In a micro-hydroelectric system, water is diverted from an elevated stream into a pipe called a penstock, through which it descends a vertical height drop \(h\) to a turbine generator at a constant speed. The mass flow rate of the water passing through the penstock is \(\dfrac{\Delta m}{\Delta t}\). Which of the following correctly identifies the sign of the work done by the gravitational force on the water as it descends, and describes how the rate of mechanical energy input to the turbine changes if the vertical drop \(h\) is doubled while the mass flow rate \(\dfrac{\Delta m}{\Delta t}\) is halved?