3. A supersonic wind tunnel uses helium as a working gas. A very large plenum contains the gas at constant stagnation pr

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3. A supersonic wind tunnel uses helium as a working gas. A very
large plenum contains the gas
at constant stagnation pressure and temperature Pt, Tt. Supersonic
flow is established in the test
section and the flow exhausts to a large tank at pressure Pa, with
no shock waves present. The
exit area Ae can be varied in order to change the flow conditions
in the tunnel, where 1 denotes
the throat and 2 is a section between the throat and exit.
Initially A2/Ae = 4, and A2/A1 = 8. The
gas temperature in the plenum is Tt = 300 K. Neglect wall friction.
Let Pt / Pa = 40.
Assume: γ=1.667, R=2077 J/kg/K.
a) Determine the Mach numbers at Ae, A1, and A2.
b) Determine the exit velocity Ue and pressure ratio Pe / Pa.
c) Suppose Ae is reduced. Determine the value of Ae / A2 which
would cause the Mach number at
Ae to approach one (from above). Suppose Ae is reduced slightly
below this value - what happens
to the supersonic flow in the tunnel? Determine Pt,e / Pt and the
Mach numbers at Ae, A1, and A2
for this case.