# Annular Orifice

Hydraulic variable orifice created by circular tube and round insert

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.

## Basic Assumptions and Limitations

Fluid inertia is not taken into account.

## Parameters

The radius of the tube. The default value is `0.01` m.

The radius of the insert. The default value is `0.0098` m.

Eccentricity

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. The default value is `0`.

Initial length

Initial overlap between the tube and the insert. The parameter must be positive. The value of initial length does not depend on the orifice orientation. The default value is `0.003` m.

Orifice orientation

The parameter is introduced to specify the effect of the control signal on the orifice overlap. The parameter can be set to one of two options: `Positive signal increases overlap` or `Negative signal increases overlap`. The default value is `Positive signal increases overlap`.

## 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.

## Ports

The block has the following ports:

`A`

Hydraulic conserving port associated with the orifice inlet.

`B`

Hydraulic conserving port associated with the orifice outlet.

`S`

Physical signal port that controls the insert displacement.

## References

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

Introduced in R2006b

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