When displacement isn't possible

Stop me if i'm wrong but displacement is, for example, when you enter a bathtub the water level rises around you.

What happens when displacement isnt possible?

I'll give an example. I have two blocks off steel, one at the top of a chamber and one at the bottom. there is a gap between the two blocks that is filled with water. There is NO gap between the two blocks and the side of the chamber (the water cannot escape)

What happens when the two block come together, in effect squashing the water? where does the water go?

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If you watch to movie "The score" with DeNiro and Ed Nortron you see they use this principle to open up a safe. This comes from an invention of archemedes to burst vessels using water pressure. –  ja72 Mar 4 '11 at 16:09
To add on to @ja72's comment, the huge resistance of water to compression is the basic operating principle behind hydraulic machinery which is how a lot of heavy-duty machinery. Construction equipment, like back-hoes and high power drills, use these principles. (Although other fluids are used in lots of hydraulics, water is still used in many applications) –  kharybdis Mar 5 '11 at 2:57

The blocks of steel and layer of water will just sit there like a sandwich.

If there is nowhere for the water to go, the blocks of steel will not come together. Instead, the water will compress slightly, increasing its pressure. This induced pressure will support the top block of steel.

If you make the top block of steel heavier and heavier, the pressure in the water will continually increase. Eventually you'll see the layer of water shrinking. The water isn't going anywhere; its density is increasing. You'll see a significant effect when the pressure on the water (the weight of the steel block divided by its area) becomes on the order of the bulk modulus of water, about 2*10^9 Pascal or 20,000 atmospheres.

The pressure at the bottom of a deep ocean trench is about 5% of this, so your slab of steel will need to be on the order of thousands of meters tall just to see a few percent change in the size of the water layer.

Eventually, you'll burst the sides of the container you're using, or a tiny gap will form. Then water will come shooting out in a jet.

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No, he said the water cannot escape. –  user1708 Mar 3 '11 at 19:12
@kakemonster You are being ridiculous. He also said the block are made of steel. Do you think steel is infinitely strong? When there are contradictions inside the question itself, I have a right to interpret it in a reasonable way. –  Mark Eichenlaub Mar 3 '11 at 19:48
You know, I'm not sure that questions like this are open to interpretation in a reasonable way. If the question says the water cannot escape, it can't escape. These thought experiments are the heart of physics. –  Duncan McGregor Mar 3 '11 at 23:19

According to the phase diagram at http://www.lsbu.ac.uk/water/phase.html, if you compress it slowly enough (so that the temperature remains constant at 300 K), the water will compress slightly and slightly more as you increase the pressure to about 1 GPa (10,000 atm), at which point it will have a density of about 1.18 g/cm$^3$ (18% greater than usual).

At this point, if you continue to apply more pressure, the water will suddenly solidify into begin forming a crystal known as ice VI. This does not have the same structure as ordinary ice (ice I), which makes sense because ordinary ice is less dense than water, so it will never be formed by compression. Ice VI, on the other hand, is more dense than water (about 1.31 g/cm$^3$), and that's what you get if you apply a pressure greater than 1 GPa.

If you increase the pressure even more, the ice VI changes phase a few more times (forming ice VII, then ice X, it looks like), before getting to the limit of pressures available in the lab.

If you somehow managed to apply much, much, more pressure than this (for example by throwing the water into a neutron star), then kakemonsteret's answer would begin to apply. The water would first become electron-degenerate matter (like a white dwarf), then the nuclei would start to fuse and it would become like neutron star material. But the pressures required for this are many orders of magnitude higher than anything available outside of a compact star, and at such pressures the steel in your experiment would suffer a similar fate.

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""At this point, if you continue to apply more pressure, the water will suddenly solidify"" Wrong! The water will solidify slowly and proportinal to the displacement of the piston compressing it. (On top of this, think of Your own statement above: ""if you compress it slowly enough (so that the temperature remains constant at 300 K),"" –  Georg Mar 4 '11 at 10:22
Good point. I was thinking that the change as a function of pressure would be "sudden", but the process certainly wouldn't happen suddenly. In fact the solidification would produce a lot of heat energy that would need to be removed in order to keep it at 300 K. –  Keenan Pepper Mar 5 '11 at 2:26

The short answer is that it will compress (increase in density) just as a gas would. But the amount of pressure required is enormous since most liquids have so small a compressibility, that they are for all practical purposes considered to be incompressible.

The Wikipedia article gives more details about the behaviour of compressibility at different temperatures and pressures.

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