Four rivers have the same volume of water flow over time but fall from different heights to power hydroelectric dams. Which dam would provide the most hydroelectric power?
a
dam C: fall height of 135 feet
b
dam A: fall height of 175 feet
c
dam D: fall height of 100 feet
d
dam B: fall height of 75 feet
The potential energy of the water is given by the formula PE = mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the height of the fall. Since the volume of water flow is the same for all four rivers, the mass of water is the same for all four dams. This means that the potential energy of the water is directly proportional to the height of the fall.
Therefore, the dam with the highest fall height, dam A with a fall height of 175 feet, would provide the most hydroelectric power.