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Variable-Displacement Pressure-Compensated Pump

(To be removed) Hydraulic pump maintaining preset pressure at outlet by regulating its flow delivery

The Hydraulics (Isothermal) library will be removed in a future release. Use the Isothermal Liquid library instead. (since R2020a)

For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.


Pumps and Motors

  • Variable-Displacement Pressure-Compensated Pump block


The Variable-Displacement Pressure-Compensated Pump block represents a positive, variable-displacement, pressure-compensated pump of any type as a data-sheet-based model. The key parameters required to parameterize the block are the pump maximum displacement, regulation range, volumetric and total efficiencies, nominal pressure, and angular velocity. All these parameters are generally provided in the data sheets or catalogs.

The following figure shows the delivery-pressure characteristic of the pump.

The pump tries to maintain preset pressure at its outlet by adjusting its delivery flow in accordance with the system requirements. If pressure differential across the pump is less than the setting pressure, the pump outputs its maximum delivery corrected for internal leakage. After the pressure setting has been reached, the output flow is regulated to maintain preset pressure by changing the pump's displacement. The displacement can be changed from its maximum value down to zero, depending upon system flow requirements. The pressure range between the preset pressure and the maximum pressure, at which the displacement is zero, is referred to as regulation range. The smaller the range, the higher the accuracy at which preset pressure is maintained. The range size also affects the pump stability, and decreasing the range generally causes stability to decrease.

The variable-displacement, pressure-compensated pump is represented with the following equations:



D={Dmaxfor p<=psetDmaxK(ppset)for pset<p<pmax0for p>=pmax







qPump delivery
pPressure differential across the pump
pP,pTGauge pressures at the block terminals
DPump instantaneous displacement
DmaxPump maximum displacement
psetPump setting pressure
pmaxMaximum pressure, at which the pump displacement is zero
TTorque at the pump driving shaft
ωPump angular velocity
kleakLeakage coefficient
kHP Hagen-Poiseuille coefficient
ηVPump volumetric efficiency
ηmechPump mechanical efficiency
νFluid kinematic viscosity
ρFluid density
ρnomNominal fluid density
pnomPump nominal pressure
ωnomPump nominal angular velocity
νnomNominal fluid kinematic viscosity

The leakage flow is determined based on the assumption that it is linearly proportional to the pressure differential across the pump and can be computed by using the Hagen-Poiseuille formula



qleakLeakage flow
d, lGeometric parameters of the leakage path
μFluid dynamic viscosity, μ = ν.ρ

The leakage flow at p = pnom and ν = νnom can be determined from the catalog data


which provides the formula to determine the Hagen-Poiseuille coefficient


The pump mechanical efficiency is not usually available in data sheets, therefore it is determined from the total and volumetric efficiencies by assuming that the hydraulic efficiency is negligibly small


The block positive direction is from port T to port P. This means that the pump transfers fluid from T to P provided that the shaft S rotates in the positive direction. The pressure differential across the pump is determined as p=pPpT.

Basic Assumptions and Limitations

  • Fluid compressibility is neglected.

  • No loading on the pump shaft, such as inertia, friction, spring, and so on, is considered.

  • Leakage inside the pump is assumed to be linearly proportional to its pressure differential.

Dialog Box and Parameters

Maximum displacement

Pump displacement. The default value is 5e-6 m^3/rad.

Setting pressure

Pump pressure setting. The default value is 1e7 Pa.

Pressure regulation range

Pressure range required to change the pump displacement from its maximum to zero. The default value is 6e5 Pa.

Volumetric efficiency

Pump volumetric efficiency specified at nominal pressure, angular velocity, and fluid viscosity. The default value is 0.85.

Total efficiency

Pump total efficiency, which is determined as a ratio between the hydraulic power at the pump outlet and mechanical power at the driving shaft at nominal pressure, angular velocity, and fluid viscosity. The default value is 0.75.

Nominal pressure

Pressure differential across the pump, at which both the volumetric and total efficiencies are specified. The default value is 1e7 Pa.

Nominal angular velocity

Angular velocity of the driving shaft, at which both the volumetric and total efficiencies are specified. The default value is 188 rad/s.

Nominal kinematic viscosity

Working fluid kinematic viscosity, at which both the volumetric and total efficiencies are specified. The default value is 18 cSt.

Nominal fluid density

Working fluid density, at which both the volumetric and total efficiencies are specified. The default value is 900 kg/m^3.

Global Parameters

Parameter determined by the type of working fluid:

  • Fluid kinematic viscosity

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.


The block has the following ports:


Hydraulic conserving port associated with the pump suction, or inlet.


Hydraulic conserving port associated with the pump outlet.


Mechanical rotational conserving port associated with the pump driving shaft.


The Closed-Loop Actuator with Variable-Displacement Pressure-Compensated Pump example illustrates the use of the Variable-Displacement Pressure-Compensated Pump block in hydraulic systems.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2006a

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