the free surface of a rotating fluid is a paraboloid.
the free surface of a rotating fluid is a paraboloid.
the free surface of a rotating fluid is?
a paraboloid
where formula_9 is the distance of the free surface from the bottom of the container along the axis of rotation. if one integrates the volume of the paraboloid formed by the free surface and then solves for the original height, one can find the height of the fluid along the centerline of the cylindrical container:









































formula_10









































the equation of the free surface at any distance formula_3 from the center becomes:









































formula_12
free surface
in a non-rotating fluid the fluid parts above the rising ball and closes in underneath it, offering relatively little resistance to the ball. in a rotating fluid, the ball needs to push up a whole column of fluid above it, and it needs to drag a whole column of fluid along beneath it in order to rise to the surface.









































a rotating fluid thus displays some degree of rigidity.









































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