eli5 : Is water near the surface of the ocean less dense than deep water

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In other words, does it take more effort for fish to swim in very deep water than in shallow water.

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Very very slightly, but the difference is small because water is almost completely incompressible. (More important factors for density are temperature and salinity.) Even though the pressure is enormous, the volume/density of the water only changes very slightly with depth, not enough to meaningfully affect swimming.

If, on the other hand, you had a column of *air* extending down to the depth of the ocean (even with just air and not water above it), the air would compress a lot. Earth’s atmosphere has a [scale height](https://en.wikipedia.org/wiki/Scale_height) of about 7.6 km, so the pressure at an elevation typical of the ocean floor would be enormous:

* At a typical ocean depth of ~2 km, it’d be e^(2 / 7.6) = 1.3 = about 30% higher pressure and therefore, approximately, density.

* At the bottom of the Mariana Trench, it’d be e^(10/7.6) = about 3.7 times higher.

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