# Can Mach number be greater than 1 if mass flow rate is decreasing?

Here is the mass flow rate equation from the NASA site(enter link description here). According to this the maximum mass flow occurs at Mach number M = 1, which I can understand. But I can substitute Mach values greater than one (M>1) in the equation, then I get a lower mass flow rate. I know that in a convergent-divergent nozzle, the Mach number grows greater than 1 in the divergent section as the back pressure at the exit of the nozzle continues to reduce. But here the mass flow rate continues to remain constant and equal to chocked mass flow rate at the nozzle throat. Is the equation correct in suggesting that the flow can accelerate past Mach 1 as long as the mass flow is reducing?

The vertical axis is labeled Normalised Mass Flow Rate ( and the brackets [-] indicates no units). It is the value calculated on the right side of the equation divided by the value of the right side with M = 1. In a convergent-divergent nozzle, the stagnation pressure and temperature ($$p_t$$ and $$T_t$$) remain constant (at least for the ideal case) and the mass flow rate remains constant. Therefore, the decrease of the curve above Mach = 1 shows area has to increase to get higher Mach number. If you try to add or remove flow you have to do a whole bunch of other calculations (see Shapiro's The Dynamics and Thermodynamics of Compressible Fluid Flow (Volume 1)for example.
$$\frac{dA}{A}=-(1-M^2)\frac{dV}{V}$$
where $$dA$$ is the increase of cross-sectional area, $$M$$ the Mach number, $$dV$$ the increase in flow velocity. Found in Fundamentals of Gas Dynamics by Owczarek (c. 1964 International Textbook Company), page 201. If you want a derivation I can add it.