A fire pump delivers water through a $6-$in$.$ main to a hydrant to which is connected a $3-$in$.$ hose, terminating in a $1-$in$.$ nozzle. The nozzle is $10$ ft above the hydrant and $60$ ft above the pump. Assuming a total frictional loss of $28$ ft from the pump to the base of the nozzle, and a loss in the nozzle of $6$ percent of the velocity head in the jet, and neglecting air resistance, what gage pressure at the pump is necessary to throw a stream $80$ ft vertically above the nozzle? Provide illustration and show complete solution.