# 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)

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]):

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

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

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

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Physical signal port that controls the insert displacement.

### Conserving

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Hydraulic conserving port associated with the orifice inlet.

Hydraulic conserving port associated with the orifice outlet.

## Parameters

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The distance between the central axes of the insert and the tube. The parameter can be a positive value, smaller than the difference between the radius of the tube and the radius of the insert, or equal to zero for coaxial configuration.

Initial overlap between the tube and the insert. The parameter must be positive. The value of the initial length does not depend on the orifice orientation.

Specifies the effect of the control signal on the orifice overlap.

## References

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

## Version History

Introduced in R2006b

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