Question FIUR

$($a$)$ From the basic assumptions, show that,$($BMarks$)$

$($b$)$A trapezoidal earth channel having side slopes $2$:$1(H$:$V)$ is designed for a maximum demand of $512\frac{V}{s}.$ If the bed slope is $0\mathrm{.}104\%,$ calculate the best dimensions. Assume a Free Board of $(0\mathrm{.}3+25\%)$ of the design depth against a minimum velocity of $0\mathrm{.}7\frac{m}{s}.$ Take Manning's n $=0\mathrm{.}013(14$ Marks$)$