Energy niagra falls problem water

[mshah3]

Homework Statement

In the Niagara Falls hydroelectric generating plant, the energy of falling water is converted into electricity. The height of the falls is about 45 meters. Assuming that the energy conversion is highly efficient, approximately how much energy is obtained from one kilogram of falling water? Therefore, approximately how many kilograms of water must go through the generators every second to produce a megawatt of power (106 watts)?

____kg/s

Homework Equations

Gravitational energy = (mass) × g × (height).

The Attempt at a Solution

I tried to find energy based on the fact one drop of water is one gram.
I ended up pluging in the values and got (45)(9.8) = 441
I found this to be incorrect.
Not sure how to relate mass to seconds to energy to height...
=/

 

[chaoseverlasting]

For 1kg of water, the energy derived=mgh joules.
For mega watts, its not 106, but 10^6 watts of power. This is equal to 10^6joules/second.

Can you work it out now?

 

[ogb p]

I would like to clarify that the mass of one drop of water is not equal to one gram. The mass of one drop of water depends on its size and can range from 0.05 grams to 0.1 grams.

To accurately calculate the energy obtained from one kilogram of falling water, we can use the equation provided in the homework statement: Gravitational energy = (mass) x g x (height). In this case, the mass is 1 kg, the gravitational acceleration (g) is 9.8 m/s^2, and the height is 45 meters. Plugging these values into the equation, we get a result of 441 joules.

To determine how many kilograms of water must go through the generators every second to produce a megawatt of power, we can use the fact that 1 watt = 1 joule/second. Therefore, to produce 1 megawatt (106 watts) of power, we would need 106 joules of energy to be produced every second. From our previous calculation, we know that 1 kg of falling water produces 441 joules of energy. Dividing 106 joules by 441 joules, we get approximately 2400 kilograms of water per second.

Therefore, the answer to the question is 2400 kg/s.