Q$2)$ A rectangular flume connecting at $\frac{U}{S}$ and $\frac{D}{S}$ with canals of trapezoidal sections by using warped transitions and with the following data:

$Q=88\frac{m^3}{sec,\frac{U}{S}}$ canal water level $=42m,\frac{U}{S}$ canal cross section area $=72m^2,$ Flume cross section area $=33m^2,\frac{D}{S}$ canal cross section area $=52m^2,C_i=Ki=0\mathrm{.}1,C_0=K_0=0\mathrm{.}2.$

$1-$ Find the resulting water levels at the flume and at the $\frac{D}{S}$ canal.

$2-$ Draw a longitudinal profile showing water levels and levels of energy line.