A cylindrical tank of radius r rim = 0.354 m rotates about its vertical axis (Fig. P473).

Question:

A cylindrical tank of radius r_rim = 0.354 m rotates about its vertical axis (Fig. P4–73). The tank is partially filled with oil. The speed of the rim is 3.61 m/s in the counterclockwise direction (looking from the top), and the tank has been spinning long enough to be in solid-body rotation. For any fluid particle in the tank, calculate the magnitude of the component of vorticity in the vertical z-direction.

Figure P4-73