# Check Valve (2P)

Check valve in a two-phase fluid network

Since R2021a

Libraries:
Simscape / Fluids / Two-Phase Fluid / Valves & Orifices / Directional Control Valves

## Description

The Check Valve (2P) block models a directional control check valve in a two-phase fluid network. The valve maintains the fluid pressure by opening above a specified pressure and allowing flow from port A to port B, but not in the reverse direction. The pressure differential that opens the valve is specified in the Opening pressure specification parameter. This value can be either the pressure difference between ports A and B or the gauge pressure at port A.

The Modeling option parameter controls the parameterization options for a valve designed for modeling either vapor or liquid, but does not impact the fluid properties. The block calculates fluid properties inside the valve from inlet conditions. There is no heat exchange between the fluid and the environment, and therefore phase change inside the orifice only occurs due to a pressure drop or a propagated phase change from another part of the model.

### Directional Control

The valve opens when the pressure in the valve, pcontrol, exceeds the cracking pressure, pcrack. The valve is fully open when the control pressure reaches the valve maximum pressure, pmax. For linear parameterizations, block calculates the opening fraction of the valve, λ, as

`$\lambda =\left(1-{f}_{leak}\right)\frac{\left({p}_{control}-{p}_{crack}\right)}{\left({p}_{\mathrm{max}}-{p}_{crack}\right)}+{f}_{leak},$`

where:

• fleak is the value of the Leakage flow fraction parameter.

• pcontrol is the control pressure, which depends on the value of the Opening pressure specification parameter.

When you set Opening pressure specification to `Pressure differential`, the control pressure is pA ̶ pB.

When you set Opening pressure specification to `Gauge pressure at port A`, the control pressure is the difference between the pressure at port A and atmospheric pressure.

The cracking pressure and maximum pressure are specified as either a differential value or a gauge value, depending on the setting of the Opening pressure specification. If the control pressure exceeds the maximum pressure, the valve opening fraction is 1.

### Liquid Valve

When Modeling option is ```Liquid operating condition```, the block parameterizations depend on the value of the Valve parameterization parameter. The block calculates the pressure loss and pressure recovery in the same way for all liquid parameterization options.

The critical pressure difference, Δpcrit, is the pressure differential where the flow transitions between laminar and turbulent flow. For all liquid parameterizations, Δpcrit is

`$\Delta {p}_{crit}=\frac{\left({p}_{A}+{p}_{B}\right)}{2}\left(1-{B}_{lam}\right),$`

where:

• pA and pB are the pressure at port A and B, respectively.

• Blam is the value of the Laminar flow pressure ratio parameter.

The block accounts for pressure loss by using the ratio of the pressure loss across the whole valve to the pressure drop immediately across the valve restriction area. This ratio, PRloss, is

`$P{R}_{loss}=\frac{\sqrt{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\frac{{A}_{valve}}{{A}_{port}}}{\sqrt{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\frac{{A}_{valve}}{{A}_{port}}},$`

where:

• Aport is the value of the Cross-sectional area at ports A and B parameter.

• Cd is the value of the Discharge coefficient parameter.

• Avalve is the valve area.

The pressure recovery is the positive pressure change in the valve due to an increase in area after the orifice hole. If you do not want to capture this increase in pressure, clear the Pressure recovery check box. In this case, PRloss is 1, which reduces the model complexity. Clear this setting if the orifice hole is quite small relative to the port area or if the next downstream component is close to the block and any jet does not have room to dissipate.

Linear - Nominal Mass Flow Rate vs. Pressure Parameterization

When you set Valve Parameterization to ```Nominal Mass Flow Rate vs. pressure```, the mass flow rate through the valve is

`$\stackrel{˙}{m}=\lambda {\stackrel{˙}{m}}_{nom}\left[\sqrt{\frac{{v}_{nom}}{2\Delta {p}_{nom}}}\right]\sqrt{\frac{2}{{v}_{in}}}\frac{\Delta p}{{\left(\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right)}^{0.25}},$`

where:

• Δp is the pressure drop over the valve, pA ̶ pB.

