A wide rectangular channel $(R=y)$ carries a specific discharge of $4\mathrm{.}8\frac{m^2}{s}.$ The channel consists of two long reaches with bed slope of $0\mathrm{.}008,0\mathrm{.}0004.$ A gate located in the

middle of second reach and the gate opening is $0\mathrm{.}4m$ as seen in Figure below. If Manning's $n=0\mathrm{.}015,$

a$.$ Determine the water depths at the beginning and end of all gradually water surface profiles that could be seen.

b$.$ Draw the water surface profiles along the entire channel. Please put the water depth immediately at the upstream of the sluice gate in the box below.