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?(1 point)
Responses
dam A: fall height of 175 feet
dam A: fall height of 175 feet
dam C: fall height of 135 feet
dam C: fall height of 135 feet
dam B: fall height of 75 feet
dam B: fall height of 75 feet
dam D: fall height of 100 feet
The dam with the greatest fall height, which is dam A with a fall height of 175 feet, would provide the most hydroelectric power.
To determine which dam would provide the most hydroelectric power, we need to consider the potential energy of the falling water. The potential energy is calculated using the formula: potential energy = mass * gravity * height. Since all four rivers have the same volume of water flow over time, we can assume that the mass of water is the same for all dams.
Now, let's compare the potential energy for each dam:
Potential energy for dam A = mass * gravity * 175 feet
Potential energy for dam C = mass * gravity * 135 feet
Potential energy for dam B = mass * gravity * 75 feet
Potential energy for dam D = mass * gravity * 100 feet
From the given information, we can see that the fall height for dam A is the highest at 175 feet. Therefore, dam A would provide the most hydroelectric power.
To determine which dam would provide the most hydroelectric power, we need to understand that the power generated by a hydroelectric dam is directly proportional to the product of the water flow rate and the height of the fall (also known as the head).
In this case, we are given that all four rivers have the same volume of water flow over time. Therefore, we can assume that the water flow rate is the same for all the dams.
Now let's compare the fall heights of the dams:
- Dam A has a fall height of 175 feet.
- Dam B has a fall height of 75 feet.
- Dam C has a fall height of 135 feet.
- Dam D has a fall height of 100 feet.
Since the water flow rate is the same for all the dams, the dam with the highest fall height will provide the most hydroelectric power. Therefore, in this case, Dam A with a fall height of 175 feet would provide the most hydroelectric power.