# Mass flow rate for compressible flow

I am confused about the relation of mass flow rate with different mach numbers in a compressible flow.
In wikipedia (http://en.wikipedia.org/wiki/Choked_flow), I read the following:

"Although the gas velocity reaches a maximum and becomes choked, the mass flow rate is not choked. The mass flow rate can still be increased if the upstream pressure is increased as this increases the density of the gas entering the orifice."

This makes me think that:
- The maximum velocity will be mach 1 and won't increase (at the minimum tube area, or throat)
- The mass flow rate will not be limited, because the higher the pressure, the higher the density, so mass flow rate will increase (mdot = mach1 * A * rho).

But then I read from nasa (http://www.grc.nasa.gov/WWW/k-12/airplane/mflchk.html):

"There is a maximum airflow limit that occurs when the Mach number is equal to one. The limiting of the mass flow rate is called choking of the flow."

And:

"If we have a tube with changing area, like the nozzle shown on the slide, the maximum mass flow rate through the system occurs when the flow is choked at the smallest area."

This seems contradictory. I might be missing something.

bigfooted
Gold Member
For isentropic processes, the maximum velocity will be reached in the throat, where M=1, so the maximum velocity will be the speed of sound.
Also, the maximum mass flow rate will be reached in the throat, but it is given by the isentropic relations.
When you modify the inlet pressure, the maximum velocity will still be the speed of sound, but the maximum mass flow rate can have a different value. Both maxima will still occur in the throat.
Note that the speed of sound can change if you modify the pressure, so even though the maximum velocity will always be the speed of sound, the value of the velocity can change.

You said that the speed of sound can change, right? But looking at this equation:
$$a = \sqrt{\gamma R T}$$
What changes when the pressure increases?
$$R_{air}=287 \frac{J}{kg K}$$
$$\gamma_{air}=1.4$$
$$T= 300 K$$ (of the atmospheric temperature? Or do I need to calculate it somehow?)

Also, the nasa site mass flow rate equation uses the Mach Number. And to calculate the Mach Number I need to calculate the dynamic pressure, but to calculate the dynamic pressure I need the Mach Number (http://en.wikipedia.org/wiki/Mach_number). So how can I calculate the Mach Number, without knowing the velocity? For example, can I calculate the Mach Number for a pressure difference in a tube with area A and length L?