Why does a supersonic nozzle have a divergent shape?

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SUMMARY

The discussion centers on the shape of supersonic nozzles, specifically their divergent design. For incompressible fluids, the conservation of mass dictates that a decrease in cross-sectional area results in an increase in velocity. However, the intriguing aspect is that supersonic nozzles are designed to be divergent, which allows for the acceleration of flow beyond the speed of sound. This design is essential for achieving supersonic speeds in various applications, including aerospace engineering.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with the conservation of mass equation
  • Knowledge of compressible versus incompressible flow
  • Basic concepts of nozzle design in aerospace engineering
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  • Research the principles of compressible flow in fluid dynamics
  • Study the design and function of converging-diverging nozzles
  • Explore the applications of supersonic nozzles in aerospace technology
  • Learn about the effects of shock waves in supersonic flows
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Aerospace engineers, fluid dynamics researchers, and students studying advanced fluid mechanics will benefit from this discussion on supersonic nozzle design and its implications in engineering applications.

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Nozzle:
Why for subsonic flow the cross-sectional area of nozzle decreases?
 
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For an incompressible fluid with a single inlet and exit the conservation of mass equation simply reduces to volumetric flow in equals volumetric flow out. It is then immediately clear that with a change in area from the inlet to the outlet, there is a corresponding change in velocity.

The common sense answer is that if you want to put the same amount of constant density material through an area of different sizes, then you'll have to use different rates.

I consider the more confusing (and interesting) question to be why a supersonic nozzle is divergent.
 

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