Air flow between sphere/cylinder and membrane

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  • Thread starter Swamp Thing
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Swamp Thing
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I got this formula for the flow through a tapering tube from a paper on valve engineering. https://www.mdpi.com/2673-4117/4/4/149


Formula for mass flow rate: fnFlow(p1_, p2_, A1_, A2_, rho_) = sqrt(p1 - p2) times sqrt(2 A2 A2 / (rho (1 - (A2/A1)^2))), with a square root over the second term.



Now in the following case, both A1 and A2 are essentially infinite compared to the narrowest part of the flow. The initial and final velocities are both practically zero. So if we assume laminar flow, can we say that in this case the flow is limited only by viscosity, and would be potentially infinite in the zero-viscosity case? Secondly, if it becomes non-laminar at some point on the outside, is there a way to get a rough estimate of the effective A2 and hence of the flow rate?


Diagram of a stretched membrane above a dome-shaped shell with a narrow gap between the shell's two rims; labelled P1 inside the dome, P2 outside, and a flat base below.