Related Resources: fluid flow

### Convergent Nozzle Flow Velocity and Area Equation and Calculator

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 p2 greater than pc, i.e. r > rc

Nozzle Outlet Velocity Equation

Nozzle Critical Pressure Ratio:

Nozzle Outlet Area Equation

When Outlet pressure p2 equal to or less than pc, i.e. r ≤ rc the following equation applies;

Nozzle Outlet Velocity Equation

Note that C2 is independent of p2 and that the nozzle flow is a maximum. In this case the nozzle is said to be ‘choked’.

where:

p1 = Inlet pressure (N / m2, Pa)
p2 = Outlet pressure (N / m2, Pa)
pc = critical pressure at throat (N / m2, Pa)
v1 = Inlet specific volume (m3)
vc = Outlet specific volume (m3)
C2 = Outlet velocity (m/sec)
Cc = Throat velocity (m/sec)

r = pressure ratio = p1 / p2

rc = critical pressure ratio

A2 = outlet area (m2)
Ac = throat area (m2)
n = index of expansion
m = mass flow rate (kg/m2)

 Fluid n rc Air (n = γ) 1.40 0.528 Initially dry saturated steam 1.135 0.577 Initially superheated steam 1.30 0.546

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