Calculating CFM for Compressed Air Venting Down to Atmospheric Pressure

[Nuttypro67]

Hello gentlemen! I'm rather new to this whole complex world we call compressed air. :) Put simply, I have spent the past 4 hours trying to find this answer anywhere and I am just not informed enough about all these numbers to get what I need to find out.

I have an air cylinder that is compressed to 150 PSI with a volume of 7.3 cu in. I am trying to find out how long it will take for the 150PSI to vent down to atmospheric pressure through an opening that is 1.77mm in diameter.

I realize I need to find CFM, Cubic Feet per Minute. But everywhere I look the calculator asks for velocity of the air. For some reason I just can't grasp why you would need the velocity of the air to figure out how much is moving through the opening. Nor do I have any idea how to figure the velocity since all the velocity equations I found are asking for the CFM!

Thanks guys!

 

[redargon]

this may or may not be helpful: http://air-dispersion.com/feature2.html hopefully the former

 

[Mech_Engineer]

I was going to post that same link. The difficult part of finding the leak time for a pressure vessel is the fact that it is a highly nonlinear coupled problem (the gas is cooling, the pressure is changing, and the flow rate may or may not be choked flow, etc...). You best bet for a plug-and-play answer are the equations provided in the posted link.

 

[tyroman]

It is a fluid dynamics problem...

see;
Boyle's Law
Bernoulli's equation

Google;
blowdown air orifice
blowdown orifice flowrate

For critical flow, see;
http://www.cheresources.com/high_dp_orifice_flow.shtml

Some of the complexities are considered here;
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JPVTAS000131000003034501000001&idtype=cvips&gifs=yes

Hope this helps.

 

[Nuttypro67]

hmmm, well I THINK I got the equation to work but the results its kicking out just don't make any sense.
According to the results, it will take 788,153 seconds or 9 days for the vessel to reach 50% density. Haha!
Thanks a MILLION for the equation, though. I am now 10 times closer to my answer than I was yesterday. You guys are great. :)