A culvert with a square cross section measuring $2\mathrm{.}0m2\mathrm{.}0m$ is intended

for a discharge $Q=6\mathrm{.}264\frac{m^3}{s}.$ The culvert has the following attributes:

The bottom slope S $0=0\mathrm{.}09,$ the length $L=40m,$ and the Manning

roughness coefficient $n=0\mathrm{.}020.$

a$)$ Identify the type of flow in the culvert and determine the flow depths

$"$y$"$ in the culvert and $"$H$"$ in the reservoir. You could think that entrance

losses are insignificant.

b$)$ What must be the water level, $H,$ in the upstream reservoir in order for

"Type $2"$ flow to occur in the culvert that conveys the same amount of

discharge, $Q=6\mathrm{.}264\frac{m^3}{s},$ from a smaller square culvert with

dimensions of $1\mathrm{.}0m1\mathrm{.}0m$ and the same properties as mentioned

above? Assume that Kent $=0\mathrm{.}5$ is the entrance loss coefficient.