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)
Critical pressures for other values of - n:
|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)
The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.
Ratios of specific heat for gases with constant pressure and volume processes.
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.