Suppose that an open container of radius R is filled with liquid to an initial height h0. It is then rotated at a constant angular velocity ω, as shown in Fig. P7.7. After an initial transient, the liquid rotates as if it were a rigid body.

Assuming that the air pressure is constant at P₀ and that surface tension and viscous stresses in the air are negligible, determine the liquid pressure P(r, z) and interface height h(r).

Transcribed Image Text:

3 h(r) N ļ Air Po Liquid Figure P7.7 Rigid-body rotation of a liquid in an open container. R