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Homework Help: Calculate the torque of a hinge in a dam

  1. Jan 29, 2012 #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 4.00m wide and is hinged along a horizontal line through its center.
    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.)

    2. Relevant equations

    3. The attempt at a solution
    I wasn't sure how to calculate torque without force, but I figured maybe I could use atmospheric pressure as follows:
    F=100000*8(area of gate)=800000N
    but then I dont know how the integration comes to play, I tried just multiplying the force by the distance between the hinge and the surface of water to find the torque:
    I assumed it is the distance r from the surface of the water to the center of the gate which is half the height of the gate
    dont know how to properly integrate the toque over the gate and if the distance I have used is correct.

    Attached Files:

    Last edited: Jan 29, 2012
  2. jcsd
  3. Jan 29, 2012 #2
    From your diagram, one edge of the gate is at the water surface. The other edge is submerged at a depth of 2m. Do you think the pressure exerted on the gate by the water will be the same at the top as at a depth of 2m? How does pressure change with depth in a column of water?

    You are right to consider a distance from the edge of the gate to the centre (axis of rotation). But don't forget that if one edge lies a distance z from the axis, the other lies a distance -z. Meaning, you should realise that the torques will cancel to some extent but not totally because the pressure is changing with depth.
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