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Math Help - Finding a flow field

  1. #1
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    Finding a flow field

    The three dimensional velocity v of a fluid around a point source is radially symmetric. It is given by v(r) = rp, where p is constant. Determine p from the condition that the divergence of the flow must vanish.

    Could someone walk me through how to do this? Thanks,

    Kim
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  2. #2
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    Quote Originally Posted by Kim Nu View Post
    The three dimensional velocity v of a fluid around a point source is radially symmetric. It is given by v(r) = rp, where p is constant. Determine p from the condition that the divergence of the flow must vanish.

    Could someone walk me through how to do this? Thanks,

    Kim
    What is meant be 'vanishing' divergence?
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  3. #3
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    Your guess is as good as mine. Thanks,

    Kim
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  4. #4
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    Quote Originally Posted by Kim Nu View Post
    Your guess is as good as mine. Thanks,

    Kim
    Also, what is r and p? Are they a position vector and pressure respectively? Or a position and density perhaps? Oh wait... r is the radius of the flow?
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  5. #5
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    I think the key to this is to use polar coordinates for divergence:

     \nabla . \vec{V} = \frac{1}{r} \frac{\partial}{\partial r}(r V_r)  + \frac{1}{r} \frac{\partial}{\partial \theta} (V_{\theta})

    Only the first term applies to your problem.
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