How Much Power Does Niagara Falls Generate?

[hshphyss]

Can anyone help me with this problem? Thaak-you
Water flows over a section of Niagara Falls at the rate of 1.1 106 kg/s and falls 46.0 m. How much power is generated by the falling water?
I know that Power is work/time... but this problem is set up differently then I'm used to.

 

[Impathy]

Well (somebody correct me if I'm wrong!) ... when water falls from a high place, its potential energy decreases. For a waterfall, the change in PE per second is equal to the rate times acceleration due to gravity times the height. When converted into electrical energy, the power is equal to the change in PE. See if that works out for ya. :)

 

[quicknote]

Hello,

I am a scientist and I am happy to assist you with your Niagara Falls power homework problem.

To calculate the power generated by the falling water at Niagara Falls, we can use the formula P = mgh/t, where P is power, m is mass, g is gravitational acceleration, h is height, and t is time.

First, we need to convert the mass flow rate of water from kg/s to kg, which is the unit used for mass in the formula. To do this, we can multiply the flow rate by the time interval that we are interested in. Let's assume that we are interested in the power generated over a period of 1 second.

So, 1.1 x 10^6 kg/s x 1 s = 1.1 x 10^6 kg.

Next, we can plug in the values into the formula:

P = (1.1 x 10^6 kg)(9.8 m/s^2)(46.0 m)/1 s

P = 5.108 x 10^8 J/s

Therefore, the power generated by the falling water at Niagara Falls is approximately 510.8 MW (megawatts).

I hope this helps you with your problem. Let me know if you have any further questions. Thank you.