# Annular Orifice

(To be removed) Hydraulic variable orifice created by circular tube and round insert

**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 Annular Orifice block annular leakage in a fully-developed laminar flow created by a circular tube and a round insert in an isothermal liquid network. The insert can be located off-center from the tube by an eccentricity value.

The flow rate is computed using the Hagen-Poiseuille equation (see [1]):

$$q=\frac{\pi R{(R-r)}^{3}}{6\nu \rho L}\xb7\left(1+\frac{3}{2}{\epsilon}^{2}\right)\xb7p$$

$$\epsilon =\frac{e}{R-r}$$

where

`q` | Flow rate |

`p` | Pressure differential |

`R` | Orifice radius |

`r` | Insert radius |

`L` | Overlap length |

ε | Eccentricity ratio |

`e` | Eccentricity |

ρ | Fluid density |

ν | Fluid kinematic viscosity |

Use this block to simulate leakage path in plungers, valves, and cylinders.

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 $$\Delta p={p}_{\text{A}}-{p}_{\text{B}},$$. Positive signal at the physical signal port `S`

increases
or decreases the overlap, depending on the value of the parameter **Orifice
orientation**.

## Assumptions and Limitations

Fluid inertia is not taken into account.

## Ports

### Input

### Conserving

## Parameters

## References

[1] Noah D. Manring,
*Hydraulic Control Systems*, John Wiley & Sons, 2005

## Extended Capabilities

## Version History

**Introduced in R2006b**