# Can Mach Number Decrease while Flow Velocity Increases?

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 $(*)$.

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