Question

In 2010, 33 miners in Chile were trapped by a collapse 700 meters underground. Their dramatic and successful rescue more than two months later was broadcast throughout the world. During the rescue, media personalities and medical experts commented that their 15 minute journey to the surface would require careful avoidance of “decompression” sickness or “the bends”, akin to scuba diving. You will calculate the severity of this rescue in this context.

a) Calculate the change in pressure (in hPa) experienced by the miners being lifted to the surface. Use a standard atmosphere scale height for these purposes. For reference, 1013 hPa = 1 atmosphere.

b) Calculate the change in pressure (in hPa) experienced by a scuba diver when ascending from 30 m below the water to the surface, an ascent where “the bends” can occur and become a lifethreatening problem. Use a nominal density of pure water for this calculation.

c) Comment on the differences between these two numbers and the extent to which the miners needed to worry about decompression sickness. For reference, airplane cabins are typically set to a pressure altitude of ~ 2 km above sea level when at cruise altitude.

Answer 1

a) The air pressure difference experienced by the miners will be calculated as

Where,

= change in air pressure

= density of air = 1.2041 kg/m³

= acceleration due to gravity = 9.8 m/s²

= change in altitude

So,

b) The pressure difference experienced by the scuba divers will be calculated as

Where,

= change in air pressure

= density of seawater = 1029 kg/m³

= acceleration due to gravity = 9.8 m/s²

= change in depth

So,

c) As we can see, the pressure difference due to seawater is nearly 37 times larger for a much smaller depth in sea, the risks of developing bends for scuba divers is more life threatening. As pressure increases, the solubility of oxygen in blood increases too. While ascending, the pressure drops and the dissolved oxygen in blood is released as bubbles. These bubbles might block the arteries and cause seizures or stop the blood flow altogether. This becomes a life threatening situation. On the other hand, the miners need not worry about such situation because risk of bends is far too less for them.