The Pressure, Volume, Density relationship.

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The Pressure, Volume, Density relationship.

Welcome to Physics class! 

One of the questions we hear often is "how long will we be able to stay down on this dive?" 

This is a difficult question to answer with all of the factors involved, but we can estimate! Fundamentally, this concept is the Pressure, Volume, Density relationship. There are many things in scuba that refer back to this relationship in our underwater environment. If we break down the three definitions first, we can then look at how they apply to scuba divers. 

Pressure - This is the force per unit area of the object on which the force is being exerted. It is defined through the equation: P(pressure) = F (force) / A (area). We don't often think about the pressure that is exerted on us by the weight of the air above us and then the water when we submerge. But, it is there!

In liquid and gasses, we find that pressure is exerted equally in all directions. This is due to their molecules being in flux and moving differently from a solid. For a scuba diver, we find that every 33ft the pressure will become equivalent to 1 atmosphere (1ATA - or 1 Atmospheres Absolute). So, imagine all of the air stacked above you as you look skyward. That is a force that is exerted on you every day of your life. As you descend into a "thicker" medium (i.e. water), the weight of the water becomes a factor for you. So, you are dealing with higher pressures as you descend into the depths! 

Volume - This is defined as the amount of space that a substance or object occupies. There are many examples of this for a scuba diver. We have air spaces in our bodies. When we dive down, we can feel the pressure changes because our ears and our sinuses are quickly affected by the application of pressure onto areas of our body that are flexible. Luckily, our body is a flexible container. We can react to the volume changes through such things as a valsalva maneuver to equalize our sinuses to the surrounding area. Our scuba tank is a inflexible container that is under pressure itself. The volume inside is also affected as the tank goes deeper. When I describe volume to Open Water students, we talk about a balloon. When that balloon is filled with air, it occupies a space that we can now see. There is a bit of pressure in the balloon, but the molecules inside are trapped. As we descend with that balloon, it will actually shrink. The molecules didn't go anywhere. They simply became closer. Thus, creating the smaller volume. 

Density - Finally, we get to density. This is the mass per unit volume of an object. Remember the balloon? Well, as I said, the descending balloon didn't magically make molecules disappear. It just brought them closer together through pressure. So, as the balloon shrinks (volume) from the pressure of the water (pressure), it creates a more dense effect on the molecules inside the balloon (density). To mathematically define it, Density = mass / volume. 

There are some other affects we see with this relationship. As gas molecules come together under pressure, they become agitated and actually create heat. The inverse is also possible. This is why your tank heats up when it is filled (what some people call a hot fill). The same is true for when you rapidly empty a tank. The cooling effect will actually freeze parts of a cylinder if you open it all the way up. This is because a massive change in the environment (releasing or increasing the pressure) has affected the molecules. 


Application - So, how does this affect us? Well, as we go deeper underwater, we see that a scuba tank will be unable to last as long on a dive. Because this pressure is affecting the volume of the scuba tank while simultaneously demanding more air from the user because their lung capacity has changed with the environment. 

If we refer to the image below, we find that every 33ft of depth something occurs. It is relatable in its occurrence as well. At 33ft, the pressure doubles for your body and your scuba tank. Meanwhile, the volume of the gasses becomes 1/2 what they would be on the surface. And, remember the balloon (the molecules went nowhere); we are experiencing twice the density. 

So, as you breath in, you are receiving twice the amount of air into your lungs than you would on the surface. 

This effect is why we pay so much attention to breathing underwater safely. You'll hear the term, "Never hold your breath". This is because our lungs are now adapted to the environment while we are actually breathing in twice the amount of gas. So, if we were to hold our breath and ascend, the expectation is that our lungs will expand to twice their size from 33ft to 0ft. This is an obvious issue and one that makes this all make sense now! 

We can deduce numerous things for that simple question we asked in the beginning. Let's say that we were descending to 66ft on a dive. What we can estimate is how long that tank could last. For ease of math, let's say that it takes you 60 minutes to breath down a cylinder of air at the surface. If you were to take that same cylinder of air down to 66ft, you can estimate that it will perform 1/3 of that capability. Or, 60/3 = 20 minutes. Obviously, there are a lot of factors involved with determining the question (your lung volume, breathing rates, etc.), but you can generally answer it now with an understanding of the Pressure, Volume, Density relationship.

Should you need any help with these types of questions as you move forward in your scuba life, let us know! We are happy to help you get through physics and train you further! 

David "D.J." Mansfield is a PADI Course Director, Technical Diving Instructor Trainer and the Director of Operations for Beach Cities Scuba. He spends his days working inside the industry and training divers all over the world. You can follow him on Instagram @djmansfield77 or catch him at the dive shops any time. 

If you have suggestions on the writing, let him know at! 

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