TITLE.PM5

COMPRESSIBLE FLOW 887

dharm

\M-therm\Th16-2.pm5

Let p 2 (= pc) = pressure in the throat when the flow is sonic for given pressure p 1.

— When the pressure in the receiver, p 3 = p 1 , there will be no flow through the nozzle, this

is shown by line a in Fig. 16.10 (b).

d e

c

b

a

f

Shock wave

fronts

Critical

p = 0.528 pc1

pc

p 1

Inlet

(p ) 1 1 Flow^2

Exit

3

Receiver

Throat

()a

()b

p 3

j

Inlet Throat Exit

Fig. 16.10. (a) Laval nozzle (convergent-divergent nozzle) ; (b) Pressure distribution through
a convergent-divergent nozzle with flow of compressible fluid.
— When the receiver pressure is reduced, flow will occur through the nozzle. As long as the
value of p 3 is such that throat pressure p 2 is greater than the critical pressure 0.528 p 1 ,
the flow in the converging and diverging sections will be subsonic. This condition is
shown by line ‘b’.
— With further reduction in p 3 , a stage is reached when p 2 is equal to critical pressure
pc = 0.528 p 1 , at this line M = 1 in the throat. This condition is shown by line ‘c’. Flow is
subsonic on the upstream as well the downstream of the throat. The flow is also isentropic.
— If p 3 is further reduced, it does not effect the flow in convergent section. The flow in
throat is sonic, downstream it is supersonic. Somewhere in the diverging section a
shock wave occurs and flow changes to subsonic (curve d). The flow across the shock is
non-isentropic. Downstream of the shock wave the flow is subsonic and decelerates.
— If the value of p 3 is further reduced, the shock wave forms somewhat downstream (curvee).
— For p 3 equal to pj, the shock wave will occur just at the exit of divergent section.
— If the value of p 3 lies before pf and pj oblique waves are formed at the exit.
Example 16.14. A large tank contains air at 284 kN/m^2 gauge pressure and 24°C
temperature. The air flows from the tank to the atmosphere through a convergent nozzle. If the
diameter at the outlet of the nozzle is 20 mm, find the maximum flow rate of air.
Take : R = 287 J/kg K, γ = 1.4 and atmospheric pressure = 100 kN/m^2.
(Punjab University)