A project demand for electricity is 25,000MW in a year. Estimate the following: The electricity is produced by a big hydroelectric station and the water level in the 10m deep reservoir is allowed to fall 100m to generate the electricity. How many square kilometer must the reservoir cover. Assume 100% efficiency.
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To estimate the required surface area of the reservoir, we can use the concepts of potential energy and the power equation.
First, let's calculate the amount of energy generated by the hydroelectric station in a year. We know that the power demand is 25,000MW, and since we assume 100% efficiency, this is also equal to the power output of the hydroelectric station.
The energy generated in one year is given by:
Energy = Power × Time
Given that there are 8760 hours in a year (365 days × 24 hours), the energy generated per year is:
Energy = 25,000MW × 8760 hours
Next, we need to calculate the potential energy of the falling water. The potential energy is given by the equation:
Potential energy = mass × gravity × height
Since we know the height (100m) and the power output (in MW), we can rearrange the equation to solve for mass:
mass = Power / (gravity × height)
Here, gravity is the acceleration due to gravity, approximately 9.8 m/s².
Now, let's calculate the mass of water required to generate the electricity:
mass = 25,000 MW / (9.8 m/s² × 100 m)
Finally, we need to calculate the volume of water required, using the formula:
Volume = mass / density
The density of water is approximately 1000 kg/m³.
Now we can calculate the volume of water:
Volume = mass / 1000 kg/m³
To find the surface area, take the volume and divide it by the depth of the reservoir (10m), since the area is equal to the volume divided by the depth:
Surface area = Volume / depth
Finally, convert the surface area to square kilometers by dividing by 1,000,000 (since there are 1,000,000 square meters in a square kilometer).
So, the formula for calculating the required surface area is:
Surface area = (25,000 MW / (9.8 m/s² × 100 m)) / 1000 kg/m³ / 10 m / 1,000,000 m²
By substituting the values into this formula, you can estimate the square kilometer area required for the reservoir.