Boyle's Law question

[BradMM]

In my book, there's a question about the actual internal volume of an 80 cf cylinder and they refer to it as "water volume." I thought the actual internal volume was 80 cf???

The formula shown is:
P1V1 = P2V2
3014.7psi x V1 = 14.7psi x 80 ft^3
V1 = 0.39 cf

I don't understand the way the formula is set up...? I don't have an actual tank in front of me but taking some guesstimate measurements, 3.14 x (.33')^2 x 2.5' = 85 cf. Pretty close to the standard 80 so the actual volume of an 80 cf tank should be 80 cf...? Not 0.39 cf. Maybe my made up numbers threw me off... I don't know the wall thickness of an alum tank.

Is the actual volume of an 80 cf tank only .39 cf? The 80 is the volume of the air before being compressed?

Thanks

 

[Lorenzoid]

The cylinder holds roughly 80 cf of gas only when the gas is at the rated pressure of the tank. "Water volume" refers to how much the cylinder could hold (i.e., its volume) if it were instead filled with an incompressible fluid like water.

 

[Scott]

An aluminum 80 is actually 77.4 cf @ 3000 psi.

 

[oszillodrom]

Is the actual volume of an 80 cf tank only .39 cf? The 80 is the volume of the air before being compressed?

Exactly.

 

[boulderjohn]

Boyle's law talks about the compression of gases under water pressure. You use the formula V1P1=V2P2 to computer the change in volume for a space occupied by a gas when changing depth.

To do that, we usually use atmospheres of pressure (ATA) rather than PSI. At sea level, there is normally one atmosphere of pressure, and every 33 feet of sea water or every 34 feet of fresh water equals another atmosphere. Thus, at 33 feet of sea water, the diver is under 2 atmospheres of pressure, and at 66 feet, the diver is under 3 atmospheres of pressure. If you plug those numbers into the formula, you will see how a volume of gas (such as in the BCD, lungs, ears, etc.) will compress if you don't do something about it. Lets use one liter as our starting volume to make the math easy.

33 feet:
1 liter X 1 ATA = V2 X 2 ATA.
Divide the left side of the equation by 2 ATA to get the new volume: (1 X 1)/2 = 1/2
So your original volume would be cut in half.

66 feet:
1 liter X 1 ATA = V2 X 3 ATA.
Divide the left side of the equation by 3 ATA to get the new volume: (1 X 1)/3 = 1/3
So your original volume would be cut to a third its original size.

 

[redacted]

Another problem: How many 80 cu ft scuba tanks can you fit in a room that is 8 ft high, 2 ft deep, and 5 feet wide?

 

[Seymour Fisch]

I don't have an actual tank in front of me but taking some guesstimate measurements, 3.14 x (.33')^2 x 2.5' = 85 cf. Pretty close to the standard 80 so the actual volume of an 80 cf tank should be 80 cf...? Not 0.39 cf. Maybe my made up numbers threw me off... I don't know the wall thickness of an alum tank.

Is the actual volume of an 80 cf tank only .39 cf? The 80 is the volume of the air before being compressed?

Thanks

Your estimates of the size of a typical AL80 were pretty close, but you got the decimal place wrong in your volume formula for a cylinder. Your "made up" numbers actually yield a volume of about 0.85 cf. By amazing coincidence, that looks like 85, which is close to the nominal "80cf" of an AL80, but it's a factor of 100 off.

A quick google gives me this page ( Catalina Aluminum Scuba Cylinder Specifications - Imperial ) showing an AL80 with a diameter of 7.25in and a length of 25.9in. Plugging these in (and assuming a perfect cylinder instead of the rounded top) gives an outside volume of about 0.61cf. Wow... so the walls are about 1/3 the volume of the cylinder!

BTW, if you want to visualize 80cf, you can think a small bedroom might be 8' x 10', so a one foot thick volume covering the floor would be 80cf. Or a phone booth or shower stall might be around 3' x 3' and if you made it extra tall at 9', you'd get 81cf. That's a LOT bigger than a scuba tank!

 

[nolatom]

I like being able to talk about Boyle's law, though I know only vaguely that it has to do with gas pressure versus volume.

Also Dalton's law which I only vaguely know has to do with adding up partial pressures of gases, uh, oxygen anyway, so you know what your Nitrox depth limit is.

And Bernoulli's Law, which we don't use in diving (?) but I do use in teaching sailing, about why that curved sail will "pull" you almost upwind because there's an "L" on the outside of the curve we move forward to fill.


Life with an English Major's understanding of science is vaguely wonderful...

 

[dumpsterDiver]

In my book, there's a question about the actual internal volume of an 80 cf cylinder and they refer to it as "water volume." I thought the actual internal volume was 80 cf???

The formula shown is:
P1V1 = P2V2
3014.7psi x V1 = 14.7psi x 80 ft^3
V1 = 0.39 cf

I don't understand the way the formula is set up...? I don't have an actual tank in front of me but taking some guesstimate measurements, 3.14 x (.33')^2 x 2.5' = 85 cf. Pretty close to the standard 80 so the actual volume of an 80 cf tank should be 80 cf...? Not 0.39 cf. Maybe my made up numbers threw me off... I don't know the wall thickness of an alum tank.

Is the actual volume of an 80 cf tank only .39 cf? The 80 is the volume of the air before being compressed?

Thanks

I think you are exactly correct, but nobody seems to see that? And Boyle's law does not necessarily have anything to do with water pressure or depth.

 

[boulderjohn]

Life with an English Major's understanding of science is vaguely wonderful...

I was originally a chemistry major, and then I switched to English. When I do this stuff I have to kick those old science brain cells and awake them from decades of laziness.