• ${\stackrel{˙}{m}}_{nom}$ is the value of the Nominal mass flow rate at maximum valve opening parameter.

• Δpnom is the value of the Nominal pressure drop rate at maximum valve opening parameter.

• vnom is the nominal inlet specific volume. The block determines this value from the tabulated fluid properties data based on the Nominal inlet specific enthalpy and Nominal inlet pressure parameters.

• vin is the inlet specific volume.

Linear - Area vs. Pressure Parameterization

When you set Valve parameterization to `Linear - Area vs. Pressure Parameterization`, the valve area is

`${\text{A}}_{valve}=\lambda {A}_{max},$`

where Amax is the value of the Maximum valve area parameter.

The mass flow rate is

`$\stackrel{˙}{m}=\frac{{C}_{d}{A}_{valve}\sqrt{\frac{2}{{v}_{in}}}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\right)}}\frac{\Delta p}{{\left[\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right]}^{1/4}}.$`

When the valve is in a near-open or near-closed position, you can maintain numerical robustness in your simulation by adjusting the parameter. If the parameter is nonzero, the block smoothly saturates the opening area between Aleak and Amax, where Aleak = fleakAmax. For more information, see Numerical Smoothing.

Tabulated Data - Area vs. Pressure Parameterization

When you set Valve Parameterization to `Tabulated data - Area vs. pressure`, the block interpolates the valve area from the Valve area vector and Opening pressure differential vector or Opening pressure (gauge) vector parameters.

The block uses the same equation as the ```Linear - Area vs. pressure``` setting to calculate the volumetric flow rate.

Fluid Specific Volume Dynamics

For all parameterizations, the block calculates the fluid specific volume during simulation based on the liquid state.

If the fluid at the valve inlet is a liquid-vapor mixture, the block calculates the specific volume as

`${v}_{in}=\left(1-{x}_{dyn}\right){v}_{liq}+{x}_{dyn}{v}_{vap},$`

where:

• xdyn is the inlet vapor quality. The block applies a first-order lag to the inlet vapor quality of the mixture.

• vliq is the liquid specific volume of the fluid.

• vvap is the vapor specific volume of the fluid.

If the inlet fluid is liquid or vapor, vin is the respective liquid or vapor specific volume.

If the inlet vapor quality is a liquid-vapor mixture, the block applies a first-order time lag,

`$\frac{d{x}_{dyn}}{dt}=\frac{{x}_{in}-{x}_{dyn}}{\tau },$`

where:

• xdyn is the dynamic vapor quality.

• xin is the current inlet vapor quality.

• τ is the value of the Inlet phase change time constant parameter.

If the inlet fluid is a subcooled liquid, xin = 0. If the inlet fluid is a superheated vapor, xin = 1.

### Vapor Valve

When Modeling option is ```Vapor operating condition```, the block behavior depends on the Valve parameterization and Opening characteristic parameters.

The flow rate in the valve depends on the parameter:

• `Linear` — The block scales the measure of flow capacity by λ to account for the valve opening area.

• `Tabulated` — The block interpolates the measure of flow capacity from either the Cv flow coefficient vector, Kv flow coefficient vector, or Orifice area vector parameters. This function uses a one-dimensional lookup table.

Cv Flow Coefficient Parameterization

When you set Valve parametrization to ```Cv flow coefficient```, the mass flow rate is

`$\stackrel{˙}{m}={C}_{v}{N}_{6}Y\sqrt{\frac{\left({p}_{in}-{p}_{out}\right)}{{v}_{in}}},$`

where:

• Cv is the flow coefficient.

• N6 is a constant equal to 27.3 when mass flow rate is in kg/hr, pressure is in bar, and density is in kg/m3.

• Y is the expansion factor.

• pin is the inlet pressure.

• pout is the outlet pressure.

• vin is the inlet specific volume.

The expansion factor is

`$Y=1-\frac{{p}_{in}-{p}_{out}}{3{p}_{in}{F}_{\gamma }{x}_{T}},$`

where:

• Fγ is the ratio of the isentropic exponent to 1.4.

