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 $u(r)=u_{\text{m}\text{a}\text{x}}(1-\frac{r^2}{R^2}),$ where $R$ is the radius of the pipe, $r$ is the radial distance from the center of the pipe, and $u_{\text{m}\text{a}\text{x}}$ is the maximum flow velocity, which occurs at the center. Obtain $($a$)$ a relation for the drag force $($synonymous to shear force in this context$)$ 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 $20C$ with $R=0\mathrm{.}08m,L=30m,u_{\text{m}\text{a}\text{x}}=3\frac{m}{s},$ and $=0\mathrm{.}0010k\frac{g}{m}*s.$

Formula: Drag force: $F=A\frac{du}{dr}$

FIGURE $2$: QUESTION $16$