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I know that we can make water solid with high pressure, so I think water will be solid in the deep ocean?

If that is true, the depth of the ocean would be limited because water will become ice? Anyone know that maximum depth?

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This is addressed in physics.stackexchange.com/questions/104544/… –  Joce Apr 17 at 15:13
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no, because water is most dense in liquid form. I.e. if you slowly apply pressure to an ice cube while keeping its temperature, it will melt. –  Jani Kovacs Apr 17 at 15:21
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@JaniKovacs If you had taken the slightest time to look up a phase diagram en.wikipedia.org/wiki/File:Phase_diagram_of_water.svg , you wouldn't have said that. Water most certainly turns solid at high pressures, pretty much regardless of temperature. Don't confuse water's amorphous behaviour with its physical state. (granted the ocean isn't deep enough to reach these pressures, but take a look at some other planets in our system) –  Carl Witthoft Apr 17 at 15:33

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You are mistaken. Actually, you can melt ice by applying pressure. This is why ice is so slippery, when you step on a frozen lake, you are melting the very first layer of water, and thus creating a very good instant lubricant for you to slide on. It is a common knowledge false fact, see comments.

Ok, granted, at very high pressures water does become solid. From the phase diagram, to get solid at around 0C you need around 650 MPa. How much is that? Pressure depends with depth as:

$$P = \rho g h$$

Assuming constant density, you need a column of water of $66\ km$ for ice to be formed. That is about six times the depth of Challenger Deep, in Mariana trench.

So the answer is no... on Earth. You will not find enormous amounts of more or less pure liquid water anywhere else in the Solar System, but if you are happy with hydrogen, helium, and other gases, you may find it around Jupiter's core. Definitely, liquid H and He.

When water is mixed with other elements, the phase diagram is perturbed. For example, salt in the sea at atmospheric pressure lowers the freezing point about a couple of degrees (depending on the concentration). If water is mixed with hydrogen, helium, methane, and company as in a gas giant, the diagram will be drastically changed, so more detailed computations would be needed.

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While your answer is correct that you don't get ice at the bottom of the ocean, some of your other statements are incorrect or debatable. 1. There is plenty of water in the solar system which is not on Earth. 2. It is not completely clear why ice is slippery. –  Chris Mueller Apr 17 at 16:01
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Like Chris said. In fact it's dead certain that, whatever the mechanism is, the slipperiness is NOT due to pressure-related melting. –  Carl Witthoft Apr 17 at 17:04
    
I stand corrected on the slipperiness. In the solar system, though you will not find big concentrations of reasonably pure water in liquid form. There are icy asteroids, and water vapour, but none of them are getting solid due to pressure. –  Davidmh Apr 18 at 14:42
    
@Davidmh: any place likely to have enough pressure to solidify ice (i.e., in Neptune's core) is not visible. –  Jerry Schirmer Apr 18 at 17:17
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Well-established models predict that several of the high-pressure phases of ice exist deep inside the icy moons of the gas giants - Ganymede, Europa, Callisto, Titan, Enceladus, Triton... One recent paper even posits a model where layers of liquid water and various phases of ice alternate in an onion-like manner. –  JohannesD Jun 2 at 13:44

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