Physics in diving (2): Underwater pressure and gas compression

We can all feel it in our ears when we descend for a dive, or when we ascend at the end of a dive. The pressure changes with depth.


Water pressure
At sea level, the pressure is 1 atmosphere or 1 bar. This pressure is caused by the weight of all these kilometers of air in the atmosphere above us.
In water it works the same. The weight of the water above us determines the pressure working on us. As a rule of thumb, every 10 meters we descend, the pressure we endure increases with 1 bar.
It is easy to calculate the pressure at any depth. Just divide the depth you are at by 10 and don't forget to add 1 for the pressure the atmosphere is already giving you.

So at 10 meters the pressure is 10/10 + 1 = 2 bar. In the table there is more.

Depth	Pressure
Surface	1 bar
10 meters	2 bar
20 meters	3 bar
30 meters	4 bar
40 meters	5 bar

So why is it important to know the pressure underwater? For one, when diving with enriched air, the pressure is needed to calculate the partial pressure.
An understanding of pressure , together with gas compression, is also needed to better understand the changes in buoyancy when changing diving depth.

Gas compression

Gas compression is very convenient in diving. It makes that you can stay underwater as long as you do. By compressing air into your tank you can take air with you to stay underwater for a long time. How does that work?

Boyle's law
Boyle's law states that at any given temperature the product of the pressure and the volume of a certain amount of gas, is constant:

P1*V1 = P2*V2 = constant 

So let´s say your underwater at 10 meters and the air in your BCD is has a volume of say 9 liters. When you descend to 20 meters, the water pressure will increase from 2 bar to three. The air pressure in your BCD will take on the same pressure. This pressure will make the volume of the air in your BCD change from 9 liters to 6 liters. 

The other way around, when you go to the surface the water pressure will decrease from 2 to 1 bar and the volume in you BCD will increase to 18 liters.

Boyle´s law can be corrected for temperature influences. This results in the combined gas law:

P1*V1/T1 = P2*V2/T2 = constant

Because when diving, temperature differences aren't that big (unless you pass through a thermocline), I will explain the temperature influence with an example of filling your tank.

You might have noticed that after you've fill your tank at the dive center, your tank feels a bit hot. Let's say that you filled your tank to 200 bar. 

Then later on when you have set up your gear to go diving and check your air supply, you might notice that your tank has cooled and when you check your air supply you will notice that you have less than 200 bar in your tank.

That is the temperature effect working. The volume of your tank is still the same, the temperature has dropped a bit, so only the pressure can decrease to make the formula work.

Pressure, compression and buoyancy

So when you change depth, the water pressure changes and the volume of air in your BCD changes with it. These changes have a direct influence on your buoyancy. Your buoyancy is dependent on your weight and volume. As your weight doesn't change when you change depth, only the air volume in your suit and BCD has an influence on your buoyancy.
When you go deeper the volume in your CD will decrease, as will your buoyancy. That is why you will have to add air to your BCD to compensate for the volume lost by the pressure. Also, when you go up, you'll have to release some air, otherwise your buoyancy will be too positive and you will shoot to the surface, with all risks that come with that....


Relates subjects:
Physics in diving (1): Buoyancy