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Water , gravitational potential energy

  1. Nov 30, 2013 #1
    Hello , I was thinking about dams and hydroelectrostations , the turbines can turn because the water before the dam is higher than after it so there is stored potential energy waiting bto be released, Now I wonder if we were to take two places one at the water surface level in the dam reservoir and the other at the deepest place at the bottom of the reservoir , from which of these two places would the outcoming water have more energy , from the bottom where all the water above it pushes on the water and so the pressure builds up or from above where the water would fall all the height of the dam and gain it's kinetic energy and then end up where the bottom of the reservoir would be at the other side ?

    I kinda think that water which comes from the bottom of the dam reservoir has higher potential energy due to all the water above it exerting a pressure on it than water which falls from the top of the reservoir over the dam, what do you think?
  2. jcsd
  3. Nov 30, 2013 #2


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    The water at the bottom has pressure energy: the dam converts potential energy into pressure energy, then the pressure energy is converted to kinetic energy. All of this is via Bernoulli's principle/equation.

    [edit] There's also an issue of reference frames in your description: Where is the turbine located? If you are leaving the turbine at the bottom of the dam and pulling water off the top and piping it to the bottom, you haven't actually changed anything.
    Last edited: Nov 30, 2013
  4. Nov 30, 2013 #3


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    I think that there is nothing I love more than a good dam question.

    I just ran a jelly-cube bowling ball simulation, and all I could come up with was: If energy is conserved, then there is no difference.

  5. Dec 1, 2013 #4
    good dam question , heh :D

    well in both cases the Potential energy of water is converted into kinetic which is then lost in turning the blades , just to clear any confusion say the dam is 10m in height , the turbine is located at point 0 at the very base of the dam , one entrance to the turbine goes through the dam at point 0 right at the other side where the bottom of the reservoir is and the other entrance is the water which spills over the top of the dam , so you are saying that both the water which falls from over the top of the dam to hit the turbine at point 0 and the water which comes through at the base from the pressure behind it both have the same KE when in terms of turning the blades of the turbine?

    The reason why this kinda confuses me is because the water which comes from the point zero entrance from the bottom of the reservoir has basically every bit of water above it exerting pressure on it , while the water which falls over the top has only it's weight which can then accelerate , now assuming steady flow the weight at each situation at the top is say almoust similar.
  6. Dec 1, 2013 #5
    You can test it with a tube inserted in the bottom of the dam.Even with all the water above the tube exerting a pressure on the water below it will not escape if you raise the tube above the top of the dam.
    It only escapes if the tube is held slightly below the level at the top.
  7. Dec 1, 2013 #6
    I wanst thinking in terms of water pressing water upwards , I was thinking purely in terms of water flowing to the turbine from the bottom of the sreservoir with huge pressure or water flowing from the top of the dam (gates slightly opened) and falling down all the height iof the dam and the hitting the same turbine blades , and does that make the same force as the water from the bottom of the reservoir , as OmCheeto says I guess it does.
  8. Dec 1, 2013 #7


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    Textbook wise, there is no difference. Realistically though.....

    Imagine the device you would have to construct to capture all of the energy of a jello cube dropped from 10 meters. It makes my head spin.

    Also, Russ mentioned earlier that

    I don't think this is correct. When opening the gate to the turbine it might be, but not in steady state. In the previous dam thread, the OP quoted his text as saying

    I think the text is correct. I figured this out by putting thousands of turbines in a fluid series configuration. If it were true that the kinetic energy of the water was being converted to electrical energy, then you could power the world with one single dam. Unfortunately, it doesn't work that way.

    Although there is a kinetic energy component to the dam problem, as you'd get no energy at all if the water wasn't moving, I don't think it has anything to do with a typical dam problem.

