Math Help - Finding a flow field

1. Finding a flow field

The three dimensional velocity v of a fluid around a point source is radially symmetric. It is given by v(r) = rp, where p is constant. Determine p from the condition that the divergence of the flow must vanish.

Could someone walk me through how to do this? Thanks,

Kim

2. Originally Posted by Kim Nu
The three dimensional velocity v of a fluid around a point source is radially symmetric. It is given by v(r) = rp, where p is constant. Determine p from the condition that the divergence of the flow must vanish.

Could someone walk me through how to do this? Thanks,

Kim
What is meant be 'vanishing' divergence?

3. Your guess is as good as mine. Thanks,

Kim

4. Originally Posted by Kim Nu
Your guess is as good as mine. Thanks,

Kim
Also, what is r and p? Are they a position vector and pressure respectively? Or a position and density perhaps? Oh wait... r is the radius of the flow?

5. I think the key to this is to use polar coordinates for divergence:

$\nabla . \vec{V} = \frac{1}{r} \frac{\partial}{\partial r}(r V_r) + \frac{1}{r} \frac{\partial}{\partial \theta} (V_{\theta})$

Only the first term applies to your problem.