Is it possible to have a Mach number greater than 1 at the throat?

[wav3 r1d3r]

I have a problem for my Gas Dynamics homework, in which the problem asks to solve for the Mach number at the throat of a converging-diverging nozzle.

I assumed that the Mach at the throat should be equal to 1 since the professor said it was impossible to have a Mach number greater then 1 at the throat.

After showing the same problem to a Graduate Student I work with he showed me that it is possible to have a Mach number greater then 1 at the throat through the area ratios.

But after speaking to my professor a second time he has again said it is not possible.

So my question is.. is it possible to have a Mach number greater than 1 at the throat.


Oh the conditions for the problem are as follows:
Mi=2
Ai=20 cm^2

Athroat=15cm^2

Shock Area=22 cm^2
Ae=25cm^2

where gamma= 1.4

according to the solutions Mach at the throat equals 1.662


I assumed it was 1 but it was not correct.


If someone could steer me in the right direction I'd appreciate it thanks!

 

[Valkarie]

Yes, it is possible to have a Mach number greater than 1 at the throat of a converging-diverging nozzle. This is due to the area ratios which change the pressure and velocity in the nozzle as the air passes through. The pressure and velocity changes result in a Mach number greater than 1 at the throat. To solve for the Mach number at the throat, you can use the equations of one-dimensional, steady flow and the given conditions to calculate the pressure ratio, temperature ratio, and density ratio. Once these values are determined, you can then use the equation for the Mach number to solve for the Mach number at the throat.