transfill question

[DaleC]

I'm having problems with my math. Here's the question:

I want to transfill a ST72 (72 cuft. @ 2250psi) from an Al80 (77 cuft. @ 3000psi).

If connected with a whip both will stabilize at 1500psi.

1500psi for the Al80 is 38.50 cuft. (77/3000x1500)

1500psi for the ST72 is 48 cuft. (72/2250x1500)

So... Where did the extra 9.50 cuft. come from?

Obviously I'm missing something here. How do I calculate pressure and volume in different sized cylinders?
Please.

 

[crpntr133]

Calculate what each PSI in each tanks equals. This should answer your question.

77 cuft divided by 3000=.025 cuft per PSI
72 cuft divided by 2250= .032 cuft per PSI

Simply multiply both number by 10, 100, 1000, 1500 etc and that will give you cubic feet at that pressure. Since air is like water and it seeks it's own level both tanks will be under equal pressure.

I think part of what is throwing you is the different pressure for the tank. The AL80 is 3000 and the 72 is 2250.

 

[DaleC]

Still doesn't make sense to me.

If I start with an Al80 @ 3000psi I have 77cuft.
If I connect it to my ST72 the pressure between the two equalizes at 1500psi.
1500psi in my Al80 = 38.5cuft.
but...
1500psi in my ST72 = 48cuft.
38.5 + 48 = 86.5 cuft.

I need a different formula.

 

[rongoodman]

I haven't got my head around the numbers yet, but I think the mistake is assuming both will equalize at 1500 psi. I haven't been able to find them yet, but I think you'll need the actual volumes of the tanks to work it out. It would be much easier in metric, where tanks are specified by their actual volume, not how much gas they hold at a given pressure.

 

[Scared Silly]

First it is 72cuft at 2250psi+10% ie. 2475psi.

The problem is you are trying to compare volumes which are dependent on different pressures with absolute (1 atm) volumes which does not work.

For instance, take your 77cuft at 3000psi and remove 1/2 of the gas. That would give 38.5cuft of gas at 1 atmosphere. Now stuff that 38.5cuft into a 72cuft and the pressure would be 1323psi. This would assume that you took the gas from pressure to 1atm and then back to pressure.

However, in your case your went from pressure to pressure. As such, the pressure when equalized at 1500psi in the 72 and the 80 so you have 43.6 cuft and 38.5 cuft respectively.

There is probably a better way to explain this point but it is not coming to me right now.

 

[rongoodman]

It was hard finding a volume for the LP72, but using 700 cubic inches, and about 680 for the AL80, I came out with a pressure of a little less than 1400 lb/square inch after they equalized, which gives close to the right volumes.

 

[Spimon]

LOL. I think I misread the original post then confused everyone. Sorry bout that
Just to clarify, the 72 is originally empty and the 80 is @ 3000 psi, right?

If one tank is at high pressure and one is low, they'll naturally want to meet 'in the middle' - well not exactly in the middle, but one will tend to increase in pressure and one will tend to decrease (laws of thermodynamics dictate this).
On the same basis, the equilised pressure cannot be greater than the highest starting pressure. The equilised pressure must lie somewhere in between. Just where, in between, is based on relative volumes and pressures (and hence masses).

I'm going to take another approach on this question. The method I'm using relies on finding the mass air air, volume and pressure in each cylinder, and then the same for both tanks as a system.
Although in this case you can find an approximate answer by averaging the two start pressures, due to the similar tank size. If you had two tanks of vastly different volumes this wouldn't work at all. You need a special formula...

The formula is *drum roll*

PV = MRT​

Where:
P = pressure (KPa)
V = volume (m^3)
m = mass (kg)
R = gas constant (KJ/Kg-K) = 0.287 for air (comes from a standard table.)
T = temperature (kelvin scale) = 298k for room temperature
(For those interested, this is called 'The Ideal Gas Equation'. Google it for more in depth info)

Excuse the metric system for those not compatible, but it really is a much simpler system to work with
While I'm talking up the metric system, this one reason why tanks 'should' be labeled according to their liquid capacity, not their gas capacity at some arbitary pressure.

Hope it all makes sense. Let me know if it's not and I'll try to explain it better.



If, like I originally assumed, both tanks are at the pressures mentioned in the original post, the working would look like this:

 

[rongoodman]

I assumed the 72 ft tank was empty in the original example, being transfilled from the 77, so the total volume of gas involved was 77 cubic feet. If they were both full, and being equalized, they should balance out at about 2700 psi. In any event, dividing the total volume of gas by the volume of the containers will give an answer in atm, which is converted back to psi.

 

[Spimon]

rongoodman, sorry about all that confusion! Your first post was right. I just totally misinterpreted the situation. I think our differences are due to using slightly different cylinder volumes.

 

[rongoodman]

It looks like the two calculations are equivalent, except that you assume a 2250 psi fill for the smaller cylinder, instead of 2475. Metric is certainly easier to work with, especially for diving calculations. I think the original poster owes us both a beer.