• xT is the value of the xT pressure differential ratio factor at choked flow parameter.

The block smoothly transitions to a linearized form of the equation when the pressure ratio, ${p}_{out}/{p}_{in}$, rises above the value of the Laminar flow pressure ratio parameter, Blam,

`$\stackrel{˙}{m}={C}_{v}{N}_{6}{Y}_{lam}\sqrt{\frac{1}{{p}_{avg}\left(1-{B}_{lam}\right){v}_{avg}}}\left({p}_{in}-{p}_{out}\right),$`

where:

`${Y}_{lam}=1-\frac{1-{B}_{lam}}{3{F}_{\gamma }{x}_{T}}.$`

When the pressure ratio, ${p}_{out}/{p}_{in}$, falls below $1-{F}_{\gamma }{x}_{T}$, the valve becomes choked and the block uses the equation

`$\stackrel{˙}{m}=\frac{2}{3}{C}_{v}{N}_{6}\sqrt{\frac{{F}_{\gamma }{x}_{T}{p}_{in}}{{v}_{in}}}.$`
Kv Flow Coefficient Parameterization

When you set Valve parametrization to ```Kv flow coefficient```, the block uses the same equations as the `Cv flow coefficient` parametrization, but replaces Cv with Kv using the relation ${K}_{v}=0.865{C}_{v}$.

Valve Area Parameterization

When you set Valve parametrization to ```Orifice area```, the mass flow rate is

`$\stackrel{˙}{m}={C}_{d}{A}_{valve}\sqrt{\frac{2\gamma }{\gamma -1}{p}_{in}\frac{1}{{v}_{in}}{\left(\frac{{p}_{out}}{{p}_{in}}\right)}^{\frac{2}{\gamma }}\left[\frac{1-{\left(\frac{{p}_{out}}{{p}_{in}}\right)}^{\frac{\gamma -1}{\gamma }}}{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}{\left(\frac{{p}_{out}}{{p}_{in}}\right)}^{\frac{2}{\gamma }}}\right]},$`

where:

• γ is the isentropic exponent.

The block smoothly transitions to a linearized form of the equation when the pressure ratio, ${p}_{out}/{p}_{in}$, rises above the value of the Laminar flow pressure ratio parameter, Blam,

`$\stackrel{˙}{m}={C}_{d}{A}_{valve}\sqrt{\frac{2\gamma }{\gamma -1}{p}_{avg}^{\frac{2-\gamma }{\gamma }}\frac{1}{{v}_{avg}}{B}_{lam}^{\frac{2}{\gamma }}\left[\frac{1-\text{\hspace{0.17em}}{B}_{lam}^{\frac{\gamma -1}{\gamma }}}{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}{B}_{lam}^{\frac{2}{\gamma }}}\right]}\left(\frac{{p}_{in}^{\frac{\gamma -1}{\gamma }}-{p}_{out}^{\frac{\gamma -1}{\gamma }}}{1-{B}_{lam}^{\frac{\gamma -1}{\gamma }}}\right).$`

When the pressure ratio, ${p}_{out}/{p}_{in}$, falls below${\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma }{\gamma -1}}$ , the valve becomes choked and the block uses the equation

`$\stackrel{˙}{m}={C}_{d}{A}_{valve}\sqrt{\frac{2\gamma }{\gamma +1}{p}_{in}\frac{1}{{v}_{in}}\frac{1}{{\left(\frac{\gamma +1}{2}\right)}^{\frac{2}{\gamma -1}}-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}}}.$`

### Mass Balance

Mass is conserved in the valve,

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0,$`

where:

• ${\stackrel{˙}{m}}_{A}$ is the mass flow rate at port A.

• ${\stackrel{˙}{m}}_{B}$ is the mass flow rate at port B.

### Energy Balance

Energy is conserved in the valve,

`${\Phi }_{A}+{\Phi }_{B}=0,$`

where:

• ΦA is the energy flow at port A.

• ΦB is the energy flow at port B.

