uThe control structure $($shown in the figure$)$ consists of $7$ radial gates, each $7$ meters high and $9$ meters wide, with intermediate piers $2$ meters thick.

a$)$ Calculate the flow rate discharged when the elevation in the reservoir is $34\mathrm{.}40$ meters and $48$ meters.

b$)$ What should be the gate opening so that, with the water at a level of $48$ meters, the total flow rate is $3,000$ m$^3/$second$?$