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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.

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: 

Air Nozzles - Critical Pressure Ratios
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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Related Topics

Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

Related Documents

Gases - Ratios of Specific Heat

Ratios of specific heat for gases with constant pressure and volume processes.

Orifice, Nozzle and Venturi Flow Rate Meters

The orifice, nozzle and venturi flow rate meters makes the use of the Bernoulli Equation to calculate fluid flow rate using pressure difference through obstructions in the flow.

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