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I recently read that all flat disk galaxies have the same rotation speed regardless of mass and size, so I was wondering if this same feature was visible in any other similar rotation such as a whirlpool.

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A whirlpool is a vortex tube, and the strength of the vortex tube determines the (irrotational) velocity outside the vortex tube. One can vary the strength of the vortex tube to get rotational velocities of different magnitudes. From little whirlpools shed behind rocks in a stream (or see this tiny whirlpool that seems to have formed in shallow still waters; I can't figure its origins) to strong whirlpools, mother Nature can make them all sizes.

P.S. For more (qualitative) understanding of vortices see this video.

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