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Question on volumes of water, excess mass, potential energy and power

  1. Jul 23, 2008 #1
    Ive done this question but from the answers Im getting I can see that I am going wrong, but I dont know where. There are lots of different parts to this question, I will show them all, followed by my attempt at working them out.

    A Harbour has an average water covered area of approx. 10km^2. On a particular day there is a 4m tide. Making clear any assumptions that you make calculate:

    a) The excess volume of water in the harbour at high tide compared with low tide:

    Here I didnt know whether I had to assume my own low tide? So I did and assumed that
    low tide was 1.5m...if Im being stupid and thats wrong please let me know, so I worked

    Volume of water at high tide = 10km x 4m = 10000m x 4m = 40,000m^3

    Volume of water at low tide = 10km x 1.5m = 15,000m^3

    Excess volume of water = 40,000 - 15,000 = 25,000m^3

    b) The excess mass of water in the harbour at high tide compared with low tide:

    Mass=density x volume = 1027 x 25,000 = 25,675,000 kg

    c) The increase in potential energy of the water in the harbour

    This is where my numbers start getting rediculously big, making me think I must have
    gone wrong somewhere

    Potential energy at low tide = mass x g x height = 15,405,000 x 9.8 x 1.5 = 226,453,500

    Potential energy at high tide = 41,080,000 x 9.8 x 4 = 1,610,336,000

    Increase = 1,610,336,000-226,453,500= 1,383,882,500 J

    d) If all of this energy could be extracted by a generator, how much power could be

    Because all my numbers before this step are so big, I dont even know where to start with
    this question.

    Please help me by telling me where and why I am going wrong with this, I realy cant work it out. Thanks alot
  2. jcsd
  3. Jul 23, 2008 #2


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    Science Advisor
    Homework Helper

    The numbers are even larger than you think. 10km^2=10*(1000m)^2=10^7m^2. 10km^2 of water piled to meter high depths is a LOT of water. Notice you are doing stuff like "10km x 4m = 10000m x 4m = 40,000m^3". The units don't work out there. m*m=m^2, not m^3. You could probably just assume low tide=0m. But this whole thing is just an order of magnitude estimate anyway. You are basically doing ok. Just watch the units. And as they said, state the assumptions you are making, which you already doing pretty well.
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