4. (15 pts) In this video a highly-viscous viscous liquid (incompressible, Newtonian, density , viscosity ) is confined between two concentric, vertical cylinders of radius Ri and Ro for the inner and outer cylinders respectively. The inner circle is rotated at an angular velocity of i which is slow enough that flow between the cylinders is laminar. a) Find an expression for the fully-developed velocity profile between the cylinders. Note 1: The relationship between angular velocity and tangential velocity u in cylindrical coordinates) is u=r. Note 2: [r1r(rru)r2u]=r(r1r(ru)) (This relationship can be derived using the product rule + algebra.) b) In which direction or directions (r,,z) will pressure be changing? Support your answer using the Navier-Stokes equation. (You don't have to actually find the pressure field; you know how to do it, but the algebra involved would take a while and be a pain). 4. (15 pts) In this video a highly-viscous viscous liquid (incompressible, Newtonian, density , viscosity ) is confined between two concentric, vertical cylinders of radius Ri and Ro for the inner and outer cylinders respectively. The inner circle is rotated at an angular velocity of i which is slow enough that flow between the cylinders is laminar. a) Find an expression for the fully-developed velocity profile between the cylinders. Note 1: The relationship between angular velocity and tangential velocity u in cylindrical coordinates) is u=r. Note 2: [r1r(rru)r2u]=r(r1r(ru)) (This relationship can be derived using the product rule + algebra.) b) In which direction or directions (r,,z) will pressure be changing? Support your answer using the Navier-Stokes equation. (You don't have to actually find the pressure field; you know how to do it, but the algebra involved would take a while and be a pain)