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

• men5j2s

#### 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.

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.