1. (?? Pts) Consider a solid catheter of radius Re placed in a small artery of radius Rant as shown in the figure below. The catheter is moving with a constant velocity along the z-axis, defined as Veat (labeled as just V in the figure Assuming: i. No gravity effects ii. Constant pressure gradient in the direction of flow only iii. Steady-state, fully developed flow iv. Radial symmetry and no change in velocity along z, i.e. v # f(0, z) V . Velocity component only in z-direction, i.e. v = [0,0, vz] TR Z RE V a. Apply the assumptions to reduce the conservation of momentum (source from Table 3.2) b. How does the above momentum balance compare to the result for the same fluid problem but without a catheter? c. State the boundary conditions for the catheter case. d. Solve the momentum balance to find a general solution for shear stress e. Assuming an incompressible, Newtonian fluid, find the general solution for velocity as a function of its independent variable f. Apply the boundary conditions to e) to find the unique solution for the velocity