A $12in.$ sch $40$ pipe, $60ft$ long, discharges water at $1$atm pressure from a reservoir. The pipe is horizontal, and the inlet is $12ft$ below the surface of the water in the reservoir.

$($a$)$ What is the flow rate in gpm$?$

$($b$)$ In order to limit the flow rate to $3,500gpm,$ an orifice is installed at the end of the pipe. What should the orifice diameter be$?$

$($c$)$ What size pipe would have to be used to limit the flow rate to $3500gpm$ without using an orifice?