Q$1)$ In a rectangular channel, the discharge rate is $Q=10\frac{m^3}{s}.$ The bottom width of

the channel is $B=4m.,$ and the side slope of the channel is $1$:$1.$ The Manning

roughness parameter is $n=0\mathrm{.}015.$ The bottom slope of the channel is $S=0\mathrm{.}0004$

a$)$ Calculate the uniform flow depth

b$)$ Calculate the critical slope

c$)$ Estimate the water surface profile type and calculate the horizontal distance between

the water depths of $y_1=2\mathrm{.}90m$ and $y_2=2\mathrm{.}7m.($ take an interval depth of $2\mathrm{.}8m)$