$5\mathrm{.}3\mathrm{.}9$ Revised. A trapezoidal channel with a bottom width of $20ft,$ a bottom slope of $0\mathrm{.}0015,$ Manning's $n$

of $0\mathrm{.}025,$ and side slope of $2$:$1(H$:$V)$ has discharge of $500cfs.$ An obstruction in this channel causes a

backwater profile with a depth of $6\mathrm{.}5ft$ just upstream of the obstruction.

$5**4=20$

$(1)$ Compute the normal depth $(y_n)$ using a chart or non$-$linear solving method.

$(2)$ Compute the critical depth $(y_c)$ using a chart or non$-$linear solving method.

$(3)$ What is the flow regime $($supercritical or subcritical$)?$ Logically explain the reason.

$(4)$ What is the classification of water surface profile? Logically explain the reason.