### Assumptions and Limitations

• There is no heat exchange between the valve and the environment.

• When Modeling option is ```Liquid operating condition```, the results may not be accurate outside of the subcooled liquid region. When Modeling option is ```Vapor operating condition```, the results may not be accurate outside of the superheated vapor region. To model a valve in a liquid-vapor mixture, set Modeling option to ```Liquid operating condition```.

## Ports

### Conserving

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Two-phase fluid conserving port associated with the fluid entry port.

Two-phase fluid conserving port associated with the fluid exit port.

## Parameters

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Modeling option for the fluid phase at the valve. Set this parameter to `Liquid operating condition` if the two-phase fluid at the block location is in a liquid state. Set this parameter to `Vapor operating condition` if the two-phase fluid at the block location is in a vapor state.

### Parameters

Method the block uses to calculate the mass flow rate from the pressure difference across the valve or the pressure difference from the mass flow rate.

When Modeling option is ```Liquid operating condition```, the choices for this parameter are:

• ```Linear - Area vs. pressure```

• ```Linear - Nominal mass flow rate vs. pressure```

• ```Tabulated data - Area vs. pressure```

When Modeling option is ```Vapor operating condition```, the choices for this parameter are:

• `Cv flow coefficient`

• `Kv flow coefficient`

• `Orifice area`

Control pressure specification:

• When this parameter is ```Pressure differential```, the valve opens when pA ̶ pB exceeds the Cracking pressure differential.

• When this parameter is ```Gauge pressure at port A```, the valve opens when pA ̶ patm exceeds the Cracking pressure (gauge).

Valve pressure threshold. When the control pressure, pA ̶ patm, exceeds the opening pressure, the valve begins to open.

#### Dependencies

To enable this parameter, set Opening pressure specification to ```Gauge pressure at port A``` and either:

• Modeling option to ```Liquid operating condition``` and Valve parameterization to ```Linear - Area vs. pressure``` or ```Linear - Nominal mass flow rate vs. pressure```.

• Modeling option to `Vapor operating condition` and Opening characteristic to `Linear`.

Valve operational pressure at which the valve is fully open. The valve begins to open at the cracking pressure value, and is fully open at pmax.

#### Dependencies

To enable this parameter, set Opening pressure specification to ```Gauge pressure at port A``` and either:

• Modeling option to ```Liquid operating condition``` and Valve parameterization to ```Linear - Area vs. pressure``` or ```Linear - Nominal mass flow rate vs. pressure```.

• Modeling option to `Vapor operating condition` and Opening characteristic to `Linear`.

Valve pressure threshold. When the control pressure, pA ̶ pB, exceeds the opening pressure, the valve begins to open.

#### Dependencies

To enable this parameter, set Opening pressure specification to ```Pressure differential``` and either:

• Modeling option to ```Liquid operating condition``` and Valve parameterization to ```Linear - Area vs. pressure``` or ```Linear - Nominal mass flow rate vs. pressure```.

• Modeling option to `Vapor operating condition` and Opening characteristic to `Linear`.

Maximum valve operational pressure. The valve begins to open at the cracking pressure value, and is fully open at pmax.

#### Dependencies

To enable this parameter, set Opening pressure specification to ```Pressure differential``` and either:

• Modeling option to ```Liquid operating condition``` and Valve parameterization to ```Linear - Area vs. pressure``` or ```Linear - Nominal mass flow rate vs. pressure```.

• Modeling option to `Vapor operating condition` and Opening characteristic to `Linear`.

Mass flow rate through a fully open valve under typical, design, or rated conditions.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition` and Valve parameterization to ```Linear - Nominal mass flow rate vs. pressure```.

Pressure drop over a fully open valve under typical, design, or rated conditions.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition` and Valve parameterization to ```Linear - Nominal mass flow rate vs. pressure```.

Method of determining the inlet fluid state. The block determines the orifice nominal inlet specific volume from the tabulated fluid properties data based on the value of the Nominal inlet pressure parameter and the setting of the Nominal inlet condition specification parameter.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition` and Valve parameterization to ```Linear - Nominal mass flow rate vs. pressure```.

