What is the relationship between Boyle's Law and Scuba Diving? Balloons are used in this example.

One of the main concepts of physics explained in scuba diving is Boyle’s Law. At a glance, it is a simple expression of a pressure and volume relationship of gases. It can, however, get complex. For the purpose of this article, we are going to keep it simple. What exactly is the relationship between Boyle’s Law and scuba diving? And how does it affect us as scuba divers?

Boyle’s Law and Scuba Diving

Even though Richard Towneley and Henry Power first noted the relationship between pressure and volume in the 17th century, it was Robert Boyle that confirmed their findings by conducting experiments. He reduced the volume of a closed gas container using mercury and noted the proportional relationship or pressure and volume.

We don’t have Mercury available. So what about a balloon? We have a closed container of gas. Now if we were to pull this balloon underwater, the water pressure increases linearly with depth. That means our flexible, closed system of gas (balloon) will decrease in volume the deeper we pull it.

This looks like this:

Boyle’s Law Table

Depth

Surface

10m

20m

30m

40m

Pressure

1 bar

2 bar

3 bar

4 bar

5 bar

Volume

1

1/2

1/3

1/4

1/5

Density

1x

2x

3x

4x

5x

What is Boyle’s Law Formula

Now that we know that we are talking about a law that describes the volume of a fixed amount of gas in a closed container when the pressure changes, we know we need pressure and volume as parameters in our formula.

So that leaves us with starting volume & starting pressure and leaves us with ending volume & ending pressure. Therefore this is what the Boyle’s Law formula is:

P1V1 = P2V2

Where P1 is first pressure, V1 first volume and after the change we have P2 for the second pressure and V2 for the second volume.

Let’s apply this formula to a dive where we take a balloon with us.

The balloon at the surface is 2.3 litres in volume and we are at the surface, so 1 bar of absolute pressure.

We want to dive to 32 meters with this balloon. Therefore, according to the Boyle’s law formula, we have:

P1V1 = P2V2 and can therefore use V2 = P1V1 / P2

(1*2.3) / 4.2 = 0.5476

This means that the new volume of the balloon at 32 meters depth would be about 0.55 liters.

Since we don’t need to know exact volumes in scuba diving this is overkill. What we do need to understand is that the relationship of gas volume exposed to pressure is proportional. What does this mean for us as divers? For example, we need to add more physical air in order to achieve neutral buoyancy deeper. Furthermore, we cannot hold our breath and ascend. Knowing these facts is why you need to be certified in order to scuba dive.

As a result of gas volume decreasing with increased pressure, we also notice a gas’s density increase. Increased density in breathing gases leads to faster air consumption rates at depth.

Read more about what divers can do for their own safety

LEAVE A REPLY

Please enter your comment!
Please enter your name here