Compressed air in a reservoir at rest at expands smoothly and isentropically through…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Waves, acoustics and compressible flow · Waves, acoustics and compressible flow

Signal Speeds in Fluids, Ch Steady compressible flow: energy, stagnation and the Mach number

Problem

Compressed air in a reservoir at rest at

T_0=350\,\mathrm{K}

expands smoothly and isentropically through a nozzle. Using

\gamma=1.4

and

R=287.05\,\mathrm{J\,kg^{-1}\,K^{-1}}

for air, find ((a)) the sonic temperature

T^*

and the sonic speed

c^*

, reached where the local Mach number is exactly

1

; ((b)) the limiting speed

u_{\max}

approached as the gas is expanded into a vacuum.

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