Orifice with restrictor plate $(10$ points$)$

The $100-$year outflow from a detention pond is governed by the diameter of the outlet pipe, and sometimes a restrictor plate, as shown below:

NEIR

The $100-$year discharge from a $40-$acre basin with class C$/$D soils is $49\mathrm{.}9cfs,$ found using the Colorado urban hydrograph procedure $($CUHP$).$ This basin is being developed with single family homes. You are to design the $100-$year orifice for a detention pond, using a pipe diameter of $30".$ Assume there is $6ft$ of head above the centroid of the orifice at the $100-$year stage, and that it is freely discharging into the outflow pipe $($orifice coefficient of $0\mathrm{.}59).$ Find the height of the restrictor plate $($above the invert, in $ft)$ so that the outflow is $90\%$ of the predevelopment discharge. Hint: you will need to revisit semi$-$full discharge in a circular cross section to determine the flow area.