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})
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
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