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Math Help - Problem

  1. #1
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    Problem

    ello guys can any1 help me with this equation;
    Water flows throught a depth of 400ml in a 500ml diametre pipe calcualte the wet premimetre of the pipe and the cross sectional area of the water.
    Is there any help you can give me with this or an equation?
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    Chaneysville, PA
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    You have ml, shouldn't that be mm?.

    A fun way to do this is with calculus. You can find the area of the water to a depth of .4 meters by using:

    2\int_{-250}^{150}\sqrt{(250)^{2}-x^{2}}dx

    Can you integrate that?.

    To find the wetted perimeter, you can use the formula for the middle ordinate.

    The middle ordinate is the distance from the top of the water to the top of the pipe. 100 mm.

    100=250(1-cos(\frac{\theta}{2}))

    Solve for theta and get {\theta}=2cos^{-1}(3/5)

    But we want the wetted perimeter. The above is the perimeter of the dry portion.

    2{\pi}-2cos^{-1}(3/5)=4.4286

    Now, we can plug that into s=r{\theta}

    s=(250)(4.4286)=1107.15 \;\ mm
    Last edited by galactus; November 24th 2008 at 06:38 AM.
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