# Fixed Orifice

(To be removed) Hydraulic orifice with constant cross-sectional area

**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.**

**Libraries:**

Simscape /
Fluids /
Hydraulics (Isothermal) /
Orifices

## Description

The Fixed Orifice block models a sharp-edged constant-area orifice, flow rate through which is proportional to the pressure differential across the orifice. The flow rate is determined according to the following equations:

$$q={C}_{D}\cdot A\sqrt{\frac{2}{\rho}}\cdot \frac{p}{{\left({p}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$$

$$\Delta p={p}_{\text{A}}-{p}_{\text{B}},$$

where

q | Flow rate |

p | Pressure differential |

p_{A},
p_{B} | Gauge pressures at the block terminals |

C_{D} | Flow discharge coefficient |

A | Orifice passage area |

ρ | Fluid density |

p_{cr} | Minimum pressure for turbulent flow |

The minimum pressure for turbulent flow, *p*_{cr}, 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:

$$\begin{array}{l}{p}_{cr}=\left({p}_{\text{avg}}+{p}_{atm}\right)\left(2-{B}_{lam}\right)\\ {p}_{\text{avg}}=\left({p}_{\text{A}}+{p}_{\text{B}}\right)/2\end{array}$$

where

*p*_{avg}Average pressure between the block terminals *p*_{atm}Atmospheric pressure, 101325 Pa *B*_{lam}Pressure 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:

$${p}_{cr}=\frac{\rho}{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu}{{C}_{D}\cdot {D}_{H}}\right)}^{2}$$

$${D}_{H}=\sqrt{\frac{4A}{\pi}}$$

where

*D*_{H}Orifice hydraulic diameter *ν*Fluid kinematic viscosity *Re*_{cr}Critical 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 $$\Delta p={p}_{\text{A}}-{p}_{\text{B}},$$.

### Variables

To set the priority and initial target values for the block variables prior to simulation, use
the **Initial Targets** section in the block dialog box or
Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model.
Using system scaling based on nominal values increases the simulation robustness. Nominal
values can come from different sources, one of which is the **Nominal
Values** section in the block dialog box or Property Inspector. For more
information, see Modify Nominal Values for a Block Variable.

## Assumptions and Limitations

Fluid inertia is not taken into account.

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2006a**