Answer:
The power of water transferred each hour through a 500m high dam if 500m² are cleared every hour is approximately 4.41 GW
Step-by-step explanation:
To answer this question, we need to know the density of water, the gravitational acceleration, and the efficiency of the dam. Let's assume that the density of water is 1000 kg/m³, the gravitational acceleration is 9.81 m/s², and the efficiency of the dam is 100%.
The power of water transferred each hour through the dam is given by the formula:
Power = Flow rate x Density x Gravity x Height x Efficiency
where Flow rate is the volume of water that passes through the dam each second, Density is the density of water, Gravity is the gravitational acceleration, Height is the height of the dam, and Efficiency is the efficiency of the dam.
First, let's calculate the flow rate:
Flow rate = Area x Velocity
where Area is the cleared area of 500m² and Velocity is the speed of water passing through the dam.
Assuming that the water is moving at a constant speed, we can use the formula:
Velocity = Height / Time
where Time is the time it takes for the water to pass through the dam.
Since the height of the dam is 500m and we want to know the power transferred each hour, we can convert the time to seconds as follows:
Time = 1 hour / 3600 seconds per hour = 0.000277778 hours
So, the velocity of the water is:
Velocity = 500m / 0.000277778 hours = 1,800,000 m/s
Now we can calculate the flow rate:
Flow rate = 500m² x 1,800,000 m/s = 900,000 m³/s
Finally, we can calculate the power of water transferred each hour through the dam:
Power = Flow rate x Density x Gravity x Height x Efficiency
Power = 900,000 m³/s x 1000 kg/m³ x 9.81 m/s² x 500m x 1
Power = 4,405,500,000 watts or approximately 4.41 GW
Therefore, the power of water transferred each hour through a 500m high dam if 500m² are cleared every hour is approximately 4.41 GW.