Fluid flow through a pin-hole of x diameter in a closed container

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SUMMARY

The discussion focuses on fluid flow through a pin-hole of diameter D in a closed cylindrical vessel, emphasizing the complexities introduced by flexible walls and compressible air. It highlights that traditional applications of Bernoulli's equation may not apply due to significant surface tension and capillary forces. The flow is characterized as unsteady, with the system alternating between gulping air and expelling liquid. Participants agree that a comprehensive understanding of the dynamics requires consideration beyond Bernoulli's principles.

PREREQUISITES
  • Understanding of Bernoulli's equation and its limitations
  • Knowledge of fluid dynamics, particularly in closed systems
  • Familiarity with surface tension and capillary action
  • Basic principles of compressible fluid flow
NEXT STEPS
  • Research the effects of surface tension on fluid flow in confined spaces
  • Study the behavior of compressible fluids in dynamic systems
  • Explore unsteady flow characteristics in flexible-walled containers
  • Investigate alternative models to Bernoulli's equation for complex fluid dynamics
USEFUL FOR

This discussion is beneficial for fluid dynamicists, mechanical engineers, and researchers studying fluid behavior in closed systems, particularly those interested in the interactions between liquid and gas phases in flexible containers.

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TL;DR
A container is filled with a specific fluid and has a hole on the side. How big can the hole be before the fluid starts flowing out while air flows in? Air must flow in since the container is closed. Capillary forces must be taken into account. The wall has a specific thickness.
Greetings,

I've come across lots of exercises regarding Bernoulli's equation. However, never seen one where the top of the vessel is closed, and fluid flow exists via gas (air) going in. Has this problem been studied in the past?
Assume a cylindrical vessel filled to the maximum with a D-sized hole on the side. The wall thickness and the surface tension/capillary forces are significant. Air must go inside the vessel for the liquid fluid to come out.
 
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It is unlikely that the flow will be steady because the walls are flexible, and the air contained above the liquid is compressible. Systems with only one port tend to gulp air, then run liquid for a while, before taking another gulp of air and repeating.

What is a D sized hole ?
 
I think you are going to have to consider surface tension. Not Bernoulli's.

 
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