Suppose that a vertical rod of radius R is rotated at a constant angular velocity w in a large container of liquid, as shown below

Suppose that a vertical rod of radius R is rotated at a constant angular velocity w in a large container of liquid, as shown below. The immersed length is L. The flow is axisymmetric and unidirectional (Vg = Ve(r) and v, = v2 = 0) and the liquid is Newtonian and incompressible. a) Define your hypotheses b) Simplify the continuity and Navier-Stokes Equation Derive the velocity profile in the fluid dj Calculate the torque, on the cylinder applied by the fluid onto the solid surface e) Calculate the pressure as function of the radius. Does the pressure increase or decrease as you ve closer to the rod? Comment on the possible consequences for rotary machinery. Gas Liquid