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Thread: 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:

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

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

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

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

    $\displaystyle 324\sqrt{y}=-t+C$

    $\displaystyle y(0)=9$

    $\displaystyle 324*\sqrt{9}=C$

    $\displaystyle C=972$

    $\displaystyle 324\sqrt{y}=-t+972$

    Substituting $\displaystyle y = 0$,

    $\displaystyle 0=-t+972$

    $\displaystyle t=972s$

    Never mind! I figured it out.
    Last edited by alexmahone; Sep 5th 2011 at 01:37 AM. Reason: Solved my own problem!
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