## Subsonic and Supersonic Nozzles - What Causes the Difference?

Hello Physics Forums!

I am currently taking an aerodynamics class at my university. About a month ago we covered supersonic nozzles and derived an area relation in terms of Mach number and ratio of specific heats for isentropic flow (the actual equation is #9 in the link at bottom of this post). However, other than telling us what happens, this equation does little to shed light on why.

In other words, mathematically the relationship between area ratio and mach number for a given ratio of specific heats is a parabola with a maximum at mach 1. Physically I understand a subsonic nozzle as functioning through the application of a higher static pressure at the nozzle entrance than exists at the exit, forcing the molecules to move into the nozzle - and because of the physical limitations of the nozzle - closer together. Since molecules have electrostatic forces repelling one another, they try to "escape" and do so towards the lower pressure area further down the nozzle - converting static pressure into dynamic pressure.

However, with supersonic nozzles the area increases, but still causes the same effect of increasing the speed of the flow. Why does this happen? What physical characteristic(s) grows significant enough at M = 1 to allow the behavior of the air to change - and why does it grow?

Here is the link to the equation and a picture: http://www.grc.nasa.gov/WWW/k-12/airplane/isentrop.html

P.S. I asked my professor about this at the time. She told me that she didn't think there was any transparent explanation for this, but she would be interested in knowing if it did exist. Also, I have been trying to find the answer for a while through google search and the textbooks available to me, but can't really seem to get what I'm looking for.
Thanks!
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