How Does a Pressurized Tank Empty Over Time Through a Hole?

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• ab042896
In summary: This is a general equation which can be used for any flow rate and orifice size.In summary, the author is trying to find a curve that can be used to compare experimental data with. They are unsure of how to apply fluid dynamics to a vessel that empties simply due to its own pressure difference through an area. Temperature can be assumed to be constant at 25C. The author finds information on how to calculate Lohm for a given size orifice and flow rate as a function of pressure.
ab042896
I having difficulty wrapping my head around a concept that I wish to solve. I have a 10L tank of compressed air at 100psi. When an outlet hole of cross-sectional area of 0.115 in^2 is opened, I wish to develop a curve of pressure vs. time from t=0 until pressure drops to atmospheric. Many things can be neglected in this situation, such as friction etc., since I would like a general curve to compare with experimental data. I am unsure of how to apply fluid dynamics to a vessel that empties simply due to its own pressure difference through an area.

Temperature can be assumed to be constant at 25C as well.

You can find engineering formula in places such as valve manufacturers, pneumatic handbooks, etc. Here is an example http://www.theleeco.com/engineering/engineering.cfm#lohm-laws-working-with-gases

You have to be aware that you will need two regimes for your problem: initially the inside pressure is greater than 1.9 x atmospheric and you need a sonic formula. At lower pressures subsonic equations will do.

Doesn't
Henryk said:
You can find engineering formula in places such as valve manufacturers, pneumatic handbooks, etc. Here is an example http://www.theleeco.com/engineering/engineering.cfm#lohm-laws-working-with-gases

You have to be aware that you will need two regimes for your problem: initially the inside pressure is greater than 1.9 x atmospheric and you need a sonic formula. At lower pressures subsonic equations will do.
100psi relative is 114psi absolute, which is nearly eight times greater than atmospheric. Are you aware of any ways that this could be done to give a rugh estimate? After all I will be testing this and ultimately have the real data to compare this to.

Follow the link. You will find a number of pages with relevant information. Lee valve company uses LOHMS concept. Find how to calculate LOHM for a give size orifice and then the flow rate as a function of pressure.

1. How does the size of the hole affect the rate at which a pressurized tank empties over time?

The size of the hole in a pressurized tank does affect the rate of emptying. The larger the hole, the faster the tank will empty. This is because a larger hole allows for a greater amount of air to escape at once, creating a larger flow rate.

2. Does the pressure inside the tank affect the rate of emptying through a hole?

Yes, the pressure inside the tank does affect the rate of emptying. The higher the pressure, the faster the tank will empty through a hole. This is because the higher pressure creates a greater force pushing the air out of the tank.

3. How does the type of gas in the tank affect the rate of emptying over time?

The type of gas in the tank does affect the rate of emptying. Gases with higher densities, such as carbon dioxide, will empty at a faster rate than gases with lower densities, such as helium. This is because denser gases have a greater mass and therefore exert a greater force on the walls of the tank.

4. Can temperature affect the rate of emptying of a pressurized tank through a hole?

Yes, temperature can affect the rate of emptying. Warmer temperatures will result in a faster rate of emptying compared to colder temperatures. This is because warmer air molecules have more energy and can escape through the hole at a faster rate.

5. Is the rate of emptying of a pressurized tank constant over time?

No, the rate of emptying is not constant over time. As the tank empties, the pressure inside decreases, resulting in a decrease in the rate of emptying. This is because there is less force pushing the air out of the tank as it becomes less pressurized.

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