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Rotating a fluid filled cylinder and calculating the equation of it's free surface is an elementry problem in fluid mechanics.

However I was wondering, if we rotate the same cylinder by an axis parallel to the main axis and passing through a point on it's circumference, what would be the equation of the free surface in this case, and what will it look like?

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still a parabola. the differential equation to calculate the surface of the liquid does not assume any information of the container other than it rotates around a specific axis. the image we all have to this question, a cylinder rotating around its center, is only imaginative. In fact, the parabola result can be applied to any axisenter image description here

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