The depth before and after the jump is $0\mathrm{.}2$ m and $0\mathrm{.}8$ m$,$ respectively in the rectangular cross section

with the width of $2$ m $($n $=0\mathrm{.}013$ and S$0=0\mathrm{.}0001).$ Compute the following. $[4*5=20]$

$(1)$ Flow rate Q $($cms$)$

$(2)$ Normal depth yn $($m$)$

$(3)$ Critical depth yc $($m$)$

$(4)$ Head loss $(\backslash$Delta E$)$ after the jump

$(5)$ Sketch the water surface profile while indicating the channel bottom, y$1,$ y$2,$ yc$,$ and yn$.$