# Incompressible flow

by coverband
Tags: flow, incompressible
 P: 167 1. The problem statement, all variables and given/known data A velocity field is given by $$\vec {u} = f(r)\vec{x}, r = | \vec{x}| = \sqrt {x^2 + y^2 + z^2}$$ written in rectangular cartesian coordinates, where f(r) is a scalar function. Find the most general form of f(r) so that $$\vec {u}$$ represents an incompressible flow 2. Relevant equations Incompressible flow implies $$\nabla . \vec {u} = 0$$. 3. The attempt at a solution The solution is $$\nabla . \vec {u} = 3f + rf' so f(r) = A/r^3$$ (A is an arbitrary constant) but I don't see how it is arrived at. Thanks