Water is pumped between two large open reservoirs through \(1.5 \mathrm{~km}\) of smooth pipe. The water surfaces in the two reservoirs are at the same elevation. When the pump adds \(20 \mathrm{~kW}\) to the water, the flowrate is \(1 \mathrm{~m}^{3} / \mathrm{s}\). If minor losses are negligible, determine the pipe diameter.