$3.$a$)$ A $100-$ft$-$long, $36-$in$.$ concrete culvert at a $1\%$ slope has a sharp$-$edged projecting entrance. At an upstream flow depth of $5$ ft$,$ find the flow discharge and determine whether this is outlet or inlet control $($Problem $12\mathrm{.}5).$

b$)$ Recalculate for problem $3$ above for a headwall and rounded entrance. Would the discharge increase at a $5$ ft flow depth? If so$,$ why?