The math around the windbag or Bernoulli bag experiment

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bernoulli%20bag400.jpg

What is the math behind this experiment? If the mass flow rate of the air coming out of the guy's mouth is M1, then what is the mass flow rate, M2, of of the air going into the bag?

I know that this is related to compressible flow. The explanations I have found on the internet are that since the pressure reduces because of the high velocity air, the surrounding air will also go through the opening of the airbag. I would like to see an expiation using equations and math and physics, or at least be pointed in the right direction. Thank You.
 

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