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

mark_usc · Oct 11, 2014

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

Fredrik · Oct 12, 2014

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.

mark_usc · Oct 12, 2014

it seems good to me. Thanks a lot

Marco Uscanga

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

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

What does the equation Vrs=r∇s+s∇r represent?

How is the cross product calculated using Vrs=r∇s+s∇r?

Can you give an example of how to use Vrs=r∇s+s∇r?

What does the equation ∇.sv=(VS.v)+s(∇.v) represent?

How is the dot product calculated using ∇.sv=(VS.v)+s(∇.v)?

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