % | 75 – 90 % | up to 200 bar |
| Axial piston pump | 92 – 98 % | 85 – 92 % | up to 450 bar |
Efficiency drops with low speed, low oil viscosity, high temperature and wear.
Where the lost power goes
The difference between input and hydraulic power turns into heat. A 14 kW drive with 85 % efficiency heats the oil by about 2 kW, before any losses in valves, hoses and actuators. That is why systems that run continuously need an oil cooler and a tank large enough to settle the oil.