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I read a book about deep water exploring in mariana's trench. They of course talked a lot about pressure, and so this question came to my mind:

If you're, say, 2km down in the Mariana's Trench there is of course a lot, lot of pressure. Would this pressure push you down to the ocean floor with high speed? Or would it just press you down to the height of a pancake and then you slowly would sink to ocean floor?

Slowly or fast?

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what the pressure would do is evenly compress your body on all sides equally. the parts of your body with air in them would be easily compressed, and so they would be crushed down into solid bone and watery tissue. You would sink slowly with your lungs smashed completely flat.

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  • $\begingroup$ I think it is worthy to mention that the pressure is not exactly equal on all sides. The parts of the body that are a little more deep in the water experience a higher pressure. This difference in pressure is what that causes a net upward force, the buoyant force, that slows down the fall in water. But the difference in pressure between the top and the bottom of your body is much smaller than the actual pressure involved. $\endgroup$ – Kevin Selva Prasanna Oct 17 '18 at 6:57
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The pressure of a fluid under gravity increases with depth. At a depth of 2 km below the surface, the pressure exerted by water on a body would be 200 times that of atmospheric pressure. This would collapse the lungs and other air pockets in the body and could damage other soft tissue.

What happens to the crushed remnants of the body depends on the net force acting on the body. If a human body is submerged under water, the parts that are at a greater depth are at a higher pressure than the parts that are higher. This pressure differential acting on the body exerts a net upward force on the body and this force is called the 'buoyant force'.

Gravity would try to pull you down and the buoyant force would try to push you up. What eventually happens depends on who wins the tug of war. And mathematically, if the density of the body is higher than the density of water, gravity wins and if not the buoyant force wins. So the density of the body would decide if the body would move up or down in water.

Normally the human body is less dense than water but if the lungs and other air pockets in the body collapse and crush, the body becomes more dense than water and hence would sink albeit slowly in water.

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It depends on your density. If you are less denser than water(and can withstand such high pressures without being compressed), the buoyant force due to the difference in pressure along your height will push you to the surface of the ocean but if the high pressure compresses and increses your density higher than that of water, you will sink.The rate at which you sink depends on the difference between the magnitude of buyant force and your weight(neglecting all the other viscous effects).

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