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If you were to sink a container to the bottom of a deep ocean and seal it there, then bring it up to the surface, would it retain its pressure?

The answer for a gas is obviously yes, but what about for a liquid like water which is incompressible? Once the crushing weight of the water column above is removed, does the water retain it's quality of "pressurizedness" or return to normal water? I guess a clear way to test this would be to bottle up a deep water fish and bring it up to the surface and see if it explodes.

While we're at it, what about a solid? Barring any elasticity and incidental temperature change, will a solid object break a non-sealed glass container which is exactly fitted to it and then placed in vacuum?

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I pity the fish, though. –  Hanno Fietz Dec 7 '12 at 11:37

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The problem in your post is that you don't consider the force resisting the water pressure, which is exerted by the walls of your container.

To do this, imagine a two-chamber container, with outer walls infinitely strong, but with a piston in between them which is maintained at its central position by some force that you exert. Chamber A is filled with air at sea level and then closed, chamber B is left open as you sink the container. The force you need to exert on the piston raises as you sink it, in proportion with water pressure, say at some depth it is area times $P_1$. Now close chamber B too. You can now bring your container anywhere, this won't change the balance inside.

And you can still exert the same pressure $P_1$ on the piston, and water is under pressure $P_1$. But you can also vary this pressure on the piston, to any value you like and bring the water to some other pressure level, without having any movement of the piston (as long as you remain in the incompressibility regime). In particular, releasing the force suddenly won't lead to a burst, because water is incompressible.

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Water is slightly compressible, so it will hold its pressure as long as the container does not stretch.

But since it's only slightly compressible, if the container bursts under pressure it will probably not be an explosive failure. This is because at the time of failure, unlike a gas, the water does not push for a long enough time on the failing part of the container to generate much speed. This is why pressure containers are often pressure tested with water or oil instead of air or other gasses.

If a solid is slightly compressible, it will retain pressure inside a container. In practice, if a incompressible solid is enclosed in a pressurized container, there will usually be some gas or liquid mixed in with it that will retain the pressure.

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Your last point is similar to the reason that nuclear plants have pressurizers. A pressure boundary filled with a nearly incompressible fluid will experience large pressure swings due to small disturbances. Classic example is that of a glass filled with water shattering epically when shot with a bullet, whereas it would only leave small bullet holes if it were filled with a gas. –  AlanSE Sep 28 '11 at 3:54

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