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