The surface elevation difference between two reservoirs, $25$ km apart, is $80$ m$.$ Ductile iron pipes with a diameter of $44$ cm are used to transport water between the reservoirs via gravity flow. $($a$)$ Assuming Darcy$-$Weisbach head loss and completely turbulent flow, determine the flowrate between the reservoirs. $($b$)$ Determine the increase in water surface elevation of the upper reservoir if the flow you found in part $($a$)$ must be increased by $50$ L$/$s$.$ Assume a water temperature of $20$ deg C$,$ and ignore minor losses.