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If I put a couple of lead bricks on my foot, there would be a definite sensation of a heavy, perhaps even painful, force. Calculating the pressure for $20 kg$ of lead over a $100 cm^2$ area of my foot, I get about $20 kPa$.

Now I stand underwater in a pool. If my foot is $2 m$ below the surface, then the hydrostatic pressure would be $\text{density} \times \text{depth} \times \text{gravity}$, or $20 kPa$. Same as above. But in this case I wouldn't feel any pain or high pressure on my foot. Why the difference in sensation when under water, even though the pressure is the same in both cases?

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  • $\begingroup$ This is a question about perception by the nervous system of surroundings and should not be in a physics.SE , though interesting as a question. My guess is that the body sees differentials and not absolutes, and as the pressure along the leg changes with depth it does not register the weight the way it would on land. $\endgroup$
    – anna v
    Commented Dec 20, 2012 at 7:15
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    $\begingroup$ Oh, I think the question belongs here and we will see some nice answers :) $\endgroup$
    – Robert Filter
    Commented Dec 20, 2012 at 9:42

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You should feel the water pressure too, but much weaker. The difference is that water pressure is isotropic and does not "deform" the body in one direction but does it uniformly - uniformly shrinking it from all directions.

Consider the animals that live very deep. They are like "baloons filled with water" (and we to some extent too). I guess the pressure does not hurt. It is deformation of the body that hurts. If you consider baloon filled with water it is pretty easy to deform it (hence cause pain) preserving the volume, but much more difficult to uniformly shrink it (as this changes the volume)

IMHO very interesting physical question

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While the other answers make some very relevant points about pressure, there really is an important physiological dimension to your question. If you look up Pressure Pain Threshold (PPA), or Algometer, you will get a host of references. I am going to go, e.g. with this one, to say that the PPA is normally a few $kg/cm^2$, around 3 in that reference. That is loosely equivalent to $3\ \mathrm{atm}$. So pain would therefore start somewhere around $30\ \mathrm{m}$ below the surface, which is a long way to go underwater, not something most of us have even been close to experiencing. I don't think it really does, due to the reasons others have outlined, and free diving depth records are getting close to ten times that depth, and I'm pretty sure it is not pain threshold that makes those athletes exceptional.

But the differences you are describing probably have much more to do with the pressure of the $20\ \mathrm{Kg}$ of lead not being evenly distributed over the whole surface of your skin, but concentrated on a few much smaller pressure spots.

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    $\begingroup$ +1 for the uneven distribution. Even Hobbits don't have $100\ \mathrm{cm}^2$ of flat surface area on their feet (I think). $\endgroup$
    – user10851
    Commented Dec 20, 2012 at 23:42
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I would guess (and it's only a guess) the nervous system responds to shear stress rather than an isotropic pressure. Since the body is mostly incompressible, immersing it in water produces little or no shear stress and hence no perception of pressure.

This bits of the body that are compressible (because they contain air) are the chest cavity and the sinuses in the head, and experience suggests that if you swim underwater you do feel a sensation of pressure in your head and chest. Divers use pressurised air to relieve this pressure difference/shear stress.

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