$30$p$-$Q$\mathrm{.}3)$ From a large reservoir, water enters at point A into a rectangular channel having a width of $5$ m $.$ The reservoir specific energy $E_r$ is defined with respect to point $A.$ The channel slope is initially $S_{01}=0\mathrm{.}0015$ up to point $B,$ then it changes to $S_{02}=0\mathrm{.}02$ on which the uniform flow depth is $y_{02}=1\mathrm{.}44m.$ The Manning roughness coefficient is constant everywhere and is equal to $n=0\mathrm{.}016.($Assume both of the channels are very long.$)$

a$)$ Compute $E_r,$

b$)$ Draw the water surface profile over the entire channel, and label the important curves and show important depths with their magnitudes on the given figure below.

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