I Air flow between sphere/cylinder and membrane

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The discussion focuses on the flow through a tapering tube, referencing a formula from valve engineering. It posits that with both inlet and outlet areas being significantly larger than the narrowest section, and with initial and final velocities near zero, laminar flow is primarily limited by viscosity. In a hypothetical zero-viscosity scenario, the flow could be considered infinite. Additionally, if the flow transitions to non-laminar, participants seek methods to estimate the effective outlet area and flow rate. The analysis presented is based on the assumption of inviscid, incompressible, steady flow conditions.
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


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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?


membrane gap flow.webp
 
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The analysis which lead to your equation assumes inviscid incompressible steady flow.
 
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