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Rotating Pail of Water

  1. Nov 3, 2007 #1
    1. The problem statement, all variables and given/known data
    A rotating pail of water with an angular velocity w has a surface curving up from the centre to the outer edge. Find the shape of the surface. The slope of the surface is dy/dx = tan(theta) at position x is y (= function of x) is the shape of the surface. You must resolve forces to find tan(theta) as a function of x, and then solve for the height, y, as a function of x.

    If the pail rotates once per second, and has a diameter of 0.45 m, how high above the centre is the outer edge?

    2. Relevant equations

    3. The attempt at a solution
    All I see is that w = 2pi rad/sec and r = 0.225 m.
  2. jcsd
  3. Nov 4, 2007 #2
    Method I:
    Ideal Fluid, by definition, can not tolerate any shear force. Use this fact.
    Assume the centre of the water surface to be origin. Let P(x,y) be a point on the water surface. Consider forces on it. Impose the condition that tangential force will be zero.
    I hope you can proceed now.
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