Filling an AL 80 from a larger tank???

[jbd]

I have a tank that holds 444 cuft of air at 4500psi. I filled one AL 80(cascade style from the larger tank and figured I should be able to fill a second AL 80 and part of a third. All I got in the second tank was 2600 psi. That seems to be a total of no more than 150 cuft, which means there should still be close to 300 cuft in the larger tank.

Can someone bring me up to speed on the math regarding volume and pressure when using a cascade set up?

 

[griffindm]

By my math, after the first tank (filled to 3000 psi) you would have 3960 psi in your larger tank. The second tank could only be filled to 2897, at which time it would have the same pressure as the larger tank. Any further fills from the larger tank would be to further decreasing pressures.

 

[Charlie99]

Can someone bring me up to speed on the math regarding volume and pressure when using a cascade set up?

The math below ignores the errors caused by the pressure-volume curve of air not being a perfect straight line.

You started with 444cubic feet at 4500psi in your bank. Since the internal volume of your bank stays contant, the pressure is just simply proportional to the amount of air in the tank.

If you remove 80 cubic feet (doesn't matter whether you blow it off to atmosphere or put it in another tank), then your tank will now have only 444-80 = 364 cubic feet and the pressure will be 364/444 * 4500 = 3689psi.

If you run the same math for the next tank, you will find that the pressure is less than 3000psi after you fill the 80 cu ft tank. The 80 cu ft tank doesn't hold 80 cu ft unless you are at 3000 psi, so you need a different method of calculating (Yes, I know that most 80 cu ft tanks are really 77.4, but I'm ignoring that).

4500psi is 4500/14.7 = 306 atm. The internal volume of the "444 cu ft tank" is 444/306=1.45 cu ft. The internal volume of a 80 cu ft at 3000psi tank is 0.392 cu ft (using the formula 80/3000*14.7).

Now lets hook up the two tanks. Pressure * Internal Volume stays constant if the amount of gas is constant. So lets see what happens when you effectively increase the size of the container from 1.45 cu ft to 1.45 + 0.392 cu ft.

3690psi * 1.45 cu ft = ?? * (1.45 + 0.392) Or ?? = 3690*1.45 / (1.45 + 0.392) = 2904psi.

Or you can just go find a gas calulator that does all this for you

Charlie

p.s. My first 3689 answer differs significantly from griffendm's 3960, but perhaps he meant 3690psi. Our second answer are within expected roundoff errors.

 

[jbd]

Thank you both for the answers and the explanantion.

BTW Charlie99, do you know if v-planner has that kind of gas calculator with it? I'm considering purchasing the new version in the next month or two. I think there was mention of a gas calculator.

 

[scubafool]

I came up with the same thing as charlie99, but now I'm confused.....

 

[jbd]

....but now I'm confused.....

About what :06:

 

[zboss]

and who said we didn't need to learn basic math in high skool.

 

[knotical]

All I got in the second tank was 2600 psi.

I’m having trouble seeing why you only got 2600 on your second fill.
Doing similar math as the others, and setting the variables in favor of getting a low second fill, I still don’t get that low:
If the first AL 80 cylinder was totally empty, actually holds 78.2 cubic feet (Luxfer’s S80), and was filled to 3000 psi, then the supply cylinder would now still hold 365.8 cubic feet at 3707 psi.
If the second AL80 was also a totally empty 78.2, the supply and load cylinders should balance out at 2932 psi. Assuming you had any air left in your “empty” tanks, or they were the more common 77.4s, the ending pressure should be even higher.

Therefore something in your original post doesn’t seem to compute. Did you overfill the first AL80? Are the gauges accurate? Was the supply tank full to start? etc. etc.

 

[scubadoguk]

Are you confusing volume with pressure?

 

[Charlie99]

The deviation of air from the ideal gas curve increases greatly between 200 and 300bar. At 4500psi/306bar the air in a cylinder is about 8% down from what one calculates with ideal gas laws. It's about equal to ideal at 232bar, and the actual amount is a tiny bit higher than ideal gas law for pressures around 200/207bar/3000psi.

2600psi vs 2904 or 2932psi is about a 9% difference. Once you take into account the Van der Waals correction, 2600psi is pretty close to what you'd expect after fully filling 1 AL80 and getting almost a full fill on the 2nd