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Pressure on a Dam

  1. Jan 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Two dams are both 25 m tall and both hold back lakes with a depth of the 20 m at the dam. The first dam holds back a lake with 100,000 m3 of water in it. The second dam holds back a lake with 300,000 m3 of water in it. What is the ratio of the pressure at the bottom of the first dam to the pressure at the bottom of the second dam?
    →3.00
    →0.33
    →0.8
    →1.25
    →The pressure is the same at the bottom of both dams.
    →You can’t tell without knowing the maximum length of the lake.


    2. Relevant equations

    F = aρhg

    3. The attempt at a solution
    My first thought was that the pressure for both dams are the same since they have the same height. But that doesn't seem to make logical sense. Logically, I believe that if the second dam has 3x the amount of water behind it the pressure should be greater by something along the line of 3x (since my equations don't have a squared or inverse square term it should be a linear relationship...either 3x or 1/3x). I believe that I'm stuck in a second guessing loop.

    I believe that the answer is .33. Since the first dam has 1/3 of the water behind it (and identical other statistics to the second dam) the force should be 1/3 that of the second dam.

    Can you please confirm/deny and if deny jog me in the right direction? Thanks.
     
  2. jcsd
  3. Jan 17, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    That first thought was correct. Static pressure depends only on the depth beneath the surface, not on the amount of water in some body. See: Static Fluid Pressure

    Counter to everyday intuition? Perhaps. Counter to 'logic'? No. :smile:
     
  4. Jan 17, 2012 #3
    Ah hah! Thanks! I am trying to get my intuitive head in line. The water at the back of the dam is supported by the 'land' at the bottom so it doesn't exert any horizontal pressure? I can almost get completely behind this because the pressure is the same at 30' regardless if you are in the ocean or in a deep pool or my gran's lake.
     
  5. Jan 17, 2012 #4

    Doc Al

    User Avatar

    Staff: Mentor

    You can think of it that way.
    Sure it does. At any given point in the water, pressure is exerted equally in all directions.
    Exactly!
     
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