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Help me to demonstrate and explain: Vrs=r∇s+s∇r and ∇.sv=(VS.v)+s(∇.v)

  1. Oct 11, 2014 #1

    Dear all:

    Please help me to know how these expressions are obtained. Please recommendme some web reference to search more about the demonstrations.



    This expressions are very important in transport phenomena and fluid mechanics.

    With all the best

    Marco Uscanga
  2. jcsd
  3. Oct 12, 2014 #2


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    Why did you write "V" in two places? Did you mean ∇? Are r and s scalar fields, and v a vector field? You should explain these things when you ask for help. Is "S" a typo?

    ##\nabla (rs)## is a vector whose ith component is ##\partial_i(rs)##. Use the product rule for derivatives.

    ##\nabla\cdot (sv)=\sum_i\partial_i(sv)_i =\sum_i\partial_i(sv_i)##. Now use the product rule again.
  4. Oct 12, 2014 #3
    it seems good to me. Thanks a lot

    Marco Uscanga
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