A rectangular channel with $5\mathrm{.}0$ m wide covers by concrete $)=(0\mathrm{.}010.$ A slope of this channet is changed firm mild slope of $00001$ to a steep slope of $0\mathrm{.}05.$ The flow rate is $25\frac{m^3}{s}.$ The flow depths are $4\mathrm{.}0$ m and $0\mathrm{.}5$ m on the mild and steep slopes, respectively. What are the water surface profile types on those siopes $($M$1-$M$3$ and S$1-$S$3)?$ is there the hydraulic jump and why?

$(10$ points$)$

Manning's equation is $0=\frac{1}{n}A{R}^{\frac{2}{3}}{S}^{\frac{1}{2}}$

Where $Q=$ Flow rate $(\frac{m^3}{s}),R=$ Hydraulic radius $(m)=$ Area$/$Wetted perimeter, $S=$ Bed slope, $A=$ Cross$-$sectional area $(m^2)$