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Math Help - Torricelli's law

  1. #1
    MHF Contributor alexmahone's Avatar
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    Torricelli's law

    Suppose that a cylindrical tank has a radius of 3 ft and it has a hole in the bottom with radius 1 in. How long will it take for the water, initially 9 ft deep, to drain completely?

    My working:

    A(y) \frac{dy}{dt}=-a\sqrt{2gy}

    \pi*3^2 \frac{dy}{dt}=-\pi*(1/12)^2*\sqrt{2*32y}

    1296\frac{dy}{\sqrt{y}} =-8dt

    162*2\sqrt{y}=-t+C

    324\sqrt{y}=-t+C

    y(0)=9

    324*\sqrt{9}=C

    C=972

    324\sqrt{y}=-t+972

    Substituting y = 0,

    0=-t+972

    t=972s

    Never mind! I figured it out.
    Last edited by alexmahone; September 5th 2011 at 02:37 AM. Reason: Solved my own problem!
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