Problem 5.29: Startup of circulatory flow in tank
At t = 0, a circular tank with radius R contains water at rest with depth h. Between 0<tt, a water hose is sprayed onto the surface of the water in the tank at a volume flow rate Q and an exit velocity Vj. The jet impacts tangentially on the water at a radius rj, with an angle q relative to the horizontal.
After the time t the hose is turned off. Eventually, because of friction within the water, all (or at least most) of the water in the tank will end up rotating like a solid body.
Derive an expression for the final angular rate of rotation W of the water, assuming the effect of shear forces between the water and the walls of the tank during the startup of the rotary flow is negligible.