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What would happen if you submerged a balloon filled with water to the bottom of the Marianas trench?

As it is filled with water, would it be crushed smaller by water pressure or remain the same size? More importantly, why?

(I'm sure this question has been answered before, but I couldn't find it anywhere.)

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We usually say that water is incompressible. That is not true. It is compressible, but requires very large pressures to show an effect we would notice. The Wikipedia article on the Mariana Trench lists the depth of the deepest part, the Challenger Deep, at slightly more than 36,000 feet. The pressure at that depth in ocean water is over 1000 atmospheres. This is great enough for seemingly incompressible water to actually be compressed a significant 4.96%. As the article points out, this is enough to reduce the volume of 100 liters of surface water to about 95 liters.

Chapter 3 of what appears to be an online oceanography course taught at the Scripps Institute at UC/San Diego has some very pertinent information. Figure 3.4 at that link (sorry, I couldn't find a pertinent hard copy to give as reference) illustrates that the density of seawater is roughly proportional to the depth.

This means that your water balloon, if filled with seawater, would be compressed because the water in the balloon would compress as the pressure increased and the balloon material, assuming it's elastic, would simply contract to form a water balloon only 95% as big as before.

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