# Volume of a cylinder formula

1. Aug 17, 2004

### betz

I want to determine the volume of air in a scuba tank. Can someone tell me the formula if I know how much water the tank holds?

2. Aug 17, 2004

### Zorodius

Hopefully, your scuba tank doesn't contain water

The volume of a cylinder is $\pi r^2 h$, where r is the radius and h is the height of the cylinder. The amount of air actually contained within the tank depends on the pressure that the gas is under, though.

3. Aug 19, 2004

### red_fox77

Better equation

Lets be a little more accurate than that. A scuba tank is actually a cylinder with two hemispheres attached. So the total volume is actually 4/3*PI*r^3 + PI*r^2*h.

But better yet, to calculate the volume of air in the tank, use the ideal gas law (close enough for pure O2) V=RT/P. What this tells you is your pressure will depend on the temperature (in K) you are swimming at. R is the ideal gas constant, and the value depends on which units you want to use for V. Search google for 'R ideal gas' for some charts on which value to use.

Will.

4. Aug 19, 2004

### vsage

I'm pretty sure the OP doesn't need to take all that into consideration if he's asking the formula for a scuba tank, but red_Fox77 is correct. Depending on what units the pressure's in, the ideal gas constant is 8.314 J/(K*mol) or 0.08206 L*atm/(mol*K). You can pretty much derive any other R's in terms of these two but I can't imagine why you'd see one not in this form. I never saw a problem in chemistry that wasn't one of these two R's.

5. Aug 19, 2004

### reilly

A gallon's volume is about 0.8 cubic feet, with a weight for water of 8.6 lbs.
Regards,
Reilly Atkinson

Last edited: Aug 19, 2004
6. Aug 19, 2004

### jimwig

water is 8.35 pounds/gallon

7. Aug 19, 2004

A scuba tank has only one hemispherical side, the other side is flat, it even curves inward a bit. The real formula is:

$$V = \frac{2}{3}\pi r^3 + \pi r^2h$$

8. Aug 19, 2004

### chroot

Staff Emeritus
You really don't need to calculate this -- all scuba tanks are made with standard internal volumes. There are several standards, but you should be able to just look up the internal volume from the manufacturer. The most common cylinder used in the US, called the aluminum-80 (AL80), holds 80 cubic feet of air at its working pressure of 3200 psi.

- Warren

9. Aug 19, 2004

### chroot

Staff Emeritus
And if you already know the volume, as you claim, the formula is quite simple. If you fill the cylinder to 200 atmospheres, it's holding 200 times as much air as it'd have at 1 atmosphere, when the tank is "empty." If it's a 10 liter cylinder, for example, it'll hold 2,000 liters of air when filled to 200 atmospheres.

- Warren

10. Aug 19, 2004

### Zorodius

It's probably worth pointing out that the ideal gas law is actually V = nRT/P, where n is the number of moles of gas present - probably the most important number, if you're interested in how much air is actually available to breathe.

The tank doesn't contain pure O2, either - from HowStuffWorks:

Typical recreational SCUBA divers breathe either compressed air (78 percent nitrogen, 21 percent oxygen) or an oxygen-enriched, nitrogen-oxygen combination called Nitrox (64 to 68 percent nitrogen, 32 to 36 percent oxygen). The gas is contained in a cylinder that you carry on your back. The typical cylinder is made of aluminum, weighs about 31 pounds (14 kg) empty and holds 80 cubic feet (2,265 L) of air at 3000 pounds per square-inch (psi), or 204 atmospheres (ATM). This volume of gas would approximately fill a phone booth and weighs about 7 pounds (3.2 kg).

11. Aug 19, 2004

### GOD__AM

Yes aluminum tanks are flat on bottom, but steel tanks are 1/2 round as said earlier. Also steel tanks may have a concave bottom as you suggest but not aluminum in my experience. Mostly I see those concave bottoms on large tanks like they lease at welding supply stores.

As chroot said the working pressure and the cubic foot should be stamped on the tank. Working pressure for an al80 is 3000 psi though not 3200...most shops will fill tanks a little over service pressure because the tanks heat up when filled and report more pressure because of the temperature.