(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A velocity field is given by

[tex] \vec {u} = f(r)\vec{x}, r = | \vec{x}| = \sqrt {x^2 + y^2 + z^2} [/tex] written in rectangular cartesian coordinates, where f(r) is a scalar function. Find the most general form of f(r) so that [tex] \vec {u} [/tex] represents an incompressible flow

2. Relevant equations

Incompressible flow implies [tex] \nabla . \vec {u} = 0 [/tex].

3. The attempt at a solution

The solution is [tex] \nabla . \vec {u} = 3f + rf' so f(r) = A/r^3 [/tex] (A is an arbitrary constant) but I don't see how it is arrived at. Thanks

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# Incompressible flow

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