A rectangular channel carries a discharge $4\mathrm{.}0\frac{m^3}{sec}$ at a slope $0\mathrm{.}001$ has a bed width $2\mathrm{.}0$ m $.$ Manning coefficient equals $0\mathrm{.}025($metric$).$ At a long distance after a sluice gate the depth is uniform. Calculate:

a$)$ The normal and critical depths.

b$)$ The Froude's number.

c$)$ The type of flow.

d$)$ The sequent depth of the possible hydraulic jump after a short distance from the gate and the Froude's number there.

e$)$ The head lost in the hydraulic jump.