Why does a supersonic nozzle have a divergent shape?

AI Thread Summary
A supersonic nozzle has a divergent shape to facilitate the acceleration of gas beyond the speed of sound. As the flow transitions from subsonic to supersonic, the area must increase to maintain mass flow continuity while allowing for a decrease in pressure. This design enables the conversion of thermal energy into kinetic energy, which is crucial for achieving supersonic speeds. The relationship between area and velocity is governed by compressible flow dynamics, where a larger area at supersonic speeds results in higher velocities. Understanding this principle is essential for the design of efficient supersonic nozzles.
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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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