1. Consider fully developed laminar blood flow in the annulus between a blood vessel and a catheter. as shown in Figure 1. The vessel walls are stationary, and the catheter moves in the x direction with speed U. The radius of the catheter is Rc and the radius of the blood vessel is equal to kRc. Assume the axial pressure gradient for flow in the annulus is zero (Op/Ox = 0). U Rc KRC Figure 1. Catheter (in gray) inserted in a blood vessel. a.) Write an appropriate equation for the motion inside the annulus.'(For the purposes of this problem, you may assume that the blood behaves as a Newtonian fluid). In order to get full credit, justify all the assumptions you make to simplify the equation. b.) Write appropriate boundary conditions (2) for the flow inside the annulus. c.) Integrate the differential equation that you obtained in part a, and write an expression for the velocity u(r) inside the annulus. d.) Sketch/plot the shape of the velocity profile u(r) inside the annulus