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I've been reading a lot about lost World War II submarines, and in the book I'm reading, they discuss the use of a diving bell to go down 5 miles to the ocean floor. I have a couple questions about what would happen at that level, if one were to dip their foot into the water. So here are my questions, assuming a diving bell with an open bottom, and a depth of 5 miles underwater:

  1. Would the water pressure be so great, that it would not be possible to even dip a foot into the water? Would it be like trying to dip your foot into solid concrete?

  2. If it would be possible, what would happen to your foot once dipped in the water? Would the pressure crush it?

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  • $\begingroup$ Humans cannot live at that depth. Research Wikipedia for maximum submersion depth that any human has ever been to, and you will find that it is FAR less than 5 miles. $\endgroup$ – David White Apr 6 '18 at 2:01
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    $\begingroup$ Nothing happens that didn"t already happen inside the diving bell because the pressure inside and out are the same $\endgroup$ – Lewis Miller Apr 6 '18 at 2:10
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    $\begingroup$ Your foot would get wet. Of course, you wouldn't notice because you'd be dead already. $\endgroup$ – Hot Licks Apr 6 '18 at 2:14
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You won't be able to get to the situation you describe in the first place. No matter what depth the diving bell is at, the pressure inside the bell is the same as that outside the bell. This applies even though the pressure inside the bell is due to air and the pressure outside is due to water.

In other words, by the time the bell gets to 5 miles deep, any human occupant of the bell would already have been crushed. Something that's capable of surviving at that pressures however (e.g., a robot) would be able to enter the water without problems.

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  • $\begingroup$ A blobfish would also suffice. $\endgroup$ – probably_someone Apr 24 '18 at 20:33
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The ideal gas law applied to this case says that $$ \frac{PV}{T} = const$$ so $$ V_{bottom} = \frac{T_{bottom}}{T_{surface}} \frac{P_{surface}}{P_{bottom}} V_{surface}$$

The temperature difference between the surface and the ocean floor is pretty minimal, especially compared to the vast relative difference in pressure; $P_{surface}=1$ atm while $P_{bottom}\approx 800$ atm at a depth of 5 miles.

This tells us that if you start with a diving bell which contains 5 cubic meters of air, then at the bottom of the ocean, the air will be compressed to a volume of a soccer ball, and the air pressure would equal the water pressure at roughly 800 times normal atmospheric pressure. So... squish.

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The human in the bell would indeed be dead before reaching a depth of 5 miles, but not from being crushed or squished. A uniform increase in pressure throughout the body does not cause structural stresses. Rather, death would be caused by oxygen poisoning. If that could be gotten around, there are probably any number bodily functions necessary for survival that would be interfered with by the tremendous pressure. Other than that though, dipping your foot in the water would be no different than at the surface.

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