e. When we consider the flow of blood through a blood vessel, such as a vein or artery, we can model the shape of the blood vessel by a cylindrical tube with radius R and length l Because of friction at the walls of the tube, the velocity v of the blood is greatest along the central axis of the tube and decreases as the distance r from the axis increases until v becomes 0 at the wal. The relation ship between v and r is given by the law of laminar flow discovered by the French physician Jean-Louis-Marie Poiseuille in 1840. This law states that where η is the viscosity of the blood and P is the pressure difference between the ends of the tube. If P and I are constant, then u is a function of r with domain [0, R] c. What is the speed of the blood at 0 a. Determine r = 0.002 cm? b. For one of the smaller human arteries we d. What is the instantaneous change of can take η = 0.027, R= 0.008cm, l = 2 cm, and P = 4000 dynes/cm2. Determine v(r) for these conditions velocity with respect to r when r = 0.002?