# Calculate the time it takes for gas to fill a chamber (high P -> low P)

• schang04
In summary, the conversation discusses the calculation of time for a high pressured gas to fill a chamber and the possible governing equations that could be used for this. It is suggested to use a website calculator for flow rate through an aperture, taking into account the pressure differences and the temperature equalization between the two chambers. It is also mentioned that for high pressure applications, the expansion cooling and compression heating effects must be considered. The accuracy and repeatability of the calculation is also brought up, as well as the potential challenges in developing a program for this.
schang04
How do you calculate the time it take a high pressured gas to fill a chamber? I have a gas in a chamber that is at 600psi and then another chamber at atmospheric pressure. When the valve between the two chambers is opened, how do you calculate the time it would take to fill the chamber? Are there any governing equations that would be helpful for this?

Thanks so much!

schang04 said:
How do you calculate the time it take a high pressured gas to fill a chamber? I have a gas in a chamber that is at 600psi and then another chamber at atmospheric pressure. When the valve between the two chambers is opened, how do you calculate the time it would take to fill the chamber? Are there any governing equations that would be helpful for this?

Thanks so much!
There is a website giving a calculator for flow rate through an aperture.
https://www.tlv.com/global/TI/calculator/air-flow-rate-through-orifice.htmlNotice that your pressure is going to fall progressively in one chamber and rise in the other, so you need to do a bit more calculating. The pressures will never reach equilibrium,so you might have to work out how long to fall a certain pressure.
The problem is very similar to discharge of a capacitor, or decay of radioactivity

For high pressure applications, the filling time is also affected by the expansion cooling in the supply tank vs the compression heating in the receiving tank; as a result, the time for the two tank's temperatures to equalize must be included for the maximum amount of gas to be transferred to the receiving tank.

As an addendum to my above post. The above assumes an equal pressure capability and final pressure for both tanks. All of the above also applies for a high pressure tank filling a lower pressure tank but with an added issue if the maximum amount of gas is to be transferred to the lower pressure tank because the transfer will have to be stopped a the point that the lower pressure tank's pressure limit is reached; and, unless a very slow transfer rate is used, there will generally be a temperature differential at that shutoff point. If the lower pressure receiving tank is to be filled to it maximum capacity then at least one or a series of additional "topping off" fills are required until the two tanks' post filling temperatures are equalized.

Thanks for your help! Do you know the equations that I need to do that?

JBA said:
As an addendum to my above post. The above assumes an equal pressure capability and final pressure for both tanks. All of the above also applies for a high pressure tank filling a lower pressure tank but with an added issue if the maximum amount of gas is to be transferred to the lower pressure tank because the transfer will have to be stopped a the point that the lower pressure tank's pressure limit is reached; and, unless a very slow transfer rate is used, there will generally be a temperature differential at that shutoff point. If the lower pressure receiving tank is to be filled to it maximum capacity then at least one or a series of additional "topping off" fills are required until the two tanks' post filling temperatures are equalized.

Is this something you expect to do repeatably i.e similar to a scuba bottle filling operation, or it more of a infrequent transfer requirement; and, how accurate and repeatable does the calculated time need to be?
Also, what are the delivery and receiving pressures for your transfer(s), for pressures above 1000 psig there is also a pressure factor Z (pressure vs mass is not linear at high pressures) that has to be incorporated into the calculation.

Part of the problem is that a tighter accuracy for the time for an amount (lbs) of gas delivered at the filled tank pressure requires an increasing amounts of data input and operating restrictions for the operator(s) if the calculation is to be of assistance; and, for frequent sequential fillings this can become a major issue.

A few years back, on another forum, there was an inquiry asking if someone could develop an "accurate" program for calculating the number of bottles of a given size and pressure limit that could be filled from a given air storage tank supply. While Bauer Storage Systems has data on this issue, they state that their data is based upon an ambient constant temperature (i.e. Isothermal) transfer.
At the time, I didn't see developing such a program as being a particularly difficult problem; however, after about four months of intensive work, multiple program revisions using verifying fill testing by the requester, it was becoming clear that due the many associated factors in this process that such a program might not be attainable; and a month or so later it became clear that accurately predicting the filling was not going be achieved, at least by my efforts. The final issue that killed the project was accurately calculating the heat loss rate from the receiving bottle as its gas temperature rises during the filling and the heat gain of the supply tank as its temperature falls during filling and rises between fillings.

I just need a general answer that I can compare experimental data to. We are trying to see how long we need to leave a valve open between the chambers so that the low pressure chamber will reach a certain pressure. The high pressure chamber will be around 800psi and the low pressure chamber will start at atmospheric pressure and then need to be increased to 600psi.

Any info you have will be helpful! Thanks!

If you have not yet done so I strongly suggest you view the the forum thread referenced in Post #2 by @Chestermiller to realize what is involved with your request. It addresses an request similar to what you are seeking; but, it is actually a simpler problem than yours because in that case the supply pressure is constant and it assumes an isothermal transfer because of its low pressures. I believe you will then understand why you are not getting any other responses to your request.

## 1. How do you calculate the time it takes for gas to fill a chamber?

To calculate the time it takes for gas to fill a chamber, you will need to know the volume of the chamber, the initial pressure of the gas, and the final pressure of the gas. You will also need to know the flow rate of the gas into the chamber. Once you have this information, you can use the ideal gas law and Bernoulli's principle to calculate the time it takes for the gas to fill the chamber.

## 2. What is the ideal gas law?

The ideal gas law is a mathematical equation that describes the relationship between the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

## 3. How does Bernoulli's principle relate to the time it takes for gas to fill a chamber?

Bernoulli's principle states that as the velocity of a fluid (such as a gas) increases, the pressure decreases. This means that as the gas flows into the chamber at a certain rate, the pressure in the chamber will decrease, allowing more gas to enter. This relationship is important in calculating the time it takes for the chamber to reach a certain pressure.

## 4. What factors can affect the time it takes for gas to fill a chamber?

The time it takes for gas to fill a chamber can be affected by several factors, including the volume of the chamber, the initial pressure of the gas, the final pressure of the gas, and the flow rate of the gas into the chamber. Other factors such as temperature and the properties of the gas being used can also play a role.

## 5. Can the time it takes for gas to fill a chamber be shortened?

Yes, the time it takes for gas to fill a chamber can be shortened by increasing the flow rate of the gas into the chamber or by decreasing the volume of the chamber. Additionally, using a gas with a higher initial pressure can also decrease the filling time. However, it is important to consider safety precautions and the limitations of the chamber when attempting to shorten the filling time.

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