How to Calculate the Power Output of a Waterfall Generator

[pooface]

Homework Statement

A waterfall is 85ft high, and 3000 cubic ft/sec flow over it driving a water wheel connected to an electric generator. If the overall efficiency is 22%, how many kilowatts does the generator develop?

Homework Equations

density of water =1000kg/cubic meter
P.E. = mgh
weight=density*g*volume

The Attempt at a Solution

Firstly convert to SI units.
85ft = 25.91m
3000 cubicft/sec = 914.4 cubic meter/sec

weight of the water being applied = (1000)(9.81)(914.4)
= 8.97 MN

P.E.=(8.97 MN)(25.91m)
=232.42 MJ
power in = 232.42 MJ /1sec = 232.42 megawatts

eff =0.22

0.22 = POUT/232.42 MW

Are my steps correct?

 

[learningphysics]

3000 cubicft/sec = 914.4 cubic meter/sec

I'm getting 3000 cubicft/sec = 84.95 cubic m/s

other than this, everything looks right to me. be sure to convert to kW when you finish...

 

[pooface]

how do you do a conversion such as 3000 cubic ft to cubic meter?

Yea, I realized i just did a ft-m conversion instead of cubic ft to cubic meter (a function on my calc).

 

[learningphysics]

how do you do a conversion such as 3000 cubic ft to cubic meter?

Yea, I realized i just did a ft-m conversion instead of cubic ft to cubic meter (a function on my calc).

I actually just used google.com. I typed in 3000 ft^3 and it automatically converted it.

But we can do it this way:

we know that 1 ft = 0.3048m

(1ft)^3 = (0.3048m)^3

so 1ft^3 = 0.0283168466 m^3

so 3000 ft^3 = 84.95 m^3

 

[pooface]

amazing...thanks a lot learningphysics. You are truly an asset to this board. I have another test this friday. Hope I do well.

 

[learningphysics]

amazing...thanks a lot learningphysics. You are truly an asset to this board. I have another test this friday. Hope I do well.

thanks so much. I appreciate it! good luck on your test! you'll do great!