At the surface, the atmosphere exerts a pressure of about 1 bar. Each 10 metres of sea water adds about another bar, so at 30 m the pressure on you is 4 times the pressure at the surface.
Your body is mostly water, which barely compresses, so pressure has little effect on its size. Gas compresses easily. Three laws, each more than 200 years old, describe what pressure does to the gas in your lungs, your cylinder and your blood. All decompression theory is based on them.
A balloon at the surface
A balloon of air tied off at the surface keeps its size because the air inside pushes outward with the same pressure as the atmosphere pushes inward: 1 bar.
The deeper you take the balloon, the more water there is above it and the higher the pressure on it.
10 m: double the pressure, half the volume
At 10 m the pressure on the balloon has doubled to 2 bar, and the same air occupies half the volume.
This is Boyle’s law: for a fixed amount of gas at constant temperature, pressure multiplied by volume stays constant. If the pressure doubles, the volume halves.
30 m: a quarter of the volume
At 30 m the pressure is 4 bar and the balloon is a quarter of its surface volume.
The curve flattens with depth. The first 10 m halved the volume; the next 20 m reduced it by only another quarter. The change in volume depends on the ratio of the starting and final pressures, so each metre has more effect near the surface than deeper down.
The last 10 m of an ascent
On the way up, the pressure halves between 10 m and the surface, and the volume doubles. This is the largest change of the whole ascent, and it happens in the last 10 m.
Your lungs follow the same law. A breath held during an ascent expands and can rupture the lung. For this reason the first rule of diving is never to hold your breath while ascending.
Partial pressure and dissolved gas
Boyle’s law gives how much a gas is compressed. The next two laws deal with the individual gases in a mix: Dalton’s law gives the pressure of each gas you breathe, and Henry’s law gives how much of it dissolves in your blood.
- Oxygen
- Nitrogen
- Helium
Partial pressure
Air is about 21% oxygen and 79% nitrogen. At the surface the 1 bar of pressure divides in the same proportions: 0.21 bar of oxygen and 0.79 bar of nitrogen.
Each gas’s share of the total is its partial pressure. Dalton’s law states that the partial pressures of the gases in a mix add up to the total pressure.
Partial pressures at depth
At 30 m the total pressure is 4 bar. The mix is unchanged, so each gas has the same share of a larger total: 0.84 bar of oxygen and 3.16 bar of nitrogen.
The effects of a gas on the body depend on its partial pressure, which depends on both its percentage and the depth. Air that is harmless at the surface is narcotic at depth, and the oxygen in it can reach toxic levels.
Helium in deep mixes
For deeper dives, divers change the mix. In trimix 18/45 at 60 m, helium replaces most of the nitrogen, which reduces narcosis. The lower oxygen fraction keeps the oxygen partial pressure under the working limit.
At 7 bar the gas is still dense: its density is above the engine’s advisory level for breathing effort. See Oxygen and Narcosis and gas density.
Henry’s law
A liquid in contact with a gas dissolves some of that gas. Henry’s law gives the amount: given enough time, the quantity dissolved is proportional to the gas’s partial pressure.
Your blood and tissues are such a liquid. Breathe air at 30 m for long enough and they hold about 4 times as much nitrogen as at the surface. How long is long enough is the subject of tissues and half-times.
Pressure release and bubbles
A sealed bottle of soda contains carbon dioxide dissolved under pressure, and no bubbles are visible. When the cap is removed, the pressure falls at once. The liquid now holds more gas than it can keep in solution, and the excess forms bubbles.
An ascent reduces the pressure on your tissues in the same way. If you ascend slowly enough, the excess gas is carried by your blood to your lungs and breathed out. If you ascend too fast, it can form bubbles in the body. That is decompression sickness.
Try it
Choose a depth and a mix. The bar shows the ambient pressure, divided by gas. The gauges show the oxygen partial pressure and the density of the gas you would be breathing, against the engine’s limits. Try air at 60 m, then find a trimix that brings both gauges back under their limit marks.
What to remember
- Pressure rises by about 1 bar for every 10 m of sea water, in addition to the 1 bar at the surface.
- Boyle: the volume of a gas falls as the pressure on it rises. The largest change is near the surface, so never hold your breath while ascending.
- Dalton: each gas in a mix exerts its own partial pressure, and the partial pressures add up to the total. The body responds to partial pressure, which depends on both the percentage and the depth.
- Henry: given enough time, a liquid dissolves a gas in proportion to its partial pressure. If the pressure is reduced too quickly, the gas comes out of solution as bubbles.
The mix limits tool
DiveLogic’s mix limits tool applies Dalton’s law to a real mix. For any mix, it gives the depths at which the oxygen, narcosis and density limits are reached, using the same engine that drew these figures.
Sources
- Boyle R. (1662). A Defence of the Doctrine Touching the Spring and Weight of the Air. Oxford. (Published with the second edition of New Experiments Physico-Mechanicall, Touching the Spring of the Air.)
- Dalton J. (1802). Experimental essays on the constitution of mixed gases. Memoirs of the Literary and Philosophical Society of Manchester 5(2): 535-602.
- Henry W. (1803). Experiments on the quantity of gases absorbed by water, at different temperatures, and under different pressures. Philosophical Transactions of the Royal Society of London 93: 29-42.
- Anthony T. G., Mitchell S. J. (2016). Respiratory physiology of rebreather diving. In: Pollock N. W., Sellers S. H., Godfrey J. M. (eds), Rebreathers and Scientific Diving. Proceedings of the NPS/NOAA/DAN/AAUS workshop, Durham, NC. (Gas density and breathing effort.)