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Models annular leakage between a circular tube and a round insert in an isothermal flow

**Library:**Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Orifices

The Annular Leakage (IL) block models annular leakage between a circular tube and a round insert in an isothermal liquid network. The insert can be located off-center from the tube and can have varying lengthwise overlap with the tube.

Ports **A** and **B** correspond with the orifice
inlet and outlet. The input ports **L** and **E** are
optional physical signal ports that model variable overlap length (L) and variable
eccentricity (E).

The leakage mass flow rate is calculated from the pressure-flow rate equation

$$\dot{m}=\frac{\pi {\left(R-r\right)}^{3}\left(R+r\right)}{12v}\frac{\left({p}_{A}-{p}_{B}\right)}{l}\left[1+3{\epsilon}_{{}_{sat}}^{2}\frac{R}{\left(R+r\right)}+\frac{3}{8}{\epsilon}^{4}\frac{\left(R-r\right)}{\left(R+r\right)}\right],$$

where:

*R*is the annulus outer radius.*r*is the annulus inner radius.*p*_{A}is the pressure at port**A**.*p*_{B}is the pressure at port**B**.*ν*is the fluid kinematic viscosity.*l*is the overlap length.ε is the eccentricity ratio, $$\epsilon =\frac{e}{R-r}$$, where

*e*is the eccentricity, which can be defined as a physical signal or constant value.*ε*_{sat}is the saturated eccentricity ratio, which is ε for constant orifices, or the physical signal connected to port**L**for variable orifices. The eccentricity ratio is always between 0 and 1.

When modeling a variable overlap length, the user-defined minimum overlap length
is used if the physical signal falls below the value of the **Minimum
overlap length** parameter.

The pressure-flow equation is valid only for fully-developed, laminar flows. The flow Reynolds number can be determined using $$\mathrm{Re}=\frac{\dot{m}{D}_{h}}{\mu \pi \left({R}^{2}-{r}^{2}\right)}$$ or by checking the simulation log in the Results Explorer or the Simulation Data Inspector. For more information, see Data Logging.