# Conceptual explanation for subsonic nozzle VS supersonic nozzle

A nozzle is a device that increases the velocity of a fluid in the expense of pressure energy drop of the fluid (The Bernoulli principle).

Now how can we explain (conceptually, no math) why a subsonic nozzle shape (a convergent channel) is different from a supersonic nozzle shape (a divergent channel)?

A supersonic nozzle needs space to contain the sonic shock wave. The shock wave does the work of converging the flow.

One explanation I seem to remember (in another lifetime) was that the supersonic nozzle offers higher pressure drop through dropping the density.

Figure: subsonic nozzle and diffuser source: wikipedia

In a subsonic flow air can be considered as incompressible. However, in the case of supersonic (or close to supersonic) the air can be considered compressible. This resuls in density variations (which are associated to the supersonic wave).

Further acceleration (to higher mach numbers) require greater drop pressure. One way that occur (at a set temperature) is through the change in density - which is related to the volume. As volume increases density decreases. However, because the last part of the equation of perfect gases is constant (at a constant temperature):

$$P\cdot V=n*R*T$$

Therefore the pressure will drop, if the volume increases. So the nozzle area diverges to increase the available volume (and result in density decrease)

Also while I was trying to remember I found another interesting interpretation of the pressure drop based on molecular dynamics. Essentially, in supersonic flows to increase the velocity there is a need to increase the quality of kinetic energy of the molecules. More specifically you need to transform the random Kinetic energy of the molecules and make it more directed (in a similar way that an electric field in a conductor makes the electrons move towards one direction). The "ordered" molecules develop a shockwave front, on the expense of the random kinetic energy -- which is associated with the pressure (thus leading to pressure drop). Again the pressure drop, can be achieved through an expanding volume -- hence the divergent shape.

in supersonic nuzzle the profile of nuzzle has been designd to convert huge heat energy to acceleration. chocking at the throat creating shockwaves.

The profile also shields low pressure flow from being supressed by ambient pressure if it exists.

The difference with a ventury nuzzle is the huge pressure drop and increased ejection velocity.

The subsonic nuzzle is a case of Bernoulli flow.