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

The critical pressure ratio is the pressure ratio which will accelerate the flow 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 the critical pressure and the initial pressure for a nozzle can expressed as

pc / p1 = ( 2 / (n + 1) )n / (n - 1)         (1)

where

pc = critical pressure (Pa)

p1 = 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 = cp / cv. There is no unique value for - n. Values for some common gases are

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

pc / p1 = ( 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

pc / p1  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

mc = Ac (n p1 ρ1)1/2 (2 / (n + 1))(n + 1)/2(n - 1)          (2)

where

mc = mass flow at sonic flow (kg/s)

Ac = nozzle area (m2)

ρ1 = initial density (kg/m3)