## Wednesday, April 7, 2010

### NO DUMB QUESTIONS, MAY 2010: A PHYSICS PRIMER FOR SCUBA DIVERS

by Alex Brylske
Photo by Joseph C. Dovala

Q: Al Pinzon had a question about tank capacity. “My wife and I are recently certified Open Water divers. I use an 80 tank and my wife uses a 50. Our question is how do we know exactly how much air is left in our tanks at the conclusion of a dive? Even though each of our submersible pressure gauges (SPGs) may both read 500 psi, we know we don’t have the same amount of air. So how do we determine the amount of air left in the smaller tank so my wife doesn’t risk running out of air?”

A: There’s a very simple way to convert psi to cubic feet. Just take the capacity of the cylinder in question and divide it by its maximum working pressure. The product is, in essence, how many cubic feet of air is accounted for by each “psi.” Let’s take the standard 80-cubic- foot cylinder as an example. By dividing 80 (its maximum capacity) by 3,000 (its maximum-rated pressure) we get 0.0266. In other words, we can assume that each psi of pressure accounts for 0.0266 cubic feet of air. Thus, if the tank is filled to only 2,000 psi, rather than its maximum 80 cubic feet, it contains only 53.2 cubic feet (2,000 X 0.0266).
In the case of your wife’s 50-cubic-foot tank, the value is 0.0166 (or if she uses the more standard 63 cubic footer it’s 0.0210). Therefore, if you each end your dive with 500 psi remaining, you have 13.3 cubic feet of air left but your wife has only 8.3 cubic feet.

Of course, even though your wife would have less air remaining, it’s likely she also uses less air, which is why you can both plan to exit the water with 500 psi. So, with all things being equal, you’d both have about the same usable reserve in terms of time underwater at the same depth.

More questions after the break...

Q: Carl Kroenig had another question involving physics — it also involved scuba tanks — but from the perspective of buoyancy. “I have one of those questions that seems to be logical, but when I try to visualize it in my mind, it doesn’t seem to make sense. So here it is: If you take a finite amount of air with you underwater, why does it affect your buoyancy only when you inflate your BC? You’re not adding anything you didn’t already have. I’m sure this must have to do with why your tank gets lighter at the end of the dive, but that’s a bit confusing to me as well. You’re probably not surprised that I didn’t do too well in school when it came to science.”

A: Don’t be so harsh on yourself; lots of phenomena are counterintuitive when it comes to diving physics. In a sense, you can ask your question in a different context: Why does a 1-pound diving weight sink like a stone, yet something as large as a ship float? Or, better yet, how could you make a 1-pound piece of lead float? The answer, of course, is to change its volume.

You’re absolutely right; every diver begins a dive with a finite amount of air. But it’s what we do with that air that determines its effect on buoyancy, and it happens in a couple of ways. First, as you’ve no doubt noticed, subtle changes in your buoyancy occur when you breathe underwater. On inhalation, you tend to rise (become slightly more positive) and on exhalation you tend to sink (become slightly more negative). The reason is that your chest cavity expands and contracts while breathing, thus slightly changing the amount of water you displace. More displacement equals more buoyant force, and less displacement means less force.
Perhaps the confusion comes from how we refer to tanks, using their potential volume of air at the surface. For example, while a standard scuba tank contains the equivalent of 80 cubic feet of air — about the size of a small closet — that large volume of air is compressed into a very small area (that’s why there’s so much pressure within the tank).

Therefore, while something with the volume of a small closet might float like a cork, a full standard scuba cylinder does not because it weighs more than the water it displaces. But while the volume of your tank doesn’t change, there is something else that does besides your chest cavity: your BC. Inflating your BC increases its volume (displacement), and therefore your buoyancy, while deflating it decreases your buoyancy by decreasing the BC’s volume.

