The efficient rectangular cross$-$section channel with a base slope of $0\mathrm{.}0006$ and Manning's roughness $n=0\mathrm{.}014$ conveys a discharge of $18\frac{m^3}{sec}.$

a$)$ Determine the dimensions of the channel and the type of uniform flow.

b$)$ Plot the specific energy curve.

c$)$ At a certain point, the channel bottom is raised by $z.$ Determine the minimum $z$ for critical flow to occur.

d$)$ If the width of the channel is narrowed to $70\%$ at the elevated section, determine the water depth at the upstream part of the channel.

e$)$ Illustrate the water surface and energy line along the channel.