Sonic velocity at the throat of a convergent-divergent nozzle

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SUMMARY

The discussion centers on the behavior of gaseous fluids released through a convergent-divergent nozzle, specifically regarding the velocity at the throat. It is established that a sufficient pressure difference between the inlet and release is necessary for achieving supersonic flow. The velocity at the throat of the nozzle is always sonic, regardless of the inlet-to-throat ratio or the geometry of the divergent section, provided the conditions for supersonic flow are met. Understanding compressible flow principles is essential for further exploration of this topic.

PREREQUISITES
  • Understanding of compressible flow principles
  • Familiarity with convergent-divergent nozzle design
  • Knowledge of pressure differentials in fluid dynamics
  • Basic concepts of supersonic and sonic flow
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  • Study the principles of compressible flow in detail
  • Research the design and analysis of convergent-divergent nozzles
  • Learn about the effects of pressure differentials on flow velocity
  • Explore the mathematical modeling of sonic and supersonic flow conditions
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Aerospace engineers, fluid dynamics researchers, and students studying compressible flow will benefit from this discussion.

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TL;DR
Sufficiently pressurised compressible fluid is being released through a convergent-divergent nozzle. I want to know that whether irrespective of the geometry and inlet to throat ratio of the nozzle, do the velocity at the throat will always remain sonic?
Sufficiently pressurised (difference between inlet and release pressure is enough to create supersonic flow) gaseous fluid is being released through a convergent-divergent nozzle. And it's a known fact that if pressure difference is sufficient, a convergent-divergent nozzle can release gaseous fluid at supersonic velocity. I want to know that whether irrespective of the inlet to throat ratio and geometry of the divergent section, do the velocity at the throat will always remain sonic or it need some factors to keep the velocity sonic at the throat.
 
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Have you done any work to try to work out this problem on your own? If you are only looking for a yes/no answer, then you could get that from Google.
 
How? Kindly guide me.
 
Have you ever taken a compressible flow course or are you otherwise familiar with compressible flow?
 

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