The second part of your question — why empty tanks weigh less than full ones — is because of yet another counterintuitive characteristic of air, and that’s that it has weight. In everyday life, it’s easy to think of air as “weightless,” but it’s not. (The weight of air is also why we have atmospheric pressure.) In fact, 80 cubic feet of air weighs about 4 pounds. That means that at the end of your dive, when your air supply is nearly depleted, your tank is about 4 pounds lighter, and therefore more buoyant, than when you began your dive. As anyone can tell you who has tried to maintain a safety stop with a near-empty tank, and didn’t start the dive with a little extra weight to compensate, that little bit of weight (or lack thereof) makes a big difference. This difference in displacement is why it’s important to determine the amount of weight you need using a near-empty about 500-psi)tank, rather than a full one.

Q: Heather Walters wrote with an incident that any traveling diver might encounter. “I recently returned from a trip to Thailand. Diving was only a small part of what my husband and I did, so we chose not to take any dive gear except our masks (we both have prescriptions). We expected to use rental gear, and were pleased to find that the equipment they provided was top-notch. However, there was one thing we forgot to consider. The dive operator catered mainly to Europeans so the gauges were all in metric units. Reading my depth in meters and making the mental translation to feet was tough but I finally figured that out well enough. But having to deal with pressure readings from my SPG in bars rather than psi made me constantly think that I was low on air. A full tank, which contains only 200 bar, seemed somehow disconcerting. Is there any quick way to make the conversion to psi?”

A: Although converting from one system of measurement to another is a simple matter of using the right formula, pulling out a pencil and calculator isn’t very practical when you’re 100 feet (excuse me, 30
meters) down. Rather than mathematics, I’ve always preferred some quick-and-dirty method of guesstimating the conversion.

Probably the best way to deal with tank pressure, for those of us schooled in the Imperial system, is to keep in mind that a “bar” equals an atmosphere, which equals about 15 psi. (OK, those values aren’t exactly equivalent, but they’re close enough for government work and recreational diving.) Using this rough equivalency guide, 200 bar is equal to 3,000 psi (15 X 200). That, of course, means that 100 bar is equal to 1,500 psi, and 50 bar equals 750 psi. So, when I’m using a metric SPG, I just remember three things: A full tank is 200 bar. A half-full tank is 100 bar. And 500 psi — the typical “return to surface” value in most circumstances — is about 35 bar. It’s kind of like watching the fuel tank on your car. Each gallon that you use isn’t accounted for, but knowing the major increments (full, half, quarter, red zone) works fine. Someday the United States will join the rest of the world in the much more sensible metric system but, as in diving, don’t hold your breath until that happens.”

Q: Jessica Fajan wrote in with a question on air consumption that I address routinely at least once every year. So, for this year, here it goes. “I’m not an advanced diver so please forgive me if this is a really stupid question. I know from practical experience that I get less air as I go deeper, but I don’t really understand why. I kind of understand all that stuff about decreasing volume with depth, but my tank certainly doesn’t decrease in size when I dive deeper. A tank of air is a tank of air, so what gives?

A: First of all, this column is called No Dumb Questions for a reason: The only dumb question is the one you don’t ask. It’s also easy to understand why you’d be confused given all that’s drummed into a diver’s head about pressure/volume relationships in relation to lung and sinus injuries. Actually, it’s the same principle with air consumption, but what’s confusing is how the pressure/volume relationship applies.

Now, if pressure increases, as it does during descent, the volume of a container decreases, but only if that container is flexible (like our lungs). The volume of a rigid container like a tank, as you stated, remains unchanged with descent, so the internal volume of a tank is the same whether it’s at the surface or at depth.
The reason we get less air out of a tank as we descend has nothing to do with what happens to your tank; it’s because of the effect of pressure on another item of equipment, your regulator. No matter your depth, your regulator always delivers air to you at the same pressure as the surrounding water. As the ambient water pressure increases, the regulator responds by drawing more molecules of air from the tank. For example, if each breath you take at the surface takes X number of molecules, then it will take 2X to fill your lungs at 33 feet (2 ATA).

At 66 feet, three times the number of molecules are required compared with at the surface. So, you see where this is going — as you go deeper more air is used to fill your lungs. That’s why the tank will last only about half as long at 33 feet, one-third at 66 and one- fourth at 99 feet. As you rightly surmised, it has nothing to do with the tank being “squeezed.”

#### 1 comment:

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