The math around the windbag or Bernoulli bag experiment

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    Bernoulli Experiment
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The discussion focuses on the mathematical principles governing the Bernoulli bag experiment, specifically the relationship between the mass flow rates of air exiting and entering the bag. The mass flow rate of air from the mouth, denoted as M1, influences the mass flow rate M2 entering the bag due to the principles of compressible flow. The reduction in pressure caused by high-velocity air creates a vacuum effect, drawing surrounding air into the bag. Participants seek a detailed mathematical explanation, including relevant equations from fluid dynamics.

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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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