Hydraulic pump flow rate

Technical article

Understand Hydraulic pump flow rate

This calculator finds the theoretical and actual delivery flow of a positive-displacement pump from its displacement and speed. It shows why real pumps always deliver somewhat less than the pure geometric flow because of internal leakage, and how volumetric efficiency describes that gap.

What does this quantity describe?

The theoretical flow Qth of a positive-displacement pump is the product of displacement VH – the volume the pump geometrically displaces per revolution – and speed n. Because part of the fluid leaks back to the suction side across internal clearances instead of reaching the outlet, the actual delivered flow Qreal is always lower than Qth; the ratio of the two is the volumetric efficiency ηvol.

Picture the pump as a row of measuring cups that fill and empty once per revolution: with perfectly sealed cups, flow is exactly cup volume times cycle rate. In a real pump, the piston, gear or vane clearances can never seal perfectly, so a small fraction of fluid seeps back along the pressure gradient before reaching the outlet — that is the leakage volumetric efficiency accounts for.

Formula and variables

Qth = n · VH; Qreal = Qth · ηvol

Qth = n · VH
Qreal = Qth · ηvol
ηvol = Qreal / Qth

Symbol / input	Meaning
Theoretical flow Qth	Flow computed purely from displacement and speed, without leakage.
Actual flow Qreal	Flow actually available at the pump outlet after internal leakage.
Displacement VH	Volume the pump theoretically displaces per revolution; given by the manufacturer in cm³/rev.
Drive speed n	Rotational speed of the pump shaft.
Volumetric efficiency ηvol	Share of theoretical flow actually delivered after clearance leakage; falls with rising pressure and falling viscosity.

Choose the inputs correctly

Displacement VH and speed n give the theoretical flow; adding volumetric efficiency ηvol gives the actual flow. VH is usually listed as cm³/rev on the pump datasheet; ηvol depends on load and viscosity and should ideally come from the manufacturer's performance map for the actual operating pressure rather than a blanket assumption.

How to use the calculator

Select the target quantity first. For actual flow, enter displacement, speed and volumetric efficiency. For a sizing question — such as the displacement needed for a target delivery — choose VH or n as the target and enter the desired flow as a known value.

Worked example

25 cm³/rev at 1,500 rpm gives Qth = 1,500 · 25 cm³ = 37,500 cm³/min = 37.5 L/min. With a volumetric efficiency of 92% at rated pressure, Qreal = 37.5 L/min · 0.92 = 34.5 L/min.

Understand the result and units

The 3 L/min gap between Qth and Qreal here corresponds to the amount recirculating across the pump's internal clearances. The higher the operating pressure and the lower the oil viscosity, the larger this leakage share becomes and the further ηvol falls — and it drops permanently further as a pump ages or wears.

Displacement is usually given in cubic centimetres per revolution, speed in rpm and flow in L/min; in SI units this is m³/s. ηvol is dimensionless and usually expressed as a percentage.

Fixed or variable-displacement pump?

In a fixed-displacement pump, VH is set by construction, so flow can only be changed via speed. Variable-displacement pumps — for example axial piston pumps with an adjustable swash plate — let VH change during operation, adjusting flow even at constant drive speed. That matters most for load-sensing hydraulic systems where energy efficiency is a design goal, since excess flow does not first have to be throttled away.

Typical applications

The relationship supports first-pass sizing of pump units, checking whether an existing pump can reach a required cylinder or motor speed, and condition monitoring: a measured ηvol noticeably below the datasheet value points to pump wear or damage.

Assumptions, limits and common mistakes

The model assumes volumetric efficiency stays constant at the operating point. In reality ηvol is a function of operating pressure, oil temperature/viscosity, speed and wear, and should come from the manufacturer's performance map for a robust design rather than being treated as one fixed constant across the whole operating range. Fluid compressibility and dynamic pressure spikes are not included.

Common mistake: A common mistake is carrying over a volumetric efficiency quoted for low-pressure catalog conditions unchanged into high-pressure operation, even though ηvol falls noticeably as pressure rises. Displacement is also sometimes confused with the swept volume of a single piston rather than of one full revolution — datasheets always state VH per revolution (cm³/rev).

Frequently asked questions

Why is actual flow always lower than theoretical flow?

Because a small share of oil leaks back toward the suction side across the pump's internal clearances — for example between piston and bore, or between gear flanks and housing — instead of reaching the outlet. Volumetric efficiency captures that share.

Why does volumetric efficiency fall at high pressure?

A larger pressure difference across the internal clearances drives more leakage flow even if the clearance geometry itself is unchanged, which is why datasheets usually list ηvol separately for several pressure levels.

Does it matter whether the pump is fixed- or variable-displacement?

Not for the formula itself — VH is simply entered as its currently set value. On a variable-displacement pump, VH can change during operation, whereas on a fixed-displacement pump it is constant.

Can I use this to size a pump for a target cylinder speed?

Yes: first use the cylinder speed calculator to find the required flow, then enter that value here as Qreal to find the displacement needed at a known speed.

Why does ηvol drop especially at low speed?

Leakage across the clearances depends mainly on the pressure difference and stays roughly similar at low and high speed, while theoretical flow itself is smaller at low speed — so the same leakage amount makes up a larger share of a smaller flow.