# Sudden Area Change (TL)

Sudden expansion or contraction in flow area

**Library:**Simscape / Fluids / Thermal Liquid / Pipes & Fittings

## Description

The Sudden Area Change (TL) block models the minor pressure losses due
to a sudden change in flow cross-sectional area. The area change is a contraction from
port **A** to port **B** and an expansion from port
**B** to port **A**. This component is adiabatic.
It does not exchange heat with its surroundings.

**Sudden Area Change Schematic**

### Mass Balance

The mass conservation equation in the sudden area change is

$${\dot{m}}_{A}+{\dot{m}}_{B}=0,$$

where:

$${\dot{m}}_{A}$$ and $${\dot{m}}_{B}$$ are the mass flow rates into the sudden area change through ports A and B.

### Momentum Balance

The momentum conservation equation in the sudden area change is

$${p}_{A}-{p}_{B}=\frac{{\dot{m}}^{2}}{2\rho}\left(\frac{1}{{S}_{B}^{2}}-\frac{1}{{S}_{A}^{2}}\right)+{\varphi}_{Loss},$$

where:

*p*_{A}and*p*_{B}are the pressures at ports A and B.$$\dot{m}$$ is the average mass flow rate.

*ρ*is the average fluid density.*S*_{A}and*S*_{B}are the flow cross-sectional areas at ports A and B.*Φ*_{Loss}is the mechanical energy loss due to the sudden area change.

The mechanical energy loss is

$${\varphi}_{Loss}={K}_{Loss}\frac{{\dot{m}}^{2}}{2\rho {S}_{B}^{2}},$$

where:

*K*_{Loss}is the loss coefficient.

If the **Loss coefficient specification** parameter is set to
`Semi-empirical formulation`

, the loss coefficient for
a sudden expansion is computed as

$${K}_{Loss}={K}_{e}{\left(1-\frac{{S}_{B}}{{S}_{A}}\right)}^{2},$$

while for a sudden contraction it is computed as

$${K}_{Loss}=\frac{{K}_{c}}{2}\left(1-\frac{{S}_{B}}{{S}_{A}}\right),$$

where:

*K*_{e}is the correction factor in the expansion zone.*K*_{c}is the correction factor in the contraction zone.

In the transition zone between sudden expansion and sudden contraction behavior, the loss coefficient is smoothed through a cubic polynomial function:

$${K}_{Loss}={K}_{e}{\left(1-\frac{{S}_{B}}{{S}_{A}}\right)}^{2}+\lambda \left[\frac{{K}_{c}}{2}\left(1-\frac{{S}_{B}}{{S}_{A}}\right)-{K}_{e}{\left(1-\frac{{S}_{B}}{{S}_{A}}\right)}^{2}\right],$$

where

$$\lambda =3{\overline{\dot{m}}}^{2}-2{\overline{\dot{m}}}^{3},$$

and

$${\dot{m}}_{Cr}={\mathrm{Re}}_{Cr}\sqrt{\frac{\pi}{4}{S}_{B}\mu .}$$

If the **Loss coefficient specification** parameter is set to
```
Tabulated data — Loss coefficient vs. Reynolds
number
```

, the block obtains the loss coefficient from tabular data
provided as a function of the Reynolds number.

### Energy Balance

The energy conservation equation in the sudden area change is

$${\varphi}_{A}+{\varphi}_{B}=0,$$

where:

*Φ*_{A}and*Φ*_{B}are the energy flow rates into the sudden area change through ports A and B.

## Assumptions and Limitations

The flow is incompressible. The fluid density is assumed constant in the sudden area change.

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2016a**