# Dynamics of pumping fluid into a cylinder with an air hole?

• Hepth
In summary: Then I opened the valve and stopped the pump. The water level in the tank was the height of the piston minus the width of the "hole". So it was a direct measure of the pressure differential across the hole.
Hepth
Gold Member
I should be able to do this, but its been a while and maybe I'm making this more difficult that it should be.

Assume you have a cylinder nearly sealed but with an outlet hole at the top. I want to pump a fluid into the canister, pushing the air out of the hole, and time how long it takes. The ultimate goal is to try and see what size the hole is, or even what its flow coefficient (if flow rate Q = Area*velocity*K)

What is the simplest way to go about this calculation? I have attached an image, the outlet hole can go anywhere. Let's say that I can control the pump's flow rate or pressure, and the air starts at 1atm both inside and outside.

What is the best approach? By work done? By number of air molecules escaping? By force balancing?

Thanks!

Any ideas?

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If you can control the pump flow rate then this is a non problem ?

Sorry, let's say that I can command a pressure only rather than flow rate.

In that case the fluid is only acting as a liquid piston . Pressure in the air space is same as in fluid . Air flow from hole is given simplistically by Bernoulli equation though much more accurate calculations are possible for specific conditions of flow .

I used something similar 40 years ago. The "air hole" was a small valve. The object was to fill a "tank" with water using a centrifugal pump (large capacity, but could only create about 2 atms of pressure) and then change over to a piston pump (low capacity, but high pressure). Looking up basic physics, I used a pressure sensor mounted right inside the "hole" and waited for the pressure to rise rapidly (at that moment there was no air left inside).

## 1. How does the size of the air hole affect the pumping dynamics?

The size of the air hole plays a significant role in the pumping dynamics. A larger air hole will allow for faster air flow, resulting in quicker pumping of fluid into the cylinder. On the other hand, a smaller air hole will slow down the air flow, leading to slower pumping. This is because the size of the air hole affects the pressure and volume of air entering the cylinder, which in turn affects the fluid flow.

## 2. What is the relationship between the pressure and flow rate in this system?

In this system, the pressure and flow rate have a direct relationship. As the pressure increases, the flow rate also increases, resulting in faster pumping. Similarly, a decrease in pressure will lead to a decrease in flow rate and slower pumping. This is due to the fact that the pressure difference between the air entering the cylinder and the fluid inside drives the flow of fluid.

## 3. How does the viscosity of the fluid impact the pumping process?

The viscosity of the fluid has a significant impact on the pumping process. A more viscous fluid will be more resistant to flow, resulting in slower and more difficult pumping. On the other hand, a less viscous fluid will flow more easily, leading to faster and smoother pumping. This is because the viscosity affects the fluid's resistance to deformation and its ability to flow under pressure.

## 4. Can the shape of the cylinder affect the pumping dynamics?

Yes, the shape of the cylinder can have an impact on the pumping dynamics. A longer and narrower cylinder will result in slower pumping compared to a shorter and wider cylinder. This is because the volume of fluid that can enter the cylinder at a given time is limited by the size and shape of the opening, and a longer and narrower cylinder will have a smaller opening compared to a shorter and wider cylinder.

## 5. How does the pumping process change with varying fluid levels in the cylinder?

The fluid level in the cylinder can affect the pumping process. As the fluid level decreases, the air trapped in the cylinder will have more space to expand, resulting in a decrease in pressure and slower pumping. On the other hand, as the fluid level increases, the air will have less space to expand, leading to an increase in pressure and faster pumping. This is because the trapped air is responsible for driving the fluid flow through the air hole.

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