A $2-$ft$-$diameter $100-$ft$-$long circular concrete culvert is constructed as a

road crossing over a stream. The culvert barrel $($f $=0\mathrm{.}016)$ has an inlet of projecting from fill, square cut end. It is laid on a slope of $0\mathrm{.}015$ and designed to convey $50$ cfs$.$ For an outlet$-$control condition, determine the HW if the TW is:

$(1)1\mathrm{.}2$ ft

$(3)2\mathrm{.}5$ ft

$($Answers: $(1)5\mathrm{.}61$ ft; $(2)5\mathrm{.}61$ ft

$(3)10\mathrm{.}05$ ft; $(4)11\mathrm{.}05$ ft$)$