The surface elevation difference between two reservoirs, $25km$ apart, is $80m.$ 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 $50\frac{L}{s}.$ Assume a water temperature of $20C,$ and ignore minor losses.