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Needle Valve

Hydraulic needle valve


Flow Control Valves


The Needle Valve block models a variable orifice created by a conical needle and a round sharp-edged orifice in thin material.

The flow rate through the valve is proportional to the valve opening and to the pressure differential across the valve. The flow rate is determined according to the following equations:





A(h)={Aleakfor h<=0π(dshsinα2cosα2)hsinα2+Aleakfor 0<h<hmaxAmax+Aleakfor h>=hmax



qFlow rate
pPressure differential
pA, pBGauge pressures at the block terminals
CDFlow discharge coefficient
A(h)Instantaneous orifice passage area
x0Initial opening
xNeedle displacement from initial position
hValve opening
hmaxMaximum needle stroke
dsOrifice diameter
αNeedle angle
ρFluid density
AleakClosed valve leakage area
AmaxMaximum valve open area
pcrMinimum pressure for turbulent flow

The minimum pressure for turbulent flow, pcr, is calculated according to the laminar transition specification method:

  • By pressure ratio — The transition from laminar to turbulent regime is defined by the following equations:

    pcr = (pavg + patm)(1 – Blam)

    pavg = (pA + pB)/2


    pavgAverage pressure between the block terminals
    patmAtmospheric pressure, 101325 Pa
    BlamPressure ratio at the transition between laminar and turbulent regimes (Laminar flow pressure ratio parameter value)

  • By Reynolds number — The transition from laminar to turbulent regime is defined by the following equations:




    DHValve instantaneous hydraulic diameter
    νFluid kinematic viscosity
    RecrCritical Reynolds number (Critical Reynolds number parameter value)

The block positive direction is from port A to port B. This means that the flow rate is positive if it flows from A to B and the pressure differential is determined as p=pApB. Positive signal at the physical signal port S opens the valve.

Basic Assumptions and Limitations

  • Fluid inertia is not taken into account.

  • The flow passage area is assumed to be equal to the frustum side surface area.


Valve orifice diameter

The diameter of the orifice of the valve. The default value is 0.005 m.

Needle cone angle

The angle of the valve conical needle. The parameter value must be in the range between 0 and 180 degrees. The default value is 90 degrees.

Initial opening

The initial opening of the valve. You can specify both positive and negative values. The default value is 0.

Flow discharge coefficient

Semi-empirical parameter for valve capacity characterization. Its value depends on the geometrical properties of the orifice, and usually is provided in textbooks or manufacturer data sheets. The default value is 0.65.

Laminar transition specification

Select how the block transitions between the laminar and turbulent regimes:

  • Pressure ratio — The transition from laminar to turbulent regime is smooth and depends on the value of the Laminar flow pressure ratio parameter. This method provides better simulation robustness.

  • Reynolds number — The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches the value specified by the Critical Reynolds number parameter.

Laminar flow pressure ratio

Pressure ratio at which the flow transitions between laminar and turbulent regimes. The default value is 0.999. This parameter is visible only if the Laminar transition specification parameter is set to Pressure ratio.

Critical Reynolds number

The maximum Reynolds number for laminar flow. The value of the parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics textbooks. The default value is 10. This parameter is visible only if the Laminar transition specification parameter is set to Reynolds number.

Leakage area

The total area of possible leaks in the completely closed valve. The main purpose of the parameter is to maintain numerical integrity of the circuit by preventing a portion of the system from getting isolated after the valve is completely closed. The parameter value must be greater than 0. The default value is 1e-12 m^2.

Global Parameters

Parameters determined by the type of working fluid:

  • Fluid density

  • 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 valve inlet.


Hydraulic conserving port associated with the valve outlet.


Physical signal port to control spool displacement.

Introduced in R2006a

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