Boyle’s law: pressure and volume

This book starts with pressure. Under water, the weight of the water above you presses on you and on everything you carry. 3 laws of physics describe what that pressure does to the gas you breathe. This chapter covers the first one, Boyle’s law. Chapter 2 covers Dalton’s law and chapter 3 covers Henry’s law.

Boyle’s law in one sentence

When you squeeze a gas, it gets smaller: double the pressure on it and it takes up half the space.

You can feel this with a bicycle pump. Put a finger over the end and push the handle. The air inside gets smaller and pushes back harder. Let go and it springs back.

Pressure under water

Divers measure pressure in ATA (atmospheres absolute, about the same as bar). 1 ATA is about the pressure of the air around you at sea level.

Water is much heavier than air. Every 10 m of sea water adds about 1 more ATA. The total pressure on you, air plus water, is the ambient pressure, also called the absolute pressure. A cylinder or depth gauge that reads 0 at the surface shows gauge pressure, which leaves out that first 1 ATA of air. The gas laws always use absolute pressure.

Every other number in this book starts from the pressure at your depth, so it is worth knowing how to work it out.

DiveLogic’s planner uses the real density of sea water and the air pressure at the dive site’s altitude, so its figures differ slightly from this rule.

Your body is mostly water, and water barely squeezes. The gas you carry does squeeze: the air in your lungs, your ears, your mask, your equipment and your cylinder.

Boyle’s law tells you how much that gas squeezes. Multiply the pressure by the volume before a change, and you get the same answer after it.

Gas spaces in your body and equipment

Boyle’s law applies to every space that holds gas. A diver carries several.

• Lungs. Your regulator keeps your lungs at the pressure around you. If you hold your breath on the way up, the trapped air expands. A rise of only a few metres can overexpand the lungs, most easily near the surface where the change is biggest. This injury is called pulmonary barotrauma. It can push air into the chest or into the blood, where a bubble can block an artery (an arterial gas embolism). Chapter 5 covers it along with decompression sickness.
• Ears and sinuses. Your middle ear is a small air space joined to your throat by a narrow tube. On the way down it gets squeezed unless you push air in through that tube. That is what equalising means. Equalise early and often in the first 10 m, where the change is fastest.
• Mask. Your mask is pressed onto your face as you go down. Breathe out gently through your nose into it to keep it the same size.
• BCD and drysuit. A BCD (buoyancy control device) is a jacket or wing you add air to so you float at the depth you want. A drysuit also holds a layer of air. On the way down this air is squeezed, so you sink more and must add air. On the way up it expands, so you float up more and must let air out. The biggest changes are in the last 10 m.

Gas use at depth

Your SAC rate (surface air consumption) is how much gas you breathe per minute, measured as if you were at the surface. Divers also call it RMV (respiratory minute volume) when it is given in litres per minute. It stays about the same at any depth for the same effort. But at depth each breath holds more gas, in step with the ambient pressure.

So to find your gas use at depth, multiply your SAC rate by the pressure in ATA. If you breathe 15 L/min at the surface, at 30 m (4 ATA) you use 15 × 4 = 60 L/min. A cylinder lasts about a quarter as long at 30 m as at the surface, and about a fifth as long at 40 m (5 ATA). Multiply by the minutes you spend there to get the gas for that part of the dive.

Think of it like packing a suitcase: at 30 m each breath is the same size case, packed 4 times as tight.

With normal scuba, called open circuit, every breath goes out into the water as bubbles. A rebreather recycles your breath, so its gas use depends far less on depth. Chapter 20 compares the two. Chapter 24 covers planning your gas, including the reserve you need to get back to the surface. You can work out the gas for a depth and time with the gas needed tool.

Where the law comes from

Robert Boyle (1627-1691) worked in Oxford. His assistant, Robert Hooke, built him an air pump, and Boyle used it to study the “spring” of the air: how it pushes back when squeezed. He published these experiments in 1660.

In 1662 he trapped air in the sealed end of a J-shaped glass tube, poured in mercury to squeeze it, and measured how much it shrank. Boyle credited the idea to Richard Towneley, who had done similar tests with Henry Power in 1661. In France the same rule is called Mariotte’s law, after Edme Mariotte, who published it on his own in 1676.