I Air flow between sphere/cylinder and membrane

[Swamp Thing]

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

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?

 

[Chestermiller]

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