2. Flow in a Circular Pipe (20 pts) Consider the following pipe with a circular cross-section: Rpipe Vout Pout Pin Vin Figure 1: Pipe flow problem diagram Answer the following questions about this pipe: a) Using integral conservation equations i. Draw and label a control volume that can be used to relate the shear and normal stresses to the x-momentum change in the fluid. (Please draw your own figure and not use the above figure to draw your control volume.) ii. Clearly show the forces/integral conservation of momentum relationship as applied to your CV. iii. Using the expression from (ii), show how the pressure gradient along the pipe (or) and wall shear stress (7) are related. b) Use the differential conservation of momentum (i.e. the Navier-Stokes equations) to show the same relationship between pressure gradient (322) and wall shear stress (7) exists (hint: you may find a Poiseuille Flow analysis will help).