Problem $1[6$ points$]$

Two watersheds share one drain inlet and a $200$ m long drainage pipeline. The watershed size $($A$),$ runoff coefficient $($C$),$ and time of concentration $(t_c)$ are as shown in the figure. Rainfall intensity of the watershed is given by the following equation: $i=\frac{250}{0\mathrm{.}3t_c+1\mathrm{.}2}$

$i=$ Rainfall intensity $(m\frac{m}{h}r)$

$t_c=$ Time of concentration $($min$)$

Determine the watershed rainfall intensity, the peak flow rate, and the pipe diameter. The pipe roughness coefficient $n=0\mathrm{.}014$ and the design velocity of the pipe flow is $0\mathrm{.}8\frac{m}{s}.$ Assume the pipeline slope is $0\mathrm{.}006.1$ hectare $={10}^4{m}^2$

$\backslash$table$[[$Intensity $(m\frac{m}{h}r),],[$Peak flow rate $(cms),],[$Pipe diameter $(m),]]$