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Molecular flow, how to calculate pressure inside domain ?

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I have a model capillary and vacuum tubes that goes through a all the Knudsen number regimes.
I have pumps and the gas pressure can vary 10^-5 Torr to 100 atm.
But I am interested in the pressure only in the center line of symmetry. I need an estimate not an exact calculation.

My question is how to calculate the pressure inside (not on the walls ) and have vacuum pumps?
The molecular flow model do not give the pressure inside. I have only pressure input and pump speed as known parameters.

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