Gas Flow (Help with Physics needed)

[IKE]

Originally Posted by EricVanWyk

ish?

Flow is proportional to the root of pressure, and inertia is (largely) negligible... I think.

This depends on the runner length (connection between volumes) and the velocities involved and the precision you are looking for with regards to timing. With air, a similar effect to "water hammering" can occur with relatively fast flows. That is how tuned intake systems for cars can actual increase torque at certain rpms by adjusting runner lengths (extra air can be pumped in due to the pulsing nature).

Basel,
Eric gave you a really good link for constant pressure systems. You could either try to work out the math for the changing pressures, or you could use excel (or some other program) to do a time based integration technique.
Time based is similar to the "Numerical Integration" technique you likely lerned in calculus.

Figure out the initial flow rate. Assume it to be nearly constant over a given small time-frame. Assuming ideal gas PV=NRT, you could then get a change in pressure of both containers after that discreet amount of flow and thus have two new pressures. Put this into an expanding table until the pressures eventually equalize....
Or,
You can make a table that has various balanced transition states. for example assuming equal volume containers, and one is at 100 psi, and the other is at 0, they should balance at 50 psi. Then take various static slices between those balance points. 100:0, 90:10, 80:20....60:40, 55:45 (I think it would be linear, but please check using the ideal gas law). By calculating flow at those various slices, you can use the average of the two ends to figure out an approximate time it would take to get between the states. While not perfect, this will give you a pretty good approximation, especially with more and more slices. A neat way of looking at this would be to compare the "answer" with various resolutions. The coarsest would be using just the two end conditions 100:0 and 50:50. Then use 3 states (2 regions), then 5 states (4 regions).....
Essentially this is the foundation of many Finite Element Analysis type tools.

I use this technique a lot for buidling simple models for dynamic phsyics problems. With a little bit practice, you can build eerily accurrate tools. Also, this will give you some insight into the "dangers" of "bad FEA". For a problem like this, you should see that your initial answer of the 2 state 1 region differs drastically from your "final" which will likely be on the order of 20+ regions. Resolution in critical errors often leads to poor decisions from bad FEA.

Also play around with using different discharge coefficients. As you can see in the table, they have a huge effect on the flow velocities, and thus the "answer". This brings up the other important thing about FEA which is boundary constraints and assumptions.

[Molten]

You must spread Reputation around before giving it to IKE again.