Chapter 9, Problem 85P

Consider liquid in a cylindrical tank. Both the tank and the liquid rotate as a rigid body (Fig. 9-85). The free surface of the surface tension effects are negligible. Discuss the boundary condary conditions required to solve this problem. Specifically, what are the velocity boundary condition in terms of cylindrical corrdinates $\left(r,\theta ,z\right)$and velocity components $\left(u_r,u_{\theta }{u}_z\right)$ at all surface, including the tank walls and the free surface? What pressure biundary conditions are apporopate for this flow fied? Write mathematical eqautions for each boundary condition and discuss.

FIGURE P9-85