All Problems Hydrodynamics
Problem 1.330
A cylindrical vessel with water is rotated about its vertical axis with a constant angular velocity \(\omega .\) 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 \(p_{0}\)
\(1.330 .\) (a) The paraboloid of revolution: \(z=\left(\omega^{2} / 2 g\right) r^{2}\), where \(z\) is the height measured from the surface of the liquid along the axis of the vessel, \(r\) is the distance from the rotation axis; (b) \(p=p_{0}+\) \(+1 / 2 \rho \omega^{2} r^{2}\)