The arithmetic of filling a small tank from a large tank?

[TallahasseeRick]

Hi, everyone. Long time lurker, first time poster.

I carry a 6 cu. ft. redundant air supply tank. I like having this gizmo, a totally redundant air system gives me great peace of mind. I fill it from my main tank, not by having it filled with a compressor. I hook up the small tank at zero pressure to the main tank at 3000 lbs, then open the valve. The pressure flows from high to low, ending when both tanks have equal pressure.

The trouble is, if I am diving with a group of divers, I am effectively starting the dive with less air than everyone else (I have taken some of my air out of my main tank and put it in a second tank, a tank I probably won’t actually use.) The small tank also isn‘t actually full. It will never get completely full because the act of filling it reduces the pressure in the tank that is doing the filling. I’ve started wondering about the arithmetic of this.

How much less air do I have in the main tank?

How much air is actually in the small tank?

The way I figure it (somewhat confirmed by “before and after“ SPG readings: ) When I fill my 6 cu. ft. tank from, say, an aluminum 80, I am spreading 80 cu. ft. of gas into 86 cu. ft. of space. Of my total gas supply, 6/86ths (7%) are now in the small tank, 80/86ths (93%) are still in the main tank.

The pressure in the main tank should end up 80/86ths (about 93%) of what it was (3000 lbs becomes 2790)

The small tank is also at 2790 lbs and, while it is rated at 6 cu. ft. @ 3000 lbs, its pressure is now 93% of 3000 lbs. The tank therefore has 93% of 6 cu. ft. in it.

Answers: I’ve got 5.58 cu. ft. (7%) less air that everyone else has and my small tank has 5.58 cu. ft. of air in it.

Is this correct?

 

[Charlie99]

Yes, your calculations are correct.

You can also derive the equations by starting with the ideal gas law,

PV = nrT

The right hand side is more or less constant (there will be some temp changes, but you can ignore that), so it just simplifies down to

Pressure * Volume = a constant.

As you figured out, increasing the volume from 80 to 86 means the pressure will be reduced to 80/86th of the start point. The common AL80 is really 77.4 cu ft, and air doesn't quite follow the ideal gas law, but your calculations are close enough for practical purposes.

 

[Don Burke]

There are a few other minor items.

You actually have a little less useable gas than that since you are not going to use the last 500psig or so. Since you are starting at 93% and going to about 17% while the rest of the crowd is starting at 100% and going to about 17%, you have about 76% of the full capacity while the others have about 83%. That puts you below 92% and even lower if you use the actual capacity of an AL80.

Since you rarely use the redundant tank, it should not need filling every time. When it does, you should have surfaced with some air in the small tank, so the calculations do not start from zero.

If you have to fill it, it might be worth your while to use "spent" tanks on the boat to get as much pressure as you can find into the tank. That will save air from your "fresh" tank since it would just be a topoff.

 

[spstar]

WHY do you need to fill this tank all the time? I would think fill it and forget it.
or is this something you are using on a regular basis? Which would bring us in to a different thread on air mangement :06:

 

[Soggy]

Nevermind...I give up.

 

[MikeFerrara]

P1V1 + P2V2 = P3 V3...where V3 = V1 + V2 and V is actual volume (water capacity).

Mathmatically there are many ways to approach this but I think this is as easy as any. Just rearrange the equation to solve for the variable of interest.

 

[TallahasseeRick]

The reason I’m filling it repeatedly is it is an older H2Odyssey system, an “always on” system, and it will lose pressure very slowly over many days or weeks. Generally it must be refilled the day I want to use it but it is good for many days after that. (The new ones have a shut off valve on them, probably a very good addition.)

I’m not filling it for every single dive. This question only comes up once for the first fill of the day and generally only for one tank I‘ll be using that day. I always check the pressure in the tanks anyway and I fill from whichever tank is most full. On a multi-tank dive day I sometimes know that, say, the second dive of the day will probably require less air than the first dive, so I’ll use the tank that I filled from on the second dive. If there’s no clear difference between the air requirements of the different dives I’ve also filled a little bit from all the tanks equally so no one tank is especially low. I also get a bit higher pressure that way.

Beginning a partial fill from a “spent” tank is a really good idea, one I hadn’t thought of, though I tend to fill it just before the first dive of the day when a spent tank is generally not available. Still, if I happen across one or find one the night before or ask the divers getting OFF the boat as I’m getting on or something…. Good idea.

Thanks for the responses, everyone!

 

[StSomewhere]

If your second dive will be shorter than your first dive (b/c you are starting the second dive with residual N2 loading from the first dive less the SI), fill the "pony" tank from the tank for the second dive.

Of course this completely ignores the questions of air managment and whether 5.xx cu ft is even remotely enough for a backup gas supply. (Right Soggy?)

 

[francousteau]

Nevermind...I give up.

Exactly!

 

[teknitroxdiver]

For a 6cf from a full 80, you will have 2784 PSI in each tank. How did I figure this?

Here ya go: http://www.qfile.de/dl/129146/SAClog.zip.html It's the last worksheet in the spreadsheet....