(1) Task 1: Use Dimension Analysis and Pi-Theorem to study blood flow in Arteries. Assume that the Artery is a cylindrical tube. Let ( denote the Blood Flow. What are the quantities that Q might depend on in the tube-artery model? (Please explain every step of your analysis) L FIGURE 1. Schematic of the artery Hint: (a) Diameter or Radius or Croas sectional Area (241, R or ~R) (b) Viscosity of Blood () (c) Pressure change (AP = Pis - Paw) (d) Thickness of Tube (h) (e) Length of the Tube (1) (f) Gravity Effect (with or against gravity (9) } (g) Density of blood (p) Note 1: A flow in a tube is related to velocity of the flow and the radius of the tube by the formula ( = VR') where 1 is the velocity and I is the radius. Note 2: Viscosity is the proportionality constant between force per unit area and change in velocity per unit length, that & SHE = / Length