A $15-ft$ wide rectangular channel $(n=0\mathrm{.}020)$ carries a steady discharge of $180f\frac{t^3}{s}$ on a slope

of $0\mathrm{.}002.$

$($a$)$ Compute normal depth $($in feet$).$

$($b$)$ Compute critical depth $($in feet$).$

$($c$)$ Compute critical slope. Is the channel mild or steep?

$($d$)$ If the actual depth of flow $($y$)$ at a certain cross$-$section is $2\mathrm{.}50ft,$ what type of water

surface profile forms? In what direction $($upstream or downstream$)$ would the flow

approach normal depth?