# Finding a flow field

• Apr 13th 2009, 04:24 AM
Kim Nu
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
• Apr 13th 2009, 04:37 AM
Mush
Quote:

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?
• Apr 13th 2009, 08:22 AM
Kim Nu
Your guess is as good as mine. Thanks,

Kim
• Apr 13th 2009, 08:33 AM
Mush
Quote:

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?
• Apr 13th 2009, 08:44 AM
Mush
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.