NUMERICAL DIFFERNTIATION (35pts). Two sets of blood velocity profile measurements were modeled based on physiological vascular flow: P10 (Poiseuille", steady flow) and PL10 (Pseudo-Power Law", pulsatile flow), as shown in the figure below. In the figure, the abscissa is the velocity normalized to the maximum velocity Umax, and the ordinate is the normalized distance from the vessel centerline (@r= 0). Velocity Profiles: Poiseuille (Blue), Pseudo-Power-Law (Red) 0.8 0.6 - r/R 0.4 - 0.2- 0.2 0.4 0.6 0.8 u/ Umax Near the wall, the actual measured velocities shown in blue squares (P10) and red circles (PL10) are (in normalized units) P10 = [0 0.190000 0.360000 0.510000] and PL10 = [0 0.521703 0.790285 0.917646] where the first value is the velocity at the wall r/R = 1 (always zero), and each value after that is the velocity at 10% (0.1) steps away from the wall (r/R = 0.9, r/R = 0.8, etc). Use 1st, 2nd, and 3rd order forward difference rules to compute the spatial gradient of blood velocity (du/dr) at the vessel wall (note this spatial gradient is directly proportional to the stress the blood imparts on the wall as it flows by). Submit the code, the values of the gradients obtained for each profile at each level of approximation, and answer the question: Do these values converge, or are they appearing to converge, as you use a higher order approximation? NUMERICAL DIFFERNTIATION (35pts). Two sets of blood velocity profile measurements were modeled based on physiological vascular flow: P10 (Poiseuille", steady flow) and PL10 (Pseudo-Power Law", pulsatile flow), as shown in the figure below. In the figure, the abscissa is the velocity normalized to the maximum velocity Umax, and the ordinate is the normalized distance from the vessel centerline (@r= 0). Velocity Profiles: Poiseuille (Blue), Pseudo-Power-Law (Red) 0.8 0.6 - r/R 0.4 - 0.2- 0.2 0.4 0.6 0.8 u/ Umax Near the wall, the actual measured velocities shown in blue squares (P10) and red circles (PL10) are (in normalized units) P10 = [0 0.190000 0.360000 0.510000] and PL10 = [0 0.521703 0.790285 0.917646] where the first value is the velocity at the wall r/R = 1 (always zero), and each value after that is the velocity at 10% (0.1) steps away from the wall (r/R = 0.9, r/R = 0.8, etc). Use 1st, 2nd, and 3rd order forward difference rules to compute the spatial gradient of blood velocity (du/dr) at the vessel wall (note this spatial gradient is directly proportional to the stress the blood imparts on the wall as it flows by). Submit the code, the values of the gradients obtained for each profile at each level of approximation, and answer the question: Do these values converge, or are they appearing to converge, as you use a higher order approximation