Flow and speed
Q = V x n / 1000: 71 cm3/rev at 1500 1/min is 106.5 l/min. A pump delivers Q x eta v; a motor turns at n = Q x 1000 x eta v / V, so 80 l/min into 160 cm3/rev is 500 1/min without leakage.
Reference tool — arithmetic, not a pump or motor selection
Hydraulic displacement calculator.
Flow · speed · torque · power · displacement
Flow, torque, power.
Type a line (pump 71 cc/rev 1500 1/min 250 bar; motor 160 cm3/rev 80 l/min 210 bar; need 120 l/min at 1800 1/min) or fill in the fields: the line and the fields stay in step. The figures in the examples are examples, not typical values.
Examples:
All 130 engineering tools
Enter the displacement of a hydraulic pump or motor with its speed, flow, pressure or torque, and the calculator works out the rest: Q = V x n / 1000, T = V x delta p / (20 x pi) and P = Q x delta p / 600, with V in cm3/rev, n in 1/min, Q in l/min, delta p the pressure difference in bar, T in N·m and P in kW. Add the volumetric and hydromechanical efficiencies from the data sheet, and it gives the pump input or the motor output with losses. In reverse, it finds the displacement for a stated flow and speed, or for a stated torque and pressure. The working is shown with your numbers, and the result is a line you can copy or add to a request.
Arithmetic only: the calculator gives no typical efficiencies, displacements, pressures or speeds, and does not size hoses or pipes. The data sheet of the pump or motor maker governs.
How it is worked out
Three relations.
Torque and pressure
T = V x delta p / (20 x pi): 160 cm3/rev at 210 bar is 534.8 N·m without losses. A motor gives T x eta hm at its shaft; a pump takes T / eta hm. Turned round, delta p = T x 20 x pi / V: a 500 cm3/rev motor needs 251.3 bar for 2000 N·m.
Power
P = Q x delta p / 600: 80 l/min at 210 bar is 28 kW of hydraulic power. A pump takes P / eta total at its shaft and a motor gives P x eta total, with eta total = eta v x eta hm. You enter the efficiencies; without them the values are shown without losses.
| Unit or constant | Equals | Basis |
|---|---|---|
| 20 x pi | 62.8319 | T [N·m] = V [cm3/rev] x delta p [bar] / (20 x pi): 1 cm3 x 1 bar = 0.1 J |
| 600 | 60000 / 100 | P [kW] = Q [l/min] x delta p [bar] / 600 |
| 1 in3/rev | 16.387064 cm3/rev | 2.54 cm cubed, exact |
| 1 US gpm | 3.785411784 l/min | US gallon, 231 in3, exact |
| 1 Imp gpm | 4.54609 l/min | Imperial gallon, exact |
| 1 m3/h | 16.6667 l/min | 1000 l in 60 min |
| 1 l/s | 60 l/min | 1 l = 1 dm3 |
| 1 MPa | 10 bar | 1 bar = 100 kPa, exact |
| 1 psi | 0.0689475729 bar | pound-force per square inch |
| 1 lbf·ft | 1.3558179483 N·m | 0.45359237 kg x 9.80665 m/s2 x 0.3048 m, exact |
| 1 hp | 745.69987 W | mechanical horsepower |
| 1 PS | 735.49875 W | metric horsepower, exact |
1/min, r/min and min-1 are the same unit, and so are cm3/rev and cc. A bare gpm is read as the US gallon a minute.
Sources
The pump relations, Q = V x n x eta v / 1000, T = V x delta p / (20 x pi x eta hm) and P = Q x delta p / (600 x eta total), stand in the data sheets of the makers of external gear pumps, in the section that works out the characteristics in SI units. The motor relations, n = Q x 1000 x eta v / V, T = V x delta p x eta hm / (20 x pi) and P = Q x delta p x eta total / 600, stand in the data sheets of external gear motors and axial piston motors, in the section with the formulas. 1 in3 = 16.387064 cm3, 1 US gallon = 231 in3 = 3.785411784 l, 1 Imperial gallon = 4.54609 l, 1 psi = 0.0689475729 bar, 1 bar = 0.1 MPa, 1 lbf·ft = 1.3558179483 N·m, 1 hp = 745.69987 W and 1 PS = 735.49875 W follow appendix B of NIST SP 811 and the Wikipedia articles on the cubic inch, the gallon, the pound per square inch, the bar, the pound-foot and horsepower; the Imperial gallon also the UK Weights and Measures Act 1985. The data sheet of the pump or motor maker always comes first.
Before you work it out
Questions about displacement, flow and torque
How is the flow of a hydraulic pump worked out from its displacement?
The flow is Q = V x n x eta v / 1000, with the displacement V in cm3/rev, the speed n in 1/min, the volumetric efficiency eta v as a fraction and the flow Q in l/min. An example pump of 71 cm3/rev at 1500 1/min gives 71 x 1500 / 1000 = 106.5 l/min without leakage; with a volumetric efficiency of 0.95 entered from its data sheet, 101.2 l/min. These figures are an example, not typical values.
At what speed does a hydraulic motor turn, and what torque does it give?
The speed is n = Q x 1000 x eta v / V and the output torque T = V x delta p x eta hm / (20 x pi), with delta p the pressure difference across the motor in bar and T in N·m; 20 x pi is 62.83. An example motor of 160 cm3/rev fed with 80 l/min at 210 bar: 80 x 1000 / 160 = 500 1/min and 160 x 210 / 62.83 = 534.8 N·m without losses. The volumetric and hydromechanical efficiencies from the data sheet of the motor bring both down.
How is the power worked out?
The hydraulic power is P = Q x delta p / 600, with Q in l/min, delta p in bar and P in kW: 80 l/min at 210 bar is 28 kW. A pump takes more at its shaft, P = Q x delta p / (600 x eta total); a motor gives less, P = Q x delta p x eta total / 600. The total efficiency is the volumetric times the hydromechanical one, and the same shaft power is T x n / 9549.3.
How do I find the displacement I need?
Turn the relations round. For a flow and a speed, V = Q x 1000 / n (for a pump, divided by eta v as well): 120 l/min at 1800 1/min needs 66.67 cm3/rev without leakage. For a torque and a pressure, V = T x 20 x pi / delta p (for a motor, divided by eta hm as well): 2000 N·m at 210 bar needs 598.4 cm3/rev without losses. The sizes on offer come from the range of the maker, which the calculator does not give.
Which units does the calculator take?
Displacement in cm3/rev (also cc/rev or cc) or in3/rev (16.387064 cm3); speed in 1/min (also r/min or min-1); flow in l/min, m3/h, l/s, US gpm (3.785411784 l) or Imp gpm (4.54609 l); pressure in bar, MPa, kPa or psi (0.0689475729 bar); torque in N·m, kN·m or lbf·ft; power in kW, W, hp or PS. The efficiencies in per cent or as a fraction, each named: eta v, eta hm or eta total.
Where do the efficiencies come from?
From the data sheet of the pump or motor maker, for the pressure, speed and oil viscosity of the duty: they change with all three and with wear. The calculator gives no typical efficiencies; without them it shows the values without losses and says so. It does not size hoses or pipes either, and the data sheet of the maker governs; the line from the calculator is a starting point for a request.
A pump, a motor or a seal kit?
Send the line and the plate.
The calculator works out the arithmetic only. When a hydraulic pump or motor, its seal kit or its parts are needed, send the line from the calculator with a photograph of the plate, and Vessel Core checks the details before an offer goes back.
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