Answer Happy

Consider an incompressible Newtonian fluid confined between two concentric circular cylinders of infinite length, as shown below. The inner cylinder is rotating with angular velocity w; in clockwise direction and the outer cylinder is rotating with angular velocity wo in counterclockwise direction. Assuming gravitational forces are negligible, obtain the velocity profile, V = u,ê, + ugêg, for the fluid. Hint: • The flow is steady, laminar, and two-dimensional in the r- plane. • Assume rotational symmetry (meaning nothing is a function of 8 coordinate). • The 2D continuity and Navier-Stoke equations in polar coordinates are: dus dt four. du u du = + (-12 (127) + Ur + dr T 08 + Ur dr + a(ru,), dug + dr де т дв =0 Liquid: p. μ R + 14,40) = -1 0 0 + μ{- ( 1³ (540)) + {2+ 2 due) +7² 08²-47²-001) a(rue) 10²u 2 du, 2002 ²00 + Wo