# Boyles Law Explained for Freediving

# Dr Otter’s Physiology Bootcamp

## Lesson #2 - Boyle’s Law

Robert Boyle was an Irish alchemist who lived through one of the most important periods in Western history, the scientific revolution. His law relating the pressure, temperature and volume of a gas is now an essential part of our understanding of what happens to our bodies as we dive, whether on a single breath, or on Scuba. He was also a very good looking chap. Here he is in his Sunday best:

Boyle’s law is extremely important for divers, and freedivers in particular to understand. It explains many of the phenomena that we experience whilst freediving, including concepts like “shallow water blackout” (coming next!), “failure depth” (coming soon) and “decompression injury” or DCI (coming later). Put simply, Boyle’s law means that where temperature remains constant (like it does inside the human body), when the volume of a gas decreases, its pressure increases. We can see that immediately if we think about what happens in a bicycle pump: Let’s imagine for a second that instead of being open at one end, the pump is completely closed. That’d be what happens if you put your finger over the end of it. Don’t know about you but I’ve had hours of fun doing that…

See how as the volume of the pump gets smaller, the molecules that make up the air inside inside it get pushed together? More on that in a minute, but hopefully it’s pretty easy to see that if you take your finger off the hole, lots of air will rush out:

That’s because with your finger over the hole and the handle pressed in, the pressure inside the pump is higher than the surrounding air. By removing your finger, you make the inside of the pump continuous with the outside, allowing the pressures to equalise. Simple so far. As we descend under the water, the pressure around us grows and the volume of the lungs decreases in proportion to the increase in pressure: when the pressure doubles, the volume of the lungs halves. When the pressure trebles, the lung volume becomes three times smaller, and so on. As we discussed in a previous post, the normal atmospheric pressure is 1bar, 1atm or 100kPa depending on which units you want to use. After that, for every 10m you descend underwater, the pressure increases by 1atm, 1bar or 100kPa which means that in the first 10m of a dive, the pressure around you doubles. Guess what happens to the volume of the lungs? Here’s a picture that’s used so often in diving education that instructors the world over see it in their dreams. It neatly summarises the points above, comparing the lungs to a gas bubble. But more on that later.

## But What Is Pressure Anyway?

This is a really good question. Pressure can be thought of in a number of different ways. In its simplest form, pressure is given by the equation:

When we’re talking about a gas or a fluid like water, we can think of the ‘force’ part of the equation as the weight of the ‘column’ of fluid pressing down on a point of a given size, hence the unit of pressure: pounds per square inch. This is nicely demonstrated by the simple experiment of filling a tube full of water and punching holes at different heights:

Notice that the jet at the bottom of the column travels the furthest because the pressure acting on it (caused by the weight of water pressing down) is highest at that point.

For a cylinder full of gas, the situation is the same, but we have to think about it in a different way to make sense of it, because the difference in weight at the bottom of the column compared to the top is tiny, unless the column is very very large:

An easier way to consider pressure differences in small volumes of gas (like the lungs for example) is to consider the way that pressure is generated at a molecular level:

The molecules of every gas in the universe, by definition, are moving very fast. When the gas is contained in something (like the lungs), pressure is generated by the collisions between the molecules that make up the gas, and the walls of the container. The larger the number of collisions per second, the higher the pressure.

This is the essence of Boyle’s law. If you want to look really smart, though, read on!

## The Mathematics of Boyle’s Law

Let’s go back to the bike-pump example.

Notice that the volumes and pressures are written as P_{1}, V_{1}, P_{2} and V_{2}. Boyle’s law can be expressed mathematically by saying that:

So, if you know the original pressure and volume, and you change the pressure, you can work out the new volume by dividing by the new pressure:

This is really useful in diving:

## Boyle’s Law and Diving

As you descend under the water, the pressure above you grows. That’s because of the weight of the water pressing down on top of you, as we said earlier. Remember from the last lesson that pressure can be measured in atmospheres? That’s because normal atmospheric pressure (100kPa) is caused by the weight of all the air in the atmosphere pressing down on us. 100kPa is the pressure exerted by the column of air (about 100km high) between the surface of the earth and outer space. Water is much denser than air, so a short column of water will exert the same pressure as a much longer column of air. In fact, the column of water required to exert 1atm of pressure is about 10,000 times shorter than the column of air it takes to exert the same pressure: 10m compared to 100km. So, for each 10m you descend under water, the pressure around you increases by 1atm (100kPa).

So that’s it for this week. Next time we’ll look at the Bohr shift. Got a burning physiology question? Dr Otter is ready and waiting for it. Drop us an email at info@freedive-earth.com, post on our Facebook page or comment below. See you next time!