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At the beginning of chamber pumpdown, I feel like I should be able to apply a combination of PV=nRT and Poiseuille's law to convert my 2.5mbar rate of pressure change into a desired flow rate, and then into an effective tube radius. When I do this, I get a result that feels pretty intuitive based on my experience. (Does this seem like a valid calculation to anyone else or have I already made an error here?)

But nearing the end of the pumpdown process, I suspect I can no longer apply Poiseuille's law in the same way since I no longer have laminar gas flow. When I try to apply the same equations the same way I get a resulting effective radius that is much smaller than would make sense. Is there a different equation I can use to calculate a required tube radius in this low pressure regime? Does it even make sense to be trying to calculate this when my desired change in pressure (2.5mbar/s) is larger than my chamber pressure (0.5mbar)? It doesn't feel like I can treat pressure over time as linear here.

Any advice for tackling this problem would be appreciated!