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Calculating Force On A Dam, Using Pressure, Area, and other Known Values

  1. Jan 17, 2009 #1
    1. The problem statement, all variables and given/known data

    Part A
    Consider a horizontal layer of the dam wall of thickness dx located a distance x above the reservoir floor. What is the magnitude of the force on this layer due to the water in the reservoir?

    Express your answer in terms of , x, dx, the magnitude of the acceleration due to gravity , g and any quantities from the problem introduction: dw(water density), L(width of the dam), h (depth of the water). For more info: See image attached.



    Part B
    The force of the water produces a torque on the dam. In a simple model, if the torque due to the water were enough to cause the dam to break free from its foundation, the dam would pivot about its base (point P). What is the magnitude of the torque T about the point P due to the water in the reservoir?

    Express your answer in terms of quantities given in the problem introduction and the magnitude of the acceleration due to gravity .



    2. Relevant equations
    (1)P=P_o+ rho*g*h
    (2)P=F/A

    3. The attempt at a solution

    Part A: rho_w*g*x=F/A Therefore, F=rho_w*g*x (A). But what is the area equal to?
    Part B: Use the equation for Torque T=r*F?
     
  2. jcsd
  3. Jan 17, 2009 #2
  4. Jan 17, 2009 #3

    LowlyPion

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    Homework Helper

    What they want is the force on a layer. The picture is a cross-section of the dam.

    But a layer of "area" is a skinny ribbon Δx high and L wide.
     
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