Supersonic

The shown figure is a cross section of a testing chamber with a converging/diverging nozzle. If a gas mixture (c = 300 m/s) experiences a normal shock wave as shown by being accelerated from 220 m/s through the chamber’s nozzle, what section(s) is supersonic?

Expand Hint
The Mach Number is a dimensionless value useful for analyzing fluid flow dynamics problems where compressibility is a significant factor.
$$$Ma=\frac{v}{c}$$$
where $$Ma$$ is the Mach number, $$v$$ is the fluid flow speed, and $$c$$ is the speed of sound.
Hint 2
Because section E expands to an ambient environment, the flow must be subsonic.
The Mach Number is a dimensionless value useful for analyzing fluid flow dynamics problems where compressibility is a significant factor.
$$$Ma=\frac{v}{c}$$$
where $$Ma$$ is the Mach number, $$v$$ is the fluid flow speed, and $$c$$ is the speed of sound (which varies based on medium conditions).
  • If the Mach number is  < 1 , the flow speed is lower than the speed of sound - and the speed is  subsonic .
  • If the Mach number is  ~ 1 , the flow speed is approximately like the speed of sound - and the speed is  transonic .
  • If the Mach number is  > 1 , the flow speed is higher than the speed of sound - and the speed is  supersonic .
  • If the Mach number is  >> 1 , the flow speed is much higher than the speed of sound - and the speed is  hypersonic .

The flow is subsonic in the chamber because $$Ma=220/300=0.73$$ , so $$Ma< 1$$ in section A. Flow in a converging/diverging nozzle transitioning from subsonic to supersonic will have $$Ma=1$$ at the throat, so section B is the transonic phase. In a normal shock situation, flow slows down from supersonic to subsonic, so section C has $$Ma>1$$ and section D $$Ma< 1$$ . Because section E expands to an ambient environment, the flow must be subsonic.
C
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