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Math Help - Hydrostatic Force

  1. #1
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    Hydrostatic Force

    I need help determining the hydrostatic force of the following problem:

    An equilateral triangle with sides 3 m is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it.

    Suggestions, anyone?

    I know that the pressure is 1000 kg/m^3 * 9.8m/s^2, but I can't figure out how to determine the rest....
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  2. #2
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    The depth is given by \sqrt{3^{2}-(3/2)^{2}}=\frac{3\sqrt{3}}{2}

    By similar triangles:

    \frac{w(x)}{3}=\frac{\frac{3\sqrt{3}}{2}-x}{\frac{3\sqrt{3}}{2}}

    w(x)=3-\frac{2x}{\sqrt{3}}

    F=\int_{0}^{\frac{3\sqrt{3}}{2}}(9810)x\left[3-\frac{2x}{\sqrt{3}}\right]dx

    Can you finish the integration?.
    Last edited by galactus; November 24th 2008 at 05:38 AM.
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