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When I shower I notice that the soapy water spinning around the drain often takes the form of a spinning galaxy, complete with spiral arms. Does this indicate that the water's speed around the drain is inversely proportional to the square of its distance from the drain? Actually, I have heard that spinning galaxies themselves don't follow this rule, hence the discovery of dark matter, so does the spinning water follow whatever rule that the spinning stars do?

Thanks.

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See the free (irrotational) vortex section of the Wikipedia article on vortices. The velocity varies linearly with distance not as the square of the distance.

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Thank you John. Linear variation sounds to me as though the soap is spinning as a solid mass, which in retrospect does seem to be the case as I don't notice the shape changing as it spins. How then do the spiral arms form? – dotancohen Jun 29 '12 at 6:48
When I shower this morning I will make a point of studying the water drainage :-) – John Rennie Jun 29 '12 at 6:49
Looking at the spinning soap this morning, in fact the center was spinning (angularly) faster than the outer edges. I don't have a way of measuring the linear velocity at each distance, but it certainly wasn't spinning as a solid body! – dotancohen Jul 4 '12 at 18:21

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