5. The velocity profile of water flowing through a pipe is parabolic at some section: r = ro r = 0 u(r) u(0) = 4 Figure 2 where u(r) = is the velocity at any position r, is a constant, is the viscosity of water, and r is the radial distance from the pipe centerline. (a) Develop an equation for u(r) assuming a parabolic velocity profile [u(r) = a r + br + c] and using the known velocities at the walls u (ro) = 0 and the center u (0) (Express your answer in terms of , , r, and ro) ). [Hint: u(r) is maximum at r = 0.] (b) Develop an equation for shear stress in the fluid at the wall of the pipe (Express your answer in terms of , , r, and ro).