- #1
quarky2001
- 34
- 0
I'm manipulating an equation, and I think I am correct in doing this, but not sure. Could someone tell me if the equality I've written below is true?
[tex]
[\nabla\cdot [\rho\vec{v}\vec{v}] ]\cdot\vec{v} = \nabla\cdot[\frac{1}{2}\rho v^2 \vec{v}]
[/tex]
(where [tex]\rho[/tex] is dependent on position)
*NOTE* that my use of [tex]\vec{v}\vec{v}[/tex] (beside each other without a dot or cross) denotes a tensor quantity, i.e. [tex] \nabla\cdot(\rho\vec{v}\vec{v}) = \rho(\vec{v}\cdot\nabla)\vec{v} + \vec{v}\nabla\cdot(\rho\vec{v}) [/tex].
[tex]
[\nabla\cdot [\rho\vec{v}\vec{v}] ]\cdot\vec{v} = \nabla\cdot[\frac{1}{2}\rho v^2 \vec{v}]
[/tex]
(where [tex]\rho[/tex] is dependent on position)
*NOTE* that my use of [tex]\vec{v}\vec{v}[/tex] (beside each other without a dot or cross) denotes a tensor quantity, i.e. [tex] \nabla\cdot(\rho\vec{v}\vec{v}) = \rho(\vec{v}\cdot\nabla)\vec{v} + \vec{v}\nabla\cdot(\rho\vec{v}) [/tex].