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There is a popular myth, owing to the rotational direction of a hurricane which is governed by the rotation of the earth, that says the water in bathtubs rotates a certain direction in the Northern Hemisphere and the opposite in the Southern Hemisphere.
The Coriolis effect, as it's called, does not determine which way the water swirls in your basin at home. The effect is too small to have any influence on the direction of such localised activity.
Water is free to swirl in either direction in basins or bath in both hemispheres. Which way it goes is determined by the geometry of a particular basin or, if things are perfectly aligned and balanced, then by chance.
Source: Space.com