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This question led me to wonder whether swimming would be the same experience for a fish in a full, sealed ball as it is normally.

If the fish is about 7cm from the walls of the tank, a pressure wave can propagate from the fish to the wall and back in .0001 seconds, while the time scale on which a fish wiggles is tenths of a second. So unlike the open ocean, the water surrounding the fish can all communicate with itself on the time scale that the fish wiggles, and unlike a normal fish tank, the water has nowhere to go and so can't change its shape.

Would the fish notice any hydrodynamic effects in a full, sealed tank compared to normal swimming?

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It would notice that the pressure of the water was highly sensitive to minute changes in its body volume, depending upon the size of the tank, but not to the viscosity of the water and its ability to swim through it. – John McVirgo Apr 26 '11 at 20:52
Fill up your bathtub and see if you can swim in it. You will find that you can just fine. – ja72 Apr 28 '11 at 23:32
@ja72 I'm not sure how that's relevant. – Mark Eichenlaub Apr 29 '11 at 0:35
up vote 1 down vote accepted

It is not sound propagation but rather momentum diffusion that makes a fish swim. The rate at which momentum diffuses is determined by the kinematic viscosity, which for water is about $10^{-6} m^2/s$.

It takes minutes for momentum to diffuse in water over distances of centimeters, while the time scale over which a fish wiggles is tenths of a second. So, during a wiggle the water surrounding the fish doesn't 'communicate' with any wall, and the fish doesn't notice any anomalous hydrodynamic effects.

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Yes, the fish will swim normally. The fish does not make itself move by radiating pressure waves to infinity, it creates and sheds small local vortices with its fins which move at a much lower speed. edit

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I did read the question, and gave the correct answer. The pressure wave (also known as a sound wave) is not relevant to the dynamics of a fish swimming. – user1631 Apr 27 '11 at 17:47
@user1631 Thanks for the answer. I'd like to accept it, but as it stands now I don't feel like I have been able to learn much of the physics yet. Do you have a reference available, or maybe have a little more detail on how we know what's involved? – Mark Eichenlaub Apr 28 '11 at 10:12
It's not transfer of pressure wave here that matters, but transfer of the water itself. In essence, the fish displaces backwards the volume of water it replaces by moving forward. The fins move forward with low friction (narrow edge), turn and push with high friction (flat side) backwards, or the whole body turns. To visualize it better, think of movement mode of a snake on sand. It really doesn't matter what's the speed of sound in sand or reflections of it against rock below. – SF. Apr 29 '11 at 11:38
it won't swim for very long though, it will pretty quickly exhaust its supply of oxygen and drown. – jwenting May 30 '11 at 5:40

Yes the fish will swim normally. Most people who have fish in an aquarium would agree. Would those fish lose the ability to swim if I lowered plate glass onto the water surface to make a totally encapulated swimming space? No.

Another way to look at it: If you had a totally encased mixing bowl, which was totally filled with water, and manufactured so as to have the mixing blades (inside the bowl) driven by shafts which passed through hermetically sealed openings in the lid of the bowl to the electric blender motor. When you turn the blender on, do the blades move? you bethcha, they do. So do fish fins.

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It seems like all this answer does is say "yes" - where is there any physics in it? – Mark Eichenlaub Jun 27 '11 at 17:59
@Mark: Physics is a branch of science. True science includes observing, making theories (hypothesizing) about the underlying principles driving what is observed, and running repeatable experiments to confirm the theories. I have constructed two virtual experiments to confirm or deny (in this case deny) an hypothesis that totally encasing water in a non-movable shell forces no movement of other bodies in that water. That is science. And since this particular bit of science is about physics, that's physics. :-) – Vintage Jun 27 '11 at 18:42
Physics is about applying physical principles, I think. – Mark Eichenlaub Jun 27 '11 at 19:38

When we compare an ocean/open water body to a sealed tank, there is an evident difference in volume and surface area. Therefore, the pressure that acts on the fish will be different since density of water will be different. Perhaps the fish might have to use its gills to form vortices to intensify from which the fins somehow harvest energy to move its fins and swim.

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