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Help with a dam problem and pressure

  1. Oct 5, 2004 #1
    Figure 15-34 shows a dam and part of the freshwater reservoir backed up behind it. The dam is made of concrete of density 3.38 g/cm3 and has the dimensions shown on the figure.

    http://www.webassign.net/hrw/15_34.gif

    (a) The force exerted by the water pushes horizontally on the dam face, and this is resisted by the force of static friction between the dam and the bedrock foundation on which it rests. The coefficient of friction is 0.42. Calculate the factor of safety against sliding, that is, the ratio of the maximum possible friction force to the force exerted by the water.

    (b) The water also tries to rotate the dam about a line running along the base of the dam through point A; see Problem 23. The torque resulting from the weight of the dam acts in the opposite sense. Calculate the factor of safety against rotation, that is, the ratio of the torque owing to the weight of the dam to the torque exerted by the water.

    Anyone have any idea how to do that? Do you think pressure of air
     
  2. jcsd
  3. Oct 5, 2004 #2

    Tide

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    The horizontal force acting on the dam is the integral of the water pressure over the area of the dam in contact with the water. Be sure to account for the fact that the pressure varies with the depth of the water.
     
  4. Oct 5, 2004 #3
    Think I would need to use air pressure of the water?
     
  5. Oct 5, 2004 #4

    Tide

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    I'm not sure what that means. If you calculate the pressure of the water properly then you know that the water pressure at the water's surface will match that of the atmosphere. Also, air pressure opposes the pressure of the water on the opposite side of the dam.
     
  6. Oct 5, 2004 #5

    Phobos

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    water pressure varies linearly with depth

    pressure head of water at a given depth = (water density) x (gravity) x (height of water column)

    As Tide said, atmospheric pressure on the water is canceled out by the atmospheric pressure around the dam.
     
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