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Gas flow through nozzles and sonic chokes.

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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.

nozzle flow

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

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


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

  • 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)


mc = mass flow at sonic flow (kg/s)

Ac = nozzle area (m2)

ρ1 = initial density (kg/m3)

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  • Engineering ToolBox, (2008). Nozzles. [online] Available at: [Accessed Day Mo. Year].

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