(Solved): In regions far from the entrance, fluid flow through a circular pipe is one dimensional, and the ve ...

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 $u(r)=u\max (1?r2/R2)$, where $R$ is the radius of the pipe, $r$ is the radial distance from the center of the pipe, and $u$ max 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 for water flow at $20^{?}\mathrm{C}$ with $R=0.08\mathrm{m},L=15\mathrm{m},u\max =6$ $\mathrm{m}/\mathrm{s}$, and $?=0.0010\mathrm{kg}/\mathrm{m}?\mathrm{s}$.