Potential Energy, Tank on Hill, water power generator downhill.

In summary, the student is trying to find out the cost of power for a year using a waterfall chart and the equations for power and density. They are having trouble understanding how to solve for the cost and are looking for help.
  • #1
Wobble
29
0

Homework Statement



Quiz4Physics.jpg


Homework Equations



KE=(0.5)mv^2

PE=mgh


The Attempt at a Solution



a.)
The tanks volume is 20m^3. I then multiply that by the density to get the mass of the water, which is 20,000 kg.

Apply that into PE=mgh for gravitational potention
(20,000)(9.8)(50)=9,800,000
-Is everything in the right units?-

b.) I have no idea how to do this part.

If I can get some help with part b, that would be greatly appreciated.
 
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  • #2
m3 = 1000 L
1 L = 1 kg H2O

20m3 = 20,000 kg times g and 50 m is your PE. So far so good.

But what does that give you? Joules?

And they want Watts? Which are what? Joules/sec?
 
  • #3
Yeah, I got that far. What about part B though?
 
  • #4
Your PE seems to be okay. As for b) what is the equation for power?

Edit: LowlyPion was faster...
 
  • #5
Hm, I've been in class all day.

Power is Energy/time. I'm looking for the volume of water to produce 1000W

P=E/t, and I get 1000J of water per second for 1000 watts of power in one second.

Then I plug that into the GPE equation GPE=mgh where I'm looking for mass

1000=m(9.8)50
m=2.04kg

Then divide that by the density to get the cubic meters of water per second, .00204m^3

That number seems really small.
 
  • #6
I'll attempt to solve the rest while waiting for a response to my answer for part b.

c.) 86,400 seconds in one day. 86,400 * .00204 = 176.256 m^3 per day.

d.) 1m^3=35.3ft^3

so .00204*35.3=.072cfs

e.) my theoretical creek would have 0.3 cfs
I'm not sure where to go from here
 
  • #7
Part b looks ok at about 2.04 L/s

1 L = .0353 cf

OK to e) so figure what they want.

It takes 2.04 L a sec to generate what you need - i.e 1000 w.

If the flow of 6 is reduced to a 1/20 that makes it 6/20 cfs *1/.0353 cfs/L 8.5 L and then 1/2.04 kw/L = 4.16 kw
 
  • #8
Ok. So then for part F

I got 4.17(.065)(86,400)(365.25)=$8,520,552 as the cost for the year.

That doesn't make any sense to me. Does it generate 4.16 kW every second?
 
  • #9
Wobble said:
Ok. So then for part F

I got 4.17(.065)(86,400)(365.25)=$8,520,552 as the cost for the year.

That doesn't make any sense to me. Does it generate 4.16 kW every second?

You mean Joules / s don't you? That's watts.

Then you must be real careful in reading your problem.

The price they quote is kw-hour = 3600 *J/s = 3600 w.
 
  • #10
Oh crap. So should I use 4.16 times 3600 (seconds in an hour), then multiply that by rate of .065?

(4.16)(3600)(.065) to get the cost for 1 hour.

Then that number times 24, then 365.25 to get the amount in a year?

That gave me $8,553,687.48
 
Last edited:
  • #11
1000j/s is 1 kw.

You need 3600 of those to make a kw-h

At the flow rate they ask about though you have 4.16 j available every second for an hour so that means the stream provides 4.16 kw-hour every hour.

How many hours in a year?

24*365 now times 4.16 kw-h and times again the price of $.065.
 
  • #12
Ugh, this is rough. I much prefer calc 2 to this stuff.

Thank you for your help.
 

What is potential energy?

Potential energy is the energy that an object possesses due to its position or condition. It is stored energy that has the potential to be converted into other forms of energy, such as kinetic energy.

How is potential energy related to a tank on a hill?

A tank on a hill has potential energy because it is positioned at a height above the ground. The higher the tank is on the hill, the more potential energy it has, as gravity can pull it down and convert the potential energy into other forms of energy.

What is a water power generator downhill?

A water power generator downhill is a type of renewable energy technology that uses the force of gravity to generate electricity. It involves using water from a higher elevation to turn a turbine, which then produces electricity.

How does a water power generator downhill work?

A water power generator downhill works by using a system of pipes or channels to direct water from a higher elevation down to a lower elevation. The force of the water turning the turbine creates mechanical energy, which is then converted into electrical energy by a generator.

What are the benefits of using a water power generator downhill?

Using a water power generator downhill has several benefits, including being a renewable energy source, producing clean electricity with no emissions, and having a low operational cost. It also has the potential to provide a consistent and reliable source of energy, making it a valuable alternative to fossil fuels.

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