In other words, does it take more effort for fish to swim in very deep water than in shallow water.
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The water down below is colder, so that’s one part of it. Water at atmospheric pressure reaches its densest around 4°C.
Water can also be compressed. You may have heard that water is incompressible, but that’s not entirely true. It’s just very very hard to compress, especially compared to air. Anything can be compressed if you push it hard enough, and all of that water on top of it is very heavy, so there’s a lot of force crushing it down.
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.
Yes, Density increases when pressure increases and decreases when pressure decreases. Think of a deep ocean. Pressure increases with depth as you have all the water above pushing down. Also temperature has a relationship with density. Density increases as water becomes cooler e.g further a way from the sunlight and also pressure can make things cooler. As you go deeper generally the colder it can get (vents and volcanic activity obviously can increase temperatures on parts of the sea floor)
It’s less dense because it’s warmer, but if you’re asking if it’s less dense due to the lower pressure, the effect is negligible. Liquids are not compressible. As far as how much effort it takes to swim in more or less dense air it’s probably a wash. The reason why you can’t swim through air is because it’s not dense; you need something to push off against. Each stroke through water gives you hundreds of times more thrust than each stroke through air. Just look how large airplane propellers have to be compared to boat propellers. [Mythbusters](https://www.youtube.com/watch?v=cG8AuhDvh4o) did an episode on this
Re fish
For this you need to look at viscosity. viscosity is the parameter to measure the thickness or thinness of a fluid. Whilst viscosity and density aren’t linked directly both are when it comes to temperature. You also have dynamic viscosity which is a ratio between viscosity and density. When a fluid is heated, its particles move far apart, and it also becomes less viscous so you can imagine more pressure would also increase viscosity. So yes fish must use more energy the deeper they go. However, very deep water fish (the bottom feeders) may not get as much energy because of less food because of less light and also have evolved to deal with high pressures which may also change the way they move. As mentioned the changes for water are not very much at all.
The pressure in the water increases by 1 atmosphere worth, every 10 meters. So, they float less. Perhaps a bit harder to swim, not sure though.
> Is water near the surface of the ocean less dense than deep water
Density is a measure of how tightly packed the molecules are in something. You can make most solid objects denser by squeezing or crushing them, thus reducing the distance between the molecules that make them up so they become “tighter”.
Water is an (almost) incompressible liquid, meaning you can’t change its volume (size) by squeezing or crushing it. After all, if you squeeze water in your hand it won’t do anything to it. What this means is that the density stays constant since the distance between the molecules remains unchanged.
So to answer the first part of your question, technically yes, but the surface is less dense by such a small amount that it can be considered a negligible difference. So for simplicity’s sake, no, it isn’t.
> In other words, does it take more effort for fish to swim in very deep water than in shallow water.
This is a different question not related to density, but rather weight and pressure. The deeper a body of water is, the more pressure there is at the bottom because the more water there is on top *pushing down* on you. At extreme depths like at the bottom of Challenger Deep, this pressure becomes strong enough to crush reinforced steel into a flat, soup like material.
So yes, it becomes exponentially harder for fish to swim the deeper they go, because they need to exert more energy to push against the enormous forces of water all around them. For this reason, animals that live in extreme depths don’t really have solid bodies, they instead have translucent bodies similar to that of a jellyfish’s membrane which won’t be crushed by the pressure and instead allows them to swim without much resistance. See images of the angler fish and some species of worms, mollusks and microorganisms that live in Challenger Deep for more info.
As a follow up question: how cold can water get at, say, 2000ft depth before it reaches freezing temp.
Does the pressure not also hurt the fish? I’ve always wondered this
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