Consider $1$D laminar flow through a cylindrical pipe, where velocity in the $x-$direction is given by $u(r)=V_{\text{m}\text{a}\text{x}}(1-(\frac{r}{R}{)}^2).($a$)$ provide the governing equation for determining the volumetric flow rate in this situation. $($b$)$ determine $vv{v}_{\text{m}\text{a}\text{x}}$ if the pipe radius, $R,$ is $1$ cm $,$ and the volumetric flow rate is $2c\frac{m^3}{s}.$