Final answer:
The amount of hydroelectric power produced by a dam is indeed proportional to the flow rate of the water. Increasing the flow rate will result in a higher power output.
Step-by-step explanation:
Hydroelectric power is generated by converting the potential energy of water into electricity. The amount of power produced by a dam is indeed proportional to the flow rate of the water. This can be explained using the equation P = mgh, where P is the power, m is the mass of water flowing per second, g is the acceleration due to gravity, and h is the height of the dam. Increasing the flow rate, or the mass of water per second, will result in a higher power output.
For example, if a dam with a flow rate of 100 m³/s has a height of 50 meters, the power produced is P = (100) * (10) * (50) = 50,000 W = 50 MW. Similarly, if the flow rate is increased to 200 m³/s, the power output would be 100 MW.