$1.$a

Find the maximum volumetric flow in a $3-$ ft by $3-$ft concrete box culvert $(n=0\mathrm{.}013)$ with a rounded entrance $(k_e=0\mathrm{.}05,C_d=0\mathrm{.}95)$ if the culvert slope is $0\mathrm{.}0065,$ the length $100$ ft $,$ and the headwater level $5$ ft above the culvert invert? Assume free outlet conditions. Neglect headwater and tailwater velocity heads.

$1.b$

Determine the flow rate through a $50ft$ long, $18-$in diameter steel culvert with a $1\%$ slope if $HW=5ft$ and $TW=2\mathrm{.}5$ ft $.$ Assume $n=0\mathrm{.}015,$ entrance coefficient $=0\mathrm{.}5,$ and orifice coefficient $Cd=0\mathrm{.}65.$