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

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• AspiringMonkey

#### 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.

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 ?

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

Lnewqban

## What factors affect the rate of fluid flow through a pin-hole?

The rate of fluid flow through a pin-hole is affected 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 temperature of the fluid.

## How does the diameter of the pin-hole impact fluid flow?

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

## What is the relationship between pressure difference and fluid flow through a pin-hole?

The greater the pressure difference between the inside and outside of the container, the higher the fluid flow rate through the pin-hole. This is because a larger pressure difference creates a greater force pushing the fluid through the hole.

## How does the viscosity of the fluid affect flow through a pin-hole?

The viscosity of the fluid, or its resistance to flow, can also impact the rate of fluid flow through a pin-hole. Thicker, more viscous fluids will flow more slowly through the hole compared to thinner, less viscous fluids.

## How does the temperature of the fluid impact flow through a pin-hole?

The temperature of the fluid can affect its viscosity, and therefore impact the rate of flow through a pin-hole. As temperature increases, the viscosity of most fluids decreases, resulting in a higher flow rate through the pin-hole.