Why does the density decrease equal the speed gain at Mach 1?

Question

In this answer, it says : "At small Mach numbers, changes in speed cause negligible changes in density, but as Mach approaches unity, both are of similar magnitude. With Ma>>1 , changes in density will become dominant. A speed increase is always coupled to a decrease in density."

Why does the density decrease equal the speed gain at Mach 1? Is it just a coincidence or a result of the Mach number? If it's not a coincidence, what makes this happen? I welcome a non-mathematical explanation, instead more of explaining what happens to the air molecules.

(it says at Mach 1 density changes will become dominant, but the 3rd paragraph of this answer might clarify what I mean)

@CamilleGoudeseune, I think this is a bit too strict of a definition. I'm pretty sure there are ample questions here that are about pure aerodynamics as opposed to applied aerodynamics (and of which it thus could also be said that they belong to Physics.SE, as you could switch the fluid) — ROIMaison, Jan 24 '24 at 09:19
But, coincidentally enough, this question was asked before on Physics.SE - Can Mach number be greater than 1 if mass flow rate is decreasing?. The formula in the accepted answer explains the different behaviours at M<1 and M>1, and how therefore mass flow should be maximum at M=1 — ROIMaison, Jan 24 '24 at 10:23
@ROIMaison, fair enough. I'm unvoting (if that is a word!) to close. — Camille Goudeseune, Jan 24 '24 at 15:54

Why does the density decrease equal the speed gain at Mach 1?

0 Answers0