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HS-experiment

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I am trying to understand how a plume of water moving at some speed carries momentum within a body of water. For instance the ‘exhaust’ from a submarine propeller. I am having a hard time understanding how momentum is conserved in such a situation. I do not care about surface effects like waves.

A traveling plume of water always displaces a volume of water equal to its own, and that volume of water effectively fills the space left behind by the plume. So the net momentum of a moving plume of water and the remainder of the system is always zero.

The submarine also displaces a volume of water equal to its own as it travels. If the submarine has the same density as the water, the system also has a momentum of zero. But if the density of the submarine is different than water, that system has a non-zero momentum.

To conclude, the ( submarine + system ) have a non-zero momentum, but the ( plume of water it generates + system ) cannot have any momentum. How is momentum conserved?

I hope I have written it so that it is comprehensible. If someone could please comment I would really appreciate it. :)