Inlet pressure in nominal conditions. The block determines the inlet specific volume from the tabulated fluid properties data based on the value of the Nominal inlet pressure parameter and the setting of the Nominal inlet condition specification parameter.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition` and Valve parameterization to ```Linear - Nominal mass flow rate vs. pressure```.

Inlet fluid temperature in nominal operating conditions.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition`, Valve parameterization to ```Linear - Nominal mass flow rate vs. pressure```, and Nominal inlet condition specification to `Temperature`.

Inlet mixture vapor quality by mass fraction in nominal operating conditions. A value of `0` means that the inlet fluid is subcooled liquid. A value of `1` means that the inlet fluid is superheated vapor.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition`, Valve parameterization to ```Linear - Nominal mass flow rate vs. pressure```, and Nominal inlet condition specification to ```Vapor quality```.

Inlet mixture volume fraction in nominal operating conditions. A value of `0` means that the inlet fluid is subcooled liquid. A value of `1` means that the inlet fluid is superheated vapor.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition`, Valve parameterization to ```Linear - Nominal mass flow rate vs. pressure```, and Nominal inlet condition specification to ```Vapor void fraction```.

Inlet specific enthalpy in nominal operating conditions.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition`, Valve parameterization to ```Linear - Nominal mass flow rate vs. pressure```, and Nominal inlet condition specification to ```Specific enthalpy```.

Inlet specific internal energy in nominal operating conditions.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition`, Valve parameterization to ```Linear - Nominal mass flow rate vs. pressure```, and Nominal inlet condition specification to ```Specific internal energy```.

Maximum valve area when it is fully open.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition` and Valve parameterization to `Linear – Area vs. pressure`.

Vector of pressure differential values for the tabulated parameterization of valve area. The values in this vector correspond one-to-one with the elements in the Valve area vector, Orifice area vector, Cv flow coefficient vector, or Kv flow coefficient vector parameters.

#### Dependencies

To enable this parameter, set Opening pressure specification to ```Pressure differential``` and either:

• Modeling option to ```Liquid operating condition``` and Valve parameterization to ```Tabulated data - Area vs. pressure```

• Modeling option to `Vapor operating condition` and Opening characteristic to `Tabulated`.

Vector of gauge pressure values for the tabulated parameterization of valve area. The values in this vector correspond one-to-one with the elements in the Valve area vector, Orifice area vector, Cv flow coefficient vector, or Kv flow coefficient vector parameters.

#### Dependencies

To enable this parameter, set Opening pressure specification to ```Gauge pressure at port A``` and either:

• Modeling option to ```Liquid operating condition``` and Valve parameterization to ```Tabulated data - Area vs. pressure```

• Modeling option to `Vapor operating condition` and Opening characteristic to `Tabulated`.

Vector of orifice area values for the tabulated parameterization of the valve area. The values in this vector correspond one-to-one with the elements in the Opening pressure differential vector or the Opening pressure (gauge) vector parameters.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition` and Valve parameterization to ```Tabulated data - Area vs. pressure```.

Ratio of actual flow rate to ideal flow rate. This parameter accounts for real-world losses that are not captured in the orifice equation.

#### Dependencies

To enable this parameter, set either:

• Modeling option to ```Liquid operating condition``` and Valve parameterization to ```Linear - Area vs. pressure``` or ```Tabulated data - Area vs. pressure```.

• Modeling option to `Vapor operating condition` and Valve parameterization to `Orifice area`.

Whether to account for the small rise in pressure after the pressure drop from the inlet to the orifice hole. When the fluid jet exits the orifice hole, it dissipates and expands to fill the port area, which causes this small pressure rise. The block does not model this pressure increase when you clear the Pressure recovery check box.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition` and Valve parameterization to `Linear - Area vs. pressure` or ```Tabulated data - Area vs. pressure```.

Method by which to parameterize the vapor valve for the chosen measure of flow capacity.

