Chapter 2, Problem 80P

Consider the flow of a fluid with viscosity $\mu$ through a circular pipe. The velocity profile in the pipe is given as $u\left(r\right)=u_{\max }\left(1-r^n/R^n\right)$, where $u_{\max }$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.
Develop a relation for the drag force exerted on the pipe wall by the fluid in the flow direction per unit length of the pipe.

Figure P2-75