diver problem?

Question

A diver rises quickly to the surface from a 8-m depth. If she did not exhale the gas from her lungs before rising, by what factor would her lungs expand? Assume the temperature to be constant and the pressure in the lungs to match the pressure outside the diver's body. The density of seawater is 1.03 times 103 kg/m3.

Answer 1

Atmospheric pressure at sea level is 101,300 pascals. As you go further underwater, the pressure is 101,300 pascals, plus the pressure exerted by all the water above you.

The pressure (from the water alone) as a function of depth is:
p = rho*g*h
where rho = water density, g = gravity, and h = depth

Plugging in our values, we get:
p = (1030 kg/m^3)(9.81 m/s^2)(8 m)
p = 80,800 pascals

So, the pressure 8 meters down is that of the air, plus that of the water:
101,300 + 80,800 = 182,100 pascals

Meanwhile, the pressure at the surface is still 101,300 pascals. The ratio between these two is:
182100 / 101300 = 1.798

So, the diver's lungs will expand by a factor of 1.798. Sounds painful.

Answer 2

If the diver does not mainyain an open airway. The lungs will over-expand. This will cause one of several problems.

The pressure at 8m seawater is 1.8 atmospheres (1 from the atmosphere).
Therefore
pressure*volume being constant (at a constant temperature)

lung volume will increase by a factor of 1.8

It is unlikely that the lungs will cope with this. Hence a lung rupture. The air from this may escape into the central chest area and exert a pressure on the heart, into the external chest cavity collapsing the lung, below the throat causing bubbles to founder the skin or, worse than that, expanding air is forced into the bloodstream (perhaps heading to the brain).


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