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. Dam A: fall height of 175 feet
2. Dam C: fall height of 135 feet
3. Dam D: fall height of 100 feet
4. Dam B: fall height of 75 feet
The amount of hydroelectric power generated by a dam depends on both the volume of water flow and the fall height. In this case, since all four dams have the same volume of water flow, the one with the highest fall height will provide the most hydroelectric power.
Therefore, 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, which is determined by the product of the volume of water flow and the height from which it falls.
Let's assume that all four dams have the same volume of water flow.
1. Dam A: fall height of 175 feet
The potential energy would be highest for Dam A because it has the highest fall height of 175 feet.
2. Dam C: fall height of 135 feet
The potential energy for Dam C would be lower than that of Dam A because its fall height is less at 135 feet.
3. Dam D: fall height of 100 feet
The potential energy for Dam D would be lower than that of Dam C and Dam A because its fall height is further reduced to 100 feet.
4. Dam B: fall height of 75 feet
The potential energy for Dam B would be the lowest among all because it has the lowest fall height of 75 feet.
Therefore, Dam A would provide the most hydroelectric power due to its higher fall height compared to the other three dams.
To determine which dam would provide the most hydroelectric power, we need to consider the concept of potential energy. The potential energy of an object is directly proportional to its height and is given by the equation P.E. = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Since all four rivers have the same volume of water flow over time, we can assume that the mass of water flowing through each dam is constant. Therefore, we can disregard the mass term in the equation.
Now, let's compare the potential energy for each dam:
1. Dam A: fall height of 175 feet
Potential Energy (A) = g * h = 32.2 ft/s^2 * 175 ft = 5635 ft*lbf/s
2. Dam C: fall height of 135 feet
Potential Energy (C) = g * h = 32.2 ft/s^2 * 135 ft = 4347 ft*lbf/s
3. Dam D: fall height of 100 feet
Potential Energy (D) = g * h = 32.2 ft/s^2 * 100 ft = 3220 ft*lbf/s
4. Dam B: fall height of 75 feet
Potential Energy (B) = g * h = 32.2 ft/s^2 * 75 ft = 2415 ft*lbf/s
From the calculations above, we can conclude that Dam A would provide the most hydroelectric power, with a potential energy of 5635 ft*lbf/s. Dam C, D, and B would provide less power in descending order.
Therefore, Dam A would be the most efficient option for generating hydroelectric power among the four dams.