Question $3$

Water flows in a very wide rectangular channel $(B>>>y)$ transitioning from a mild to steep slope, with a flow rate of $2\mathrm{.}34\frac{m^3}{s}$ per meter. Given the slope and Manning's roughness coefficient as $0\mathrm{.}0016$ and $0\mathrm{.}018$ respectively: $($Use FOUR $(4)$ decimal places for all answers$)$

a$)$ Calculate

i$.$ The normal depth for the channel,

ii$.$ The critical depth for the channel,

iii. The conveyance factor, K for the channel,

iv$.$ The channel section factor, Z for the channel,

b$)$ Calculate the distance upstream from the normal depth to the section of the slope transition $($critical depth$)$ using the direct step method with three points.

c$)$ Identify the type of water surface profile.