5. Problem 2.12 (from textbook) nnel, shown in Figure 2.37. In this ws from a source in a radial direction tric flow rate at any radial position r is If is driven by an unspecified pressure or the velocity profile. Use your solu- stant-flow-rate condition to show that ess at y = -b/2 is 3μQ arh² Tw (2.10.7) fiber dialysis unit is one design that irface area between blood and dialysate R 2.12 Consider a catheter of radius R, placed in a small artery of radius R as shown in Figure 2.38. The catheter moves at a constant speed V. In addition, blood flows through the annular region between R, and R under a pressure gradient Ap/L that only varies in the direction. We want to determine the effect of the catheter upon the shear stress at r= R. Assume steady, fully developed flow of a Newtonian fluid. (a) State the momentum balance and boundary conditions. (b) Sketch the velocity profile and provide a justifica- tion for its shape. Re FIGURE 2.38 A catheter moving in a blood vessel. D (c) Solve the momentum balance; substitute Newton's law of viscosity and solve. Apply the boundary conditions to determine the velocity. (d) Calculate the shear stress. (e) Use the following values to determine the shear stress acting on the blood vessel surface, r= R: R=0.17 cm; R₂ = 0.15 cm; V=10 cm s¹; p=0.03 gcm¹s¹; Ap/L=100 dyn cm³ For part a) no need to set up the momentum balance over control volume. Just start with differential equation of the momentum balance (as shown in the lecture).

Fig: 1