Calculating Energy at Niagara Falls

[BioGuy]

I have a question... is there any way to figure out the amount of energy going over the Niagara Falls in 1sec. ?

I know the dimensions but don't know what formula to use..

height: 167ft
Deepest depth: 41ft
Fastest Speed: 68mph (2-3ft per sec.)
375,000gal per/sec

please help...

 

[Delphi51]

I don't like the look of that "fastest speed" so I would just use the potential energy the water has at the top (and loses on the way down). It will take a bit of work with a density formula and unit conversions to get the mass that goes over in one second.

 

[BioGuy]

i can't really find any information relating to physics terms about niagara falls.. and then to turn that into watts? to figure out energy? My professors crazy...

 

[sylas]

i can't really find any information relating to physics terms about niagara falls.. and then to turn that into watts? to figure out energy? My professors crazy...

What is the change in potential energy of 1 gallon of water falling 167 feet?

Do you know the physics equations for potential energy?

Felicitations -- sylas

 

[jdwood983]

Total Energy is Potential Energy + Kinetic Energy, you should work from there:

$$E=mgh+\frac{1}{2}mv^2$$

To get the mass, use dimensional analysis to convert gallons into lbs (assuming you want to continue in the US standard, rather than metric units). I imagine this number would be pretty high since there's like 20 power plants on both sides.

 

[Phrak]

One gallon is 8 pints or 8 pounds.

Energy can be measured in foot-pounds.

Power can be measured in foot-pounds per second.

How fast is 68 mph in feet per second again?

You should use E = mgh = weight times height.

 

[Phrak]

I think I gave you too much information.

Anyway, you should do the research--either your textbook or the internet and look-up potential energy.

Second, how many feet per second is 68 miles per hour?

 

[Phrak]

The fps part is for the kinetic energy part of the problem, of the water as exits over the fall. You'll need the 99.7 fps for this.

In this problem the units are given in pounds, feet, and seconds. So energy is going to be in foot-pounds. You don't need to convert to meters.

You have 3,000,000 pounds per second of falling water. Potential energy is expressed in pounds times distance fallen.