Library / Hydraulics, open channels and fluid power / HYD-44
Hydraulics, open channels and fluid power
Actual delivery of a displacement pump
Flow delivered by a positive-displacement pump from its displacement per revolution Vd, shaft speed N in rev/min and volumetric efficiency ηv at the duty point.
- Ref
- HYD-44
- Rev
- v1
- Field
- Hydraulics, open channels and fluid power
- Result
- Q [m³/s]
Each revolution a positive-displacement pump moves a volume Vd, so the ideal flow is Vd N/60 for N in rev/min. Internal leakage makes the actual delivery smaller, by the volumetric efficiency ηv, which falls as the pressure rises and the oil thins. Q = ηv Vd N/60. It does not apply to centrifugal pumps, whose flow depends on the system curve.
Flow delivered by a positive-displacement pump from its displacement per revolution Vd, shaft speed N in rev/min and volumetric efficiency ηv at the duty point.
Calculator
- Delivered flow in litres per minute27 L/min
- Ideal flow with no leakage, Vd N/605×10−4 m³/s
- Leakage flow, (1 − ηv) Vd N/605×10−5 m³/s
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The pump delivers 4.5×10−4 m³/s (27 L/min) at 1,200 rev/min, losing 3 L/min to leakage.
- Halving the speed halves the flow, and the leakage depends on pressure, not speed, so the efficiency drops at low speed.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m³/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Vd Displacement per revolution | 1e-6 to 0.01 m³/rev | 1.8e-5 | 0.18 | 0.18 | +10% | +10 % |
| N Shaft speed | 100 to 6,000 rev/min | 3.75e-5 | 0.00225 | 0.002213 | +10% | +10 % |
| ηv Volumetric efficiency | 0.3 to 1 | 1.5e-4 | 5e-4 | 3.5e-4 | +10% | +10 % |
Sweep of Shaft speed
| Shaft speed (rev/min) | Delivered flow (m³/s) |
|---|---|
| 100 | 3.75e-5 |
| 837.5 | 3.141e-4 |
| 1,575 | 5.906e-4 |
| 2,313 | 8.672e-4 |
| 3,050 | 0.001144 |
| 3,788 | 0.00142 |
| 4,525 | 0.001697 |
| 5,263 | 0.001973 |
| 6,000 | 0.00225 |
Sweep one variable
Variables and how each one contributes
Delivered flow
What the equation gives you. Everything else feeds it.
Volumetric efficiency
The volumetric efficiency at the duty point, between 0 and 1. Raises the flow in direct proportion. Raising it by 10 % (to 0.99) moves the result by +10 %, from 4.5×10−4 to 4.95×10−4 m³/s.
Displacement per revolution
The displacement per revolution, in m³/rev. Raises the flow in direct proportion. Raising it by 10 % (to 2.75×10−5) moves the result by +10 %, from 4.5×10−4 to 4.95×10−4 m³/s.
Shaft speed
The shaft speed, in rev/min. Raises the flow in direct proportion. Raising it by 10 % (to 1,320) moves the result by +10 %, from 4.5×10−4 to 4.95×10−4 m³/s.
Worked example with the values above
- Ideal flow: Vd N/60 = 2.5×10−5 × 1,200 / 60 = 5×10−4 m³/s.
- Multiply by the efficiency 0.9.
- Q = 4.5×10−4 m³/s.
Assumptions and limits
- An incompressible fluid with no leakage, except where an efficiency is given.
- Gauge pressures and steady operation, with friction and inertia not included unless stated.
Common mistakes
- Using the piston area where the annular area is needed, or the reverse.
- Mixing rev/min and rad/s.
- Forgetting back pressure on the other side of the piston.
Statistics and uncertainty
Real actuators lose force to seal friction and flow to leakage, and oil bulk modulus drops sharply with entrained air, so the stiffness and speed here are best-case figures.
Where it is used
- Sizing hydraulic cylinders, pumps and motors.
- Estimating drive speed, stiffness and natural frequency of a hydraulic actuator.
Maths you need
- Pascal’s law: pressure acts equally in all directions in a closed fluid
- Displacement: volume moved per revolution or stroke
- Bulk modulus: B, the pressure per unit volume change of the fluid