To determine which dam would provide the most hydroelectric power, we can use the principle that hydroelectric power is proportional to both the volume of water and the height from which it falls. The potential energy (and thus the power) generated by a dam can be estimated using the formula:
\[ \text{Power} = \text{Flow Rate} \times \text{Height} \times \text{Gravitational Acceleration} \]
Since all four dams have the same volume of water flow over time, the primary factor that differentiates the amount of power generated is the fall height.
Here are the fall heights for each dam:
- Dam A: 175 feet
- Dam B: 75 feet
- Dam C: 135 feet
- Dam D: 100 feet
Among these options, Dam A has the highest fall height of 175 feet. Therefore, it would provide the most hydroelectric power.
So, the answer is dam A: fall height of 175 feet.