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

[AspiringMonkey]

TL;DR Summary

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.

 

[Baluncore]

Welcome to PF.

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 ?

 

[erobz]

I think you are going to have to consider surface tension. Not Bernoulli's.