Air flow between sphere/cylinder and membrane

  • Context: Undergrad 
  • Thread starter Thread starter Swamp Thing
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SUMMARY

The discussion centers on the flow dynamics through a tapering tube, referencing a formula derived from valve engineering literature. The participants explore the implications of laminar flow, particularly when both inlet and outlet areas (A1 and A2) are significantly larger than the narrowest section of the tube. It is concluded that under laminar conditions, flow is primarily constrained by viscosity, suggesting that in a hypothetical zero-viscosity scenario, flow could be infinite. Additionally, the conversation addresses the transition to non-laminar flow and the challenges in estimating effective outlet area (A2) and flow rate under those conditions.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly laminar and non-laminar flow.
  • Familiarity with the concepts of viscosity and its impact on flow rates.
  • Knowledge of inviscid incompressible flow assumptions.
  • Basic grasp of flow area calculations in tapering tubes.
NEXT STEPS
  • Research the Navier-Stokes equations to understand flow behavior in viscous fluids.
  • Learn about the Reynolds number and its significance in determining flow regimes.
  • Explore methods for estimating effective flow areas in non-laminar conditions.
  • Investigate the implications of inviscid flow assumptions in practical engineering applications.
USEFUL FOR

Fluid dynamics engineers, mechanical engineers, and researchers in valve engineering or related fields will find this discussion beneficial for understanding flow behavior in tapering tubes and the effects of viscosity on flow rates.

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


1749089170771.webp



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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