Expert: Paul Soderman - 11/5/2009

Question
Hello Paul,
I am trying to understand the relationship’s involved with a carbon fiber pressure vessel filled with a compressed gas / air at 4500psi. The volume of the vessel is 20inch^3. How would I calculate the amount of volume of gas and speed of the gas being release so that the constant flow would last 15 minutes?  Also any material you could refer me to help understand solving the problem would be appreciated.

If you were not the right person to ask this question to, could you please refer me to a expert that might be able to help or point me in the right direction because I have found it very difficult to find any material  on the internet about solving this problem.

Thank you for your help Paul.
-Russell

Answer
Russell
Assuming ambient temperature, the ideal gas laws indicate that your vessel would contain 0.27 lb of air and would expand to about 6115 in^3 at atmospheric pressure.  But the velocity and time of discharge is complicated by the fact that the flow starts out supersonic.  As the pressure in the vessel decreases the velocity decreases and eventually goes subsonic.  Without some kind of variable throttle it would not be possible to hold constant flow rate.  Knowing more about the problem I might be able to solve it, but you haven't explained your objectives or constraints.  An expert in gas dynamics could solve this for you.  I haven't worked this kind of problem in 40 years and would have to dig out my old text books to spin up.  So unless it is really important, I will have to pass.
Paul