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## Main Question or Discussion Point

**Gas Flow into Vacuum Paradox ?!?!**

Hi,

I've just been reading up on 1-D isentropic, compressible flow through a nozzle (constant cross-sectional area) and have hit a bit of a conceptual road block which I was hoping someone would help resolve.

I'm interested in the mass flow rate of the gas through the pipe which should be proportional to the difference in pressures between the two ends of the nozzle. Thus if we hold the front pressure constant and reduce the back pressure (or do vice versa), then presumably the mass flow would increase (proportionally with respect to the difference in pressure) until the advent of choked flow whereupon the mass flow would attain a constant value and be independent of further reductions in the back pressure. The critical pressure at which this occurs can be easily obtained from the stagnation pressure via the specific heat ratio of the gas.

Now what if start our experiment with the back pressure set to 0 (a vacuum) and have a gas in the reservoir at a pressure P that is just a tiny bit greater than 0, say 0.001 Pa. Based on my understanding of the equations, it seems that the flow will be choked no matter what the front pressure is, as long as it is nonzero. This seems hard to believe; the pressure gradient is tiny but we still have choked flow !?!? Is this true at all ?

Does anyone know any resources that will help to understand the compressible flow of a gas into a vacuum ?

Thank you very much.