$\{$Hydraulic Engineering:

Please show all work for deriving coefficients and necessary terms! The correct answer is provided to check against. Please do not report incorrect answer, but adjust your strategy accordingly!$\}$

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Determine the discharge on an overflow spillway designed for a maximum head of $8$ ft above the crest. The overflow section is $12$ ft high and $100$ ft long. The tailwater can rise $6\mathrm{.}5$ ft above the crest level. The upstream face of the spillway has a slope of $1($horizontal$)$:$3($vertical$).$ There are no piers and the abutment walls have square section.

$\{$Correct ans.: Q $=8,257$ cfs $\}$