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Math Help - rate of flow

  1. #1
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    rate of flow

    A fluid with density 1230 flows with the velocity V = yi + j + zk. Find the rate of flow (of mass) upward through the paraboloid z = 9 - \frac{1}{4}(x^2 + y^2), x^2 + y^2 \leq 36.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    the density is mass/volume

    Flux is Volume/time

    You want then mass/time = density*flux

    N = x/2i + y/2 j + k

    V*N = xy/2 + y/2 + z = xy/2 +y/2 + 9-1/4(x^2 +y^2)

    convert to Polar coordinates

    and integrate over the disk of radius 6

    If you have trouble see the attachment in the following post
    Last edited by Calculus26; May 25th 2009 at 03:28 PM.
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  3. #3
    MHF Contributor Calculus26's Avatar
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    See attachment
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