#### Dependencies

To enable this parameter, set Modeling option to `Vapor operating condition`.

Value of the Cv flow coefficient when the restriction area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

#### Dependencies

To enable this parameter, set Modeling option to `Vapor operating condition`, Valve parameterization to ```Cv flow coefficient```, and Opening characteristic to `Linear`.

Vector of Cv flow coefficients. Each coefficient corresponds to a value in the Opening pressure differential vector or the Opening pressure (gauge) vector parameters. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

#### Dependencies

To enable this parameter, set Modeling option to `Vapor operating condition`, Valve parameterization to ```Cv flow coefficient```, and Opening characteristic to `Tabulated`.

Value of the Kv flow coefficient when the restriction area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

#### Dependencies

To enable this parameter, set Modeling option to `Vapor operating condition`, Valve parameterization to ```Kv flow coefficient```, and Opening characteristic to `Linear`.

Vector of Kv flow coefficients. Each coefficient corresponds to a value in the Opening pressure differential vector or the Opening pressure (gauge) vector parameters. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

#### Dependencies

To enable this parameter, set Modeling option to `Vapor operating condition`, Valve parameterization to ```Kv flow coefficient```, and Opening characteristic to `Tabulated`.

Ratio between the inlet pressure, pin, and the outlet pressure, pout, defined as $\left({p}_{in}-{p}_{out}\right)/{p}_{in}$ where choking first occurs.

#### Dependencies

To enable this parameter, Modeling option to `Vapor operating condition` and Valve parameterization to ```Cv flow coefficient``` or ```Kv flow coefficient```.

Maximum valve area when the valve is fully open.

#### Dependencies

To enable this parameter, set Modeling option to `Vapor operating condition`, Valve parameterization to `Orifice area`, and Opening characteristic to `Linear`.

Vector of orifice area values for the tabulated parameterization of the vapor valve area. The values in this vector correspond one-to-one with the elements in the Opening pressure differential vector or the Opening pressure (gauge) vector parameters.

#### Dependencies

To enable this parameter, set Modeling option to `Vapor operating condition`, Valve parameterization to `Orifice area`, and Opening characteristic to `Tabulated`.

Ratio of the flow rate of the valve when it is closed to when it is open.

#### Dependencies

To enable this parameter, set either:

• Modeling option to ```Liquid operating condition``` and Valve parameterization to ```Linear - Nominal mass flow rate vs. pressure``` or ```Linear - Area vs. pressure```.

• Modeling option to `Vapor operating condition` and Opening characteristic to `Linear`.

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the valve is in near-open or near-closed positions. Set this parameter to a nonzero value less than one to increase the stability of your simulation in these regions.

#### Dependencies

To enable this parameter, set either:

• Modeling option to ```Liquid operating condition``` and Valve parameterization to ```Linear - Nominal mass flow rate vs. pressure``` or ```Linear - Area vs. pressure```.

• Modeling option to `Vapor operating condition` and Opening characteristic to `Linear`.

Time lag for liquid-vapor mixtures in computing the fluid specific volume.

#### Dependencies

To enable this parameter, set Modeling option to `Liquid operating condition`.

Ratio of the valve outlet pressure to valve inlet pressure at which the fluid transitions between the laminar and turbulent regimes. The pressure loss corresponds to the mass flow rate linearly in laminar flows and quadratically in turbulent flows.

Area of the ports A and B.

## References

[1] ISO 6358-3. "Pneumatic fluid power – Determination of flow-rate characteristics of components using compressible fluids – Part 3: Method for calculating steady-state flow rate characteristics of systems". 2014.

[2] IEC 60534-2-3. "Industrial-process control valves – Part 2-3: Flow capacity – Test procedures". 2015.

[3] ANSI/ISA-75.01.01. "Industrial-Process Control Valves – Part 2-1: Flow capacity – Sizing equations for fluid flow underinstalled conditions". 2012.

[4] P. Beater. Pneumatic Drives. Springer-Verlag Berlin Heidelberg. 2007.

## Version History

Introduced in R2021a

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