    On a somewhat related topic, a couple of years back I decided that it would be a great idea to harness the kinetic energy of the river that flows by my house. Unfortunately, I think I made a math error somewhere:



    I suppose this is why I wouldn't make a good "real" crackpot. I do the math.
  9. Dec 1, 2013 #8
    Ok I get it now , I mean I got it before but now I get the turbine thing and gravity, I guess the difference is that a water wheel turns because water flows and touches one small side of that wheel at a time so it can turn , if you would ut the whole wheel into a river nothing would ahppen as the pressure from both sides would be equal , also if you would submerge a turbine blade into a steady river it wouldnt turn because again the pressure would equal out, the turbine only works when there is a higher pressure at one side of the blade than at the other side , just like putting force on a door handle so the door opens , if the same force would be put from the other side the dir would saty where it was and no movement, is this right ?

    So the gravitational potential energy that is used in a dam basically comes from the fact that we haev more water at one side than at the other, more water more mass , and it's at a higher place so it wants to get to a lower place.

    So that kinda leads me to my last question in this series , if we ahve two dams , dam A and dam B both have indentical reservoir volume capacities , the only difference that dam A is narrow but high and dam B is wide and low in height.
    Woudl there be a difference in water force if identical water holes would be opened at both dams at the base of the reservoir ?

    Since the volumes are the same it kinda makes me think there shouldn't be a difference but then I get kinda confused because of the heigth.Just like in the ocean , the ocea say Pacific ocean is very wide too yet still the biggest pressures are at the narrow but deep trenches like the Mariana trench.
    I guess because for a given volume of water the pressure at a given place at the bottom of a tank will be more if the tank will be higher and narrower than lower and wider is my reasoning correct , would love to hear some thoughts.
  10. Dec 1, 2013 #9


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    It is probably easier to use the more common type of turbine that primarily utilizes the pressure energy, not the kinetic energy. Obviously, the water has to go though the turbine and keep going otherwise it would build-up. So in order to utilize kinetic energy, you have to have an outlet that is much larger than the inlet (see: pelton turbine). Most don't do that.
    If they are using the same type of turbine that works on the same principle, then they act exactly the same, yes.
    This is an issue of how pressure works. Pressure depends on the height of the column of water only. Since the height is the same, the pressure at the bottom is the same.
  11. Dec 1, 2013 #10


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    I'm not clear on what your objection is and I do understand/agree that most turbines utilize the pressure energy, not the kinetic energy of the water. Indeed, I would favor setting up the two cases to have the same type of turbine and thus utilize the same properties.
  12. Dec 1, 2013 #11


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    Back to my jelly cube model:


    There is mathematically more energy in the tall reservoir vs the short reservoir.

    Imagine a stick. If you stand it upright, the top of the stick has lots of potential energy. The bits on the way to the ground have proportionally less energy.

    Now imagine the stick laying on the ground. Same stick. Zero potential energy.

    So you're saying, we should pipe the effluent of the Bonneville dam to the bottom of the Mariana Trench, where the pressure is really, really, really high, and pump the water back into lake Bonneville?

    It don't work that way. :tongue:

    Another aside:

    As a condition to join the navy, I had to take an 80 question exam. I missed 10 questions. After attending the school which was to teach me everything on the exam, I missed 1 question.

    It was very similar to this question.

    I think that's why I love these damn questions. They take me back. :smile:
  13. Dec 1, 2013 #12


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    As I mentioned in the previous thread

    or something to that effect.

    Bring it on! :thumbs:

    ps. I won't have any time off until next Thursday, so don't hold your breath.
  14. Dec 2, 2013 #13
    When are you finally going to do away with those feet/pounds/miles etc?

    7500 m^3/sec multiplied with the density of water gives 7.5 * 10^6 kg/sec of mass flow.
    Your answer is somehow nearly 5 times higher.
    You can just multiply the mass flow with the kinetic energy for each kg of water (2J/kg)
    to get a power of 15 MW of power. I have no idea what the rest of the calculation is supposed to do. If you want another hydroelectric station, you need at least 20 cm of altitude difference between the two to get the speed of the water up to 2 m/s again.
  15. Dec 2, 2013 #14
    @Om Cheeto , yes I do understand that taking the water froma deep trench up again just to do work on a turbine dopesn't work , the trench example was just there to make me or perhaps someone ever readin this thread understand that same volume of water but more narrow and higher tank makes a bihgger pressure at a given place at the bottom of the tank/reservoir.

    thanks for the answers.
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