The Physics of Scuba Diving and Decompression Sickness

Decompression sickness is a harmful side effect of unsafe SCUBA diving habits. It occurs when a person rises too quickly from a great depth. When exposed to rapid pressure decreases, such as going from a great depth of water to the surface, nitrogen that is dissolved in the blood comes out of solution in small bubbles. When these bubbles are exposed to less pressure as the person rises, they grow larger in the blood stream. Side effects of The Bends can be serious and include blocking blood flow and stretching or tearing blood vessels and nerves. The Bends can affect just about any part of the body ranging from joints, lungs, the heart, skin and the brain.

            Thinking about this, I wondered how much a small bubble could grow when a person was ascending in their dive. With a typical dive depth of 35 meters and assuming unsafe ascending practices as to incite The Bends, I determined the pressure difference between 35m and 0m experienced by the bubble.

Pressure experienced by bubble at 35m:

P=ρgh + P₀

P=(1000 kg/m³) * (9.8) * (35m) + 1.01*10⁵ = 444000 Pa

Pressure experienced by bubble at 0m:

P=ρgh + P₀

P=(1000 kg/m³) * (9.8) * (0m) + 1.01*10⁵ = 101000 Pa

Pressure difference=

Pressure at 0m – pressure at 35m

101000 Pa - 444000 Pa = -343000 Pa decrease.

Next, I wanted to see how this pressure decrease related to an increase in bubble size. I can examine the relationship between pressure and volume of the bubble using Boyles Law. I assumed that at a depth of 35m, the radius of the preliminary bubble would be 0.001m.

P₁V₁=P₂V₂

P₁(4/3)πr³=P₂(4/3)πr³

444000(4/3)π(0.001³)=101000(4/3)π(r³)

At 0m, r=0.002m

This calculation demonstrates that the decrease in pressure caused by ascending to the surface from 35m causes an almost double diameter increase in the bubble. Without taking proper precautions to avoid this, the drastic increase in the nitrogen bubble could have serious implications for the unsafe diver.