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

In summary, the conversation discusses a unique problem involving Bernoulli's equation where the top of a closed vessel is filled with air and fluid flow occurs through a D-sized hole on the side. There is also a mention of the significance of wall thickness and surface tension, as well as the potential for unsteady flow due to flexible walls and compressible air. The question of whether surface tension rather than Bernoulli's equation should be considered is also raised.
  • #1
AspiringMonkey
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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.
 
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  • #2
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 ?
 
  • #3
I think you are going to have to consider surface tension. Not Bernoulli's.

 
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Likes Lnewqban

1. How does the diameter of the pin-hole affect the fluid flow rate?

The diameter of the pin-hole has a direct impact on the fluid flow rate. A larger diameter hole will allow more fluid to flow through at a faster rate, while a smaller diameter hole will restrict the flow and result in a slower rate.

2. What factors influence the fluid flow through a pin-hole?

The fluid flow through a pin-hole is influenced by several factors, including the diameter of the hole, the pressure difference between the inside and outside of the container, the viscosity of the fluid, and the length of the pin-hole.

3. Can the fluid flow rate be controlled by adjusting the pressure difference?

Yes, the fluid flow rate through a pin-hole can be controlled by adjusting the pressure difference between the inside and outside of the container. A higher pressure difference will result in a faster flow rate, while a lower pressure difference will result in a slower flow rate.

4. How does the viscosity of the fluid affect the flow rate through a pin-hole?

The viscosity of the fluid plays a significant role in the flow rate through a pin-hole. A more viscous fluid will have a slower flow rate compared to a less viscous fluid, as it will experience more resistance while passing through the pin-hole.

5. Is the flow rate through a pin-hole constant?

No, the flow rate through a pin-hole is not constant. It will vary depending on the factors mentioned above, such as the pressure difference, viscosity, and diameter of the hole. Additionally, as the fluid level inside the container decreases, the flow rate will also decrease due to a decrease in pressure difference.

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