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Hydrodynamics

Problem 1.330

A cylindrical vessel with water is rotated about its vertical axis with a constant angular velocity ω.\omega . Find: (a) the shape of the free surface of the water; (b) the water pressure distribution over the bottom of the vessel along its radius provided the pressure at the central point is equal to p0p_{0}

Reveal Answer
1.330.1.330 . (a) The paraboloid of revolution: z=(ω2/2g)r2z=\left(\omega^{2} / 2 g\right) r^{2}, where zz is the height measured from the surface of the liquid along the axis of the vessel, rr is the distance from the rotation axis; (b) p=p0+p=p_{0}+ +1/2ρω2r2+1 / 2 \rho \omega^{2} r^{2}
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