$50$ pts

Problem IV: A $10-$ft$-$wide, $50-$ft$-$long rectangular channel $($Manning$\text{'}$s $n=0\mathrm{.}013,S_0=0\mathrm{.}001)$ carries a flow of $30$ cfs $.$ The water depth at the entrance is $1\mathrm{.}2ft.$ Perform the following analyses:

$5$ pt

$(1)$ Classify the water surface profile.

$10$ pt

$(2)$ Compute and sketch the water surface profile using the Format$-$I governing equation.

$10$ pt

$(3)$ Compute and sketch the water surface profile using the Format$-$II governing equation.

$5$ pt

$(4)$ Classify the water surface profile if the water depth at the entrance is reduced to $0\mathrm{.}85$ ft $,$ while all other conditions remain unchanged.

$5$ pt

$(5)$ Classify the water surface profile if the water depth at the entrance is reduced to $0\mathrm{.}50$ ft $,$ while all other conditions remain unchanged.

$5$ pt

$(6)$ Classify the water surface profile if the discharge is increased to $60$ cfs $,$ while the water depth at the entrance remains unchanged.

$5$ pt

$(7)$ Classify the water surface profile if the channel bed slope is changed to $S_0=0\mathrm{.}02,$ while all other conditions are unchanged.

$5$ pt

$(8)$ Classify the water surface profile if the Manning's is changed to $0\mathrm{.}025,$ while all other conditions remain unchanged.