$[50$ points$]$ What is the maximum flow rate through the pipe shown in the figure below if the elevation difference of the reservoir surface is $200m.[K_{\text{e}\text{n}\text{t}\text{r}\text{a}\text{n}\text{c}\text{e}}=0\mathrm{.}8,K_{\text{e}\text{x}\text{i}\text{t}}=1\mathrm{.}0,$ and Figure $7\mathrm{.}13$ Moody Diagram as attached$]$