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 C: 225 ft.
Dam C: 225 ft.
Dam D: 316 ft.
Dam D: 316 ft.
Dam A: 175 ft.
Dam A: 175 ft.
Dam B: 55 ft.
Dam D: 316 ft.
To determine which dam would provide the most hydroelectric power, we need to compare the power output of each dam. The power output of a hydroelectric dam is calculated using the formula:
Power (in kilowatts) = Water flow rate (in cubic feet per second) * Height (in feet) * Conversion factor
Since the water flow rate is the same for all four rivers, we only need to compare the height of each dam to determine which one provides the most power.
Let's compare the heights of the four dams:
- Dam A: 175 ft
- Dam B: 55 ft
- Dam C: 225 ft
- Dam D: 316 ft
Based on the heights alone, we can conclude that Dam D, with a height of 316 ft, 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 formula for potential energy is given by:
Potential Energy = mass × g × height
Where:
- mass is the volume of water flow over time (given as the same for all dams)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Let's calculate the potential energies for each dam:
Dam C:
Potential Energy (C) = mass × g × height (C)
Potential Energy (C) = same mass × 9.8 m/s^2 × 225 ft (converting to meters)
(Note: 1 ft = 0.3048 m)
Potential Energy (C) = same mass × 9.8 m/s^2 × 68.58 m
Estimated Potential Energy (C) = same mass × 672.744 N-m
Dam D:
Potential Energy (D) = mass × g × height (D)
Potential Energy (D) = same mass × 9.8 m/s^2 × 316 ft (converting to meters)
Potential Energy (D) = same mass × 9.8 m/s^2 × 96.01 m
Estimated Potential Energy (D) = same mass × 941.098 N-m
Dam A:
Potential Energy (A) = mass × g × height (A)
Potential Energy (A) = same mass × 9.8 m/s^2 × 175 ft (converting to meters)
Potential Energy (A) = same mass × 9.8 m/s^2 × 53.34 m
Estimated Potential Energy (A) = same mass × 521.532 N-m
Dam B:
Potential Energy (B) = mass × g × height (B)
Potential Energy (B) = same mass × 9.8 m/s^2 × 55 ft (converting to meters)
Potential Energy (B) = same mass × 9.8 m/s^2 × 16.76 m
Estimated Potential Energy (B) = same mass × 164.248 N-m
Comparing the estimated potential energies of each dam:
Dam C: 672.744 N-m
Dam D: 941.098 N-m
Dam A: 521.532 N-m
Dam B: 164.248 N-m
Therefore, Dam D with a fall height of 316 ft would provide the most hydroelectric power.