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Water dam torque problem

  1. Nov 10, 2014 #1
    1. The problem statement, all variables and given/known data
    The upper edge of a gate in a dam runs along the water surface. The gate is 2.00 m high and 4.00 m wide and is hinged along a horizontal line through its center (Figure 1)

    Calculate the torque about the hinge arising from the force due to the water. (Hint: Calculate the torque on a thin, horizontal strip at a depth h and integrate this over the gate.)

    O6QW4ya.png

    2. Relevant equations
    F = Pressure * Area
    M = Density * Volume
    Torque = Force * Moment-Arm
    Pressure = Density * gravity * depth (edit: I recently found this out)

    3. The attempt at a solution
    I found out that pressure would be:
    1x103 * gravity * depth
    And since we want the total pressure we will have to integrate correct?
    Therefore our varying variable will be h (height) so pressure would be:
    ∫ from 0 - 1 (the middle of that gate) of (1x103 * gravity * h) dh correct?
    And do I now multiply the answer from that by the area ( 4 * 2 = 8) to get the force?
    Then multiply that force by the moment arm? (Not sure how to get this though.)

    Any and all help is appreciated.
     
    Last edited: Nov 10, 2014
  2. jcsd
  3. Nov 10, 2014 #2

    SteamKing

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    Why don't you draw a sketch of the gate, showing how the pressure acts on the gate above and below the hinge?

    For each strip which is dh high, what is the force acting on the gate due to the water pressure? What is the moment of this force acting about the hinge?
     
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