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Why should the water start rotating? There are lots of explanations, but here is one way to think about it (and this way happens to apply to black holes as well as it does to drains). Imagine you are a particle in the water, and you are being pulled toward the suction that the drain creates. You are accelerating toward the point of suction. However, because of your previous momentum, the number of other particles getting sucked toward the point and other factors, chances are that you are going to be off to one side of the point of suction when you arrive. That deflection sets you up on a spiraling path into the point of suction, like a moth spiraling in toward a light. Once the spiral has started in one direction, it tends to influence all of the other particles as they arrive. A very strong spiraling tendency is created. Eventually, there is enough spiraling energy to create a vortex.
Given that you see vortexes all the time in tubs and sinks, it is obviously a fairly common phenomenon. In a tornado, the same sort of thing happens, except with air instead of water.
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