Water in a cylindrical container of radius 50 cm rotates as a rigid body. The water level at the wall rises 10 cm from its initial level. Find the fall of the centre level in cm.
The free surface is a paraboloid, z(r)=z_c+ar². Its area-averaged height is z_c+aR²/2, fixed by volume conservation. Thus the initial level lies halfway between the new centre and rim levels. The centre falls by the same amount that the rim rises: 10 cm.
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