Consider the flow of a fluid with viscosity  through a circular pipe. the velocity profile in the pipe is given as u(r) = umax(1 - r n /r n ), where umax is the maximum flow velocity, which occurs at the centerline; r is the radial distance from the centerline; and u(r) is the flow velocity at any position r. a) (10 points) if n=3, develop an expression for the mass flow rate through the pipe. b) (10 points) what is the average velocity in the pipe?