Rate of Gaseous Diffusion into a Vacuum

[RandyP]

Hello Everyone,

I have a question regarding the diffusion of a gas (or mixture of gases) into an evacuated space. The situation I am picturing is one where you have two vessels of equal volume, one contains a gas at room temperature, some known pressure (say ~760torr), and the other at static high vacuum (say ~1e-5 torr). Joining the vessels is a length of tubing with a valve at the center.

Upon opening the valve, obviously the gas will diffuse from the pressurized side to the evacuated side until an equilibrium is reached. My real question is how can I make a good approximation of how quickly that will occur? I realize it will be dependent on:

differential pressure
length of tubing
diameter of tubing
identity of the gas/gas mixture

...and probably some other factors I am not considering at the moment. Can anyone provide some insight for a rough determination?

Thanks much,

Randy

 

[BvU]

Hello Randy,

I wouldn't call that diffusion but pressure-driven flow. Never mind.

Depending on whether you want to learn something or just need a quick answer.
For the first you need to learn about "pressure drop in gas flow" (which google)
For the second you could use a calculator on the net

 

[RandyP]

Pressure driven flow it is. Thanks for the link to that calculator - requires a license but they do provide equations that may help. I am putting something together where I'd like to get a feel for the flow rates. Would like to know ahead of time if I am talking 2 minutes to equilibrate - or 2 hours.

Randy

 

[BvU]

Oops. Maybe this one ? They have limitations on pipe/orifice diameters, but it's a start.
I'd expect that your concern should be that it goes too fast initially and things break, not that you have to wait for hours. But I don't know any dimensions, so I don't know if you can have the valve wide open...