# Can I calculate the flow rate of a compressed gas from pressure?

• men5j2s
In summary, the conversation discusses the use of a compressed gas tank to fill an empty container. It is suggested to use a pressure transducer to determine when the container has reached the desired pressure of 6bar. However, it is mentioned that the use of the ideal gas law to calculate the flow rate may not be accurate and it is recommended to use a flow meter and pressure transducer instead, despite the added cost. It is also noted that the placement of the sensors is important for accurate measurements. The use of poor equipment to save costs can lead to more problems and expenses in the long run.
men5j2s
TL;DR Summary
If I am using a pressure transducer to determine when a vessel has been filled to 6bar, can I use the information I gain from it to derive the flow rate mathematically?
I am using a compressed gas tank to fill an otherwise empty container, The gas tank is around 50bar and the container will be filled to 6bar.

If I am using a pressure transducer to determine when the container has been filled to 6bar, can I use the information I gain from it to derive the flow rate mathematically?

If not, how can I determine the flow rate whilst filling?

I'll be using helium for this

Welcome to PF.

If you have P and T, then you can use the perfect gas law PV=nRT to calculate the change in n (proportional to mass) between two time intervals.

anorlunda said:
Welcome to PF.

If you have P and T, then you can use the perfect gas law PV=nRT to calculate the change in n (proportional to mass) between two time intervals.

So I can obtain the pressure in the vessel that I'm filling at t=0 (1atm as its empty), then Pressure at t=1s, 2s, 3s...etc (likely to be in millisecs) and and use the mass in grams (derived from the mols of helium as given by the ideal gas law) to work out a mass flow rate in kg/s (m-dot).

Pressure will be constantly increasing, and there will be an initial drop in T for sure (adiabatic cooling?) so i will need to monitor temperature and pressure of the vessel throughout the filling to get an accurate measure?

Or can I assume that after a couple of milliseconds, the temperature will have stabilized to whatever the temp of compressed helium is?OR... will this be constantly changing due to the increasing pressure in a fixed vessel?

Thank you for nudging me in the right direction, I'm confident this can be done experimentally now, I'm just trying to understand which sensors I will need (thermo-couple and a pressure transducer so far) and where abouts I need to place them (at the mouth of the vessel i think).

You needed both P and T.

I would not call this method accurate. If you need accurate flow rate, then measure it directly.

I've decided to use a flow meter and pressure transducer, but this is going to be costly as I need 5 of each :(

You have made the right (if costly) decision and it will be money well spent. Building a poor system to save money up front will in the long run probably not be a savings at all, when it creates operational problems and costs more later to remove and replace it with the correct equipment to fix the problem.
Unfortunately, this happens often when there is pressure to keep cost low when building a new facility; and, afterward the system operators have to deal with the problems it creates and, in some cases, having to replace the problem components in the system.

## 1. How do I calculate the flow rate of a compressed gas from pressure?

The flow rate of a compressed gas can be calculated using the ideal gas law, which states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT. By rearranging this equation, we can solve for the flow rate (n/t) by dividing the change in pressure (P2-P1) by the change in time (t) and multiplying by the volume (V) and the gas constant (R).

## 2. What units should I use when calculating the flow rate of a compressed gas?

The units used for calculating flow rate will depend on the units used for pressure, volume, and time. It is important to ensure that all units are consistent and in the correct SI units. For example, if pressure is measured in Pascals (Pa), volume in cubic meters (m3), and time in seconds (s), then the flow rate will be in moles per second (mol/s).

## 3. Can I calculate the flow rate of any compressed gas using this method?

The ideal gas law can be used to calculate the flow rate of any gas, as long as the gas behaves like an ideal gas. This means that the gas molecules are not interacting with each other and the volume of the gas is much larger than the size of the molecules. In most cases, this assumption is valid for compressed gases.

## 4. What other factors should I consider when calculating the flow rate of a compressed gas?

In addition to pressure, volume, and temperature, other factors that can affect the flow rate of a compressed gas include the type of gas, the size and shape of the container, and the presence of any obstructions or restrictions in the flow path. These factors may need to be taken into account for a more accurate calculation.

## 5. Is there a more accurate method for calculating the flow rate of a compressed gas?

While the ideal gas law provides a good estimate for the flow rate of a compressed gas, there are other methods that may be more accurate for certain situations. For example, if the gas is not behaving like an ideal gas, a more complex equation, such as the Van der Waals equation, may be used. Additionally, experimental methods, such as flow meters, can also provide more accurate measurements of flow rate.

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