# Nozzles

## Gas flow through nozzles and sonic chokes.

The maximum gas flow through a nozzle is determined by **critical pressure**.

*critical pressure ratio*is the pressure ratio where the flow is accelerated to a velocity equal to the local*velocity of sound*in the fluid

**Critical flow nozzles** are also called **sonic chokes**. By establishing a shock wave the sonic choke establish a fixed flow rate unaffected by the differential pressure, any fluctuations or changes in downstream pressure. A sonic choke may provide a simple way to regulate a gas flow.

The ratio between critical pressure and initial pressure for a nozzle can expressed as

p_{c}/ p_{1}= ( 2 / (n + 1) )^{n / (n - 1)}(1)

where

p_{c}= critical pressure (Pa)

p_{1}= inlet pressure (Pa)

n = index of isentropic expansion or compression - or polytropic constant

For a perfect gas undergoing an adiabatic process the index - *n* - is the ratio of specific heats - *k = c _{p} / c_{v}*. There is no unique value for -

*n*. Values for some common gases

- Steam where most of the process occurs in the wet region :
*n = 1.135* - Steam superheated :
*n = 1.30* - Air :
*n = 1.4* - Methane :
*n = 1.31* - Helium
*: n = 1.667*

### Example - Air Nozzles and Critical Pressure Ratios

The critical pressure ratio for an air nozzle can be calculated as

p_{c}/ p_{1}= ( 2 / (1.4 + 1) )^{1.4 / (1.4 - 1)}

= 0.528

Critical pressures for other values of *- n:*

n |
1.135 | 1.300 | 1.400 | 1.667 |

p_{c} / p_{1} |
0.577 | 0.546 | 0.528 | 0.487 |

### Mass Flow through Nozzles

The mass flow through a nozzle with sonic flow where the **minimum pressure equals the critical pressure** can be expressed as

m_{c}= A_{c}(n p_{1}ρ_{1})^{1/2}(2 / (n + 1))^{(n + 1)/2(n - 1)}(2)

where

m_{c}= mass flow at sonic flow (kg/s)

A_{c}= nozzle area (m^{2})

ρ_{1}= initial density (kg/m^{3})