Calculation
nth = Q/VH; nreal = nth · ηvol
Speed rises with flow and falls with larger displacement; internal leakage lowers actual speed below the theoretical value.
n = V̇/VH
Hydraulic motor speed
Speed rises with flow and falls with larger displacement; internal leakage lowers actual speed below the theoretical value.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Theoretical speed nth — Output speed computed purely from flow rate and displacement.
- Actual speed nreal — Output speed after subtracting the flow fraction lost to internal leakage.
- Supplied flow Q — Flow rate supplied to the motor.
- Displacement VH — Volume the motor theoretically requires per revolution; given by the manufacturer in cm³/rev.
- Volumetric efficiency ηvol — Share of supplied flow that actually contributes to displacement instead of leaking internally.
Example
40 L/min at 80 cm³/rev gives a theoretical speed of 500 rpm; with ηvol = 0.92 the actual speed is 460 rpm.
Assumptions and limits
Constant flow and volumetric efficiency assumed constant at the operating point; starting torque and load-dependence of leakage are not modeled separately.
Understand Hydraulic motor speed
This calculator finds the theoretical and actual output speed of a hydraulic motor from supplied flow rate and displacement. It shows why a hydraulic motor turns more slowly for a given flow the larger its displacement is, and why real speed falls below the theoretical value because of internal leakage.
What does this quantity describe?
A hydraulic motor's theoretical speed follows from the ratio of supplied flow Q to displacement VH, the volume required per revolution: nth = Q/VH. Because part of the supplied flow leaks past the displacement mechanism's internal clearances instead of actually turning the motor, real speed nreal = nth · ηvol is always lower than nth.
Displacement acts like a hydraulic gear ratio: a small displacement means little oil is needed per revolution, so the motor spins fast but with low torque at a given flow — similar to a small pinion. A large displacement is like a large gear: slower, but with more torque at the same oil pressure.
Formula and variables
nth = Q/VH; nreal = nth · ηvol
nth = Q/VHnreal = nth · ηvolηvol = nreal/nth
| Symbol / input | Meaning |
|---|---|
| Theoretical speed nth | Output speed computed purely from flow rate and displacement. |
| Actual speed nreal | Output speed after subtracting the flow fraction lost to internal leakage. |
| Supplied flow Q | Flow rate supplied to the motor. |
| Displacement VH | Volume the motor theoretically requires per revolution; given by the manufacturer in cm³/rev. |
| Volumetric efficiency ηvol | Share of supplied flow that actually contributes to displacement instead of leaking internally. |
Choose the inputs correctly
Flow Q and displacement VH give theoretical speed; adding volumetric efficiency ηvol gives actual speed. VH is listed as cm³/rev on the datasheet; ηvol depends on load and pressure and falls proportionally more at low speed, because leakage then makes up a larger share of the smaller flow.
How to use the calculator
Select the target quantity. For actual speed, enter flow, displacement and volumetric efficiency. For a sizing question — the flow needed for a target speed — choose Q or VH as the target.
Worked example
40 L/min with an 80 cm³/rev displacement gives nth = 40,000 cm³/min / 80 cm³ = 500 rpm. With ηvol = 0.92, nreal = 500 rpm · 0.92 = 460 rpm.
Understand the result and units
The 40 rpm gap between theoretical and real speed corresponds to the flow fraction lost across the motor's internal clearances instead of contributing to rotation. This leakage share becomes especially noticeable at low speed and high load and can cause rough, uneven rotation.
Flow is usually given in L/min, displacement in cm³/rev and speed in rpm; ηvol is dimensionless, usually expressed as a percentage.
Typical applications
The relationship is used to size drive motors, winches and slew drives, to choose the displacement needed for a target speed at a given pump flow, and to judge whether a motor still runs smoothly enough at low speed.
Assumptions, limits and common mistakes
The model assumes volumetric efficiency stays constant at the operating point; in reality ηvol depends on pressure, viscosity, speed and wear. Starting torque, the load-dependence of leakage at very low speeds, and dynamic rotational irregularity are not included.
Common mistake: A common mistake is equating a motor's displacement with a pump's displacement, even though both share the same unit (cm³/rev) but opposite meaning: for a motor it is the volume needed per revolution, for a pump the volume delivered per revolution. It is also easy to overlook that the relative leakage share rises at very low speeds, which can hurt smoothness of rotation.
Frequently asked questions
Why does a motor with larger displacement turn more slowly?
Because at a given flow, more time per revolution is needed to supply the larger oil volume required per turn; in exchange, a larger displacement delivers more torque at the same pressure.
Why is real speed lower than theoretical speed?
Because part of the supplied flow leaks past the displacement mechanism's internal clearances instead of contributing to rotation; volumetric efficiency captures that share.
Is a motor's displacement the same as a pump's displacement?
Same unit (cm³/rev), different meaning: for a pump it is the volume delivered per revolution, for a motor the volume required per revolution.
How are speed and torque related?
At a given hydraulic power, speed and torque trade off against each other: a motor with small displacement spins fast at low torque, one with large displacement spins slowly at high torque.
Why does a hydraulic motor often run roughly at very low speed?
Because the largely speed-independent leakage becomes a larger share of the overall small flow at low speed, which can cause uneven rotation; dedicated low-speed motors with reduced leakage tendency are often used for very low speeds.