Chapter 2, Problem 83P

In regions far from the entrance, fluid flow through a circular pipe is one dimensional, and the velocity profile for laminar flow is given by $u\left(r\right)=u_{\max }\left(1-r^2/R^2\right)$, where R is the radius of the pipe, r is the radial distance from the center of the pipe, and u is the maximum flow velocity, which occurs at the center. Obtain (a) a relation for the drag force applied by the fluid on a section of the pipe of length L and (b) the value of the drag force forwaterflowat20°Cwith $R=0.008\text{m, }L=30\text{m,}{u}_{\max }=3m/s$ , and $\mu =0.0010$ kg/m.s.

FIGURE P2-83