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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.

    Vrs=r∇s+s∇r

    ∇.sv=(VS.v)+s(∇.v)

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

    With all the best

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

    Fredrik

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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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