Solving a CO2 Air Tank Problem

[sroderi]

ok so it has been a few years since I have worked on things like this and I am needing some help

I have a CO2 tank that weighs 22.17 oz's when full. There is 9 oz's of CO2 in the tank. The problem I am working on is that I need to find out how far the tank will go when the safety burst disk goes off as well as its velocity. The exit hole is around 1.9 mm and it goes off at 3000 psi. The volume of the tank is around 19.5865 in^3

I started off by doing (3000 psi) X (.00439 in^2) which gave me the force coming out of the jet. I then divided it by the total weight of the tank which gave me an acceleration of 9.52622 ft/s^2. I questioned this considering the pressure, acceleration, and weight will be decreasing and changing I just didn’t know how to do it the right way.

I then started working on trying to find out how long it would take to empty the tank. I used Boyle law (P1V1=P2V2) = (2982.3*19.865in^3) = (14.7*(X)) When I found X I was going to divide it by the flow rate to give me the time it takes to empty.

Well flow rate is Velocity X Area so I am having problems finding the velocity of the CO2 leaving the tank. I tried messing with Bernoulli’s equation but had a hard time with the density of the CO2 which I was assuming a temperature of 20 C anything around that will work.

Once I find that velocity of the CO2 I can find the discharge time. I think I can put it in the equation (D=.5a(t)^2) to get distance

I may be way off it has been a long time since I worked on this stuff so if anyone could help me with this I would greatly appreciate it

Thanks

 

[Bob S]

Where does the 3000 psi come from? I attach a CO2 vapor pressure curve. It is about 40,000 mmHg at room temperature, equivalent to to 53 atm, or 775 psi. It is about 73 atm at 31 deg C, when it becomes a supercritical fluid. See thumbnail.

 

[sroderi]

yes CO2 usually stays around 800 psi but we had a problem with the tank heating up and blowing the 3000 psi safety disk. the tank is rated at 5000 psi so that is why there is a 3000 psi safety burst disk. I am unsure what the temperature needs to get to to reach 3000 psi though.