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Divergence operator

  1. Dec 24, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm trying to find the divergence of a vector field (a fluid flow vector), but the vector takes the form u = u(x,y,z,t)

    3. The attempt at a solution

    I only really know how to take the divergence of a time-independent vector, so I'm guessing I just take the partial derivatives with respect to x,y,z and hold t= constant...is that right?
    I am interested in knowing whether the divergence operator is even defined for time-varying vectors, or whether divergence is only defined for a given point in time.

    Thanks
     
  2. jcsd
  3. Dec 24, 2012 #2
    Del operates on spatial dimensions*. So yes, you just take the partial derivatives with respect to x, y and z.

    *Unless otherwise specified.
     
  4. Dec 24, 2012 #3
    Thanks very much.
     
  5. Dec 24, 2012 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    I agree with DeIdeal. The divergence operator involves partial derivatives with respect to x, y, z and so t is treated as a constant.
     
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