Related Resources: fluid flow
Convergent Nozzle Flow Velocity and Area Equation and Calculator
Hydraulic & Pneumatics
Fluids Design and Engineering Data
Convergent Nozzle Flow Velocity and Area Equation and Calculator
Nozzles are used in steam and gas turbines, in rocket motors, in jet engines and in many other applications. Two types of nozzle are considered: the ‘convergent nozzle’, where the flow is subsonic; and the ‘convergent divergent nozzle’, for supersonic flow.
Outlet pressure p_{2} greater than p_{c}, i.e. r > r_{c}
Nozzle Outlet Velocity Equation
Nozzle Critical Pressure Ratio:
Nozzle Outlet Area Equation
When Outlet pressure p_{2} equal to or less than p_{c}, i.e. r ≤ r_{c} the following equation applies;
Nozzle Outlet Velocity Equation
Note that C_{2} is independent of p_{2} and that the nozzle flow is a maximum. In this case the nozzle is said to be ‘choked’.
where:
p_{1} = Inlet pressure (N / m^{2}, Pa)
p_{2} = Outlet pressure (N / m^{2}, Pa)
p_{c} = critical pressure at throat (N / m^{2}, Pa)
v_{1} = Inlet specific volume (m^{3})
v_{c} = Outlet specific volume (m^{3})
C_{2} = Outlet velocity (m/sec)
C_{c} = Throat velocity (m/sec)
r = pressure ratio = p_{1} / p_{2}
r_{c} = critical pressure ratio
A_{2} = outlet area (m^{2})
A_{c} = throat area (m^{2})
n = index of expansion
m = mass flow rate (kg/m^{2})
Fluid 
n

r_{c}

Air (n = γ) 
1.40

0.528

Initially dry saturated steam 
1.135 
0.577

Initially superheated steam 
1.30

0.546
