Problem $1(30$pts$)$: A flow of $100\frac{m^3}{sec}$ occurs in a trapezoidal canal having a bottom width of $10m,$ a bottom slope of $0\mathrm{.}1\%,$ a side slope of $2$:$1(H$:$V),$ and $n=0\mathrm{.}017.$

Calculate the normal depth $(5\text{'})$ and critical depth $(5\text{'})$

Determine the flow region $($subcritical or supercritical$)$ and classify water surface profiles when the water depth is $1$ meter or $3$ meters, respectively $(20)$