As in the question statement, I am wondering whether it is possible for Mach number to increase while local flow velocity decreases. I am basing myself on the simple case of an ideal gas, in which:

$$M=\frac{v}{\sqrt{\gamma R T}}\ \tag{*}$$

If we take a diverging supersonic flow ($dA>0, M>1$), for example, the flow velocity must decrease due to the area-velocity relation below:

$$\frac{dv}{v}=\frac{1}{M^2-1}\frac{dA}{A} \ \tag{**}$$

What happens now? Velocity decreased but (from the corresponding temperature relation), the temperature must increase so the Mach number can go either way from equation $(*)$.

  • $\begingroup$ What do you mean by descent ? $\endgroup$ – john melon Apr 12 '18 at 1:15
  • $\begingroup$ @MikeDunlavey That sounds like it should be an answer, not a comment. Please don't posts answers in the comment section. $\endgroup$ – David Z Apr 12 '18 at 2:12

Speed of sound increases with air density, so Mach number (the fraction of speed of sound) could decrease with descent (going to a lower altitude), even if airspeed increased.


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