A hydrological analysis was completed for a basin above a proposed roadway and culvert crossing on SR $530.$ The analysis found that the $25-$year flow event was $300$ cfs and the $100-$year flow event was $390$ cfs $.$ In the vicinity of the round culvert, the preferable roadway profile would place the centerline at elevation $1,530$ feet, about $10$ feet higher than the existing channel bottom. The tailwater depth was found to be $5$ feet during the $25$ year flow event and $5\mathrm{.}5$ feet during the $100-$year flow event. Also, there are no fish passage concerns at this location. Assume that the culvert will be $100$ ft long and will match the existing channel slope of $\backslash (0\mathrm{.}005\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$ft$\}\backslash )\backslash ((0\mathrm{.}5\backslash \%)\backslash ).$ Determine the culvert size, and calculate the controlling headwater elevation and corresponding outlet velocity for both the $25-$ and $100-$year events.

Assumptions:

$-$ Culvert will be circular and concrete

$-$ Headwater to diameter ratio will be $\backslash (<mtext></mtext><mi>\backslash </mi><mi>)</mi>$ or $\backslash (=1\mathrm{.}25\backslash )$ for the $25-$year flow

$-$ Culvert end will be left projecting out of the fill since the culvert ends will be out of the clear zone