Problem 1 Based on experience, that the wall shear stress (Tw) in pipe flow depends only on the distance from the inlet ( x ), the diameter of the pipe ( D ), the velocity of the pipe flow (v), the density of the fluid (p), the viscosity of the fluid (ul), and the roughness of the pipe (E). (a) List the dimensions of all of the quantities. (For example,tw: M/LT? and : L) (b) Use dimensional analysis to find out the four dimensionless groups of the system. Please write down in detail how you derive them. Problem 2 Air at 3 atm and 100 C is flowing at 1.0 m/s in a 1.5-cm tube. Calculations indicate that the flow is laminar, with a Reynolds number very near the critical value. Would the flow become turbulent if (a) the temperature were increased to 200 C (b) the tube size were increased to 2.0-cm (c) the pressure were increased to 5 atm? (The molar flow is assumed to be constant for all three cases.)