Kyle
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 Jul16 comment Definition of a geodesic ball? This is "geodesic" in a completely different sense than what is meant by the term in the context of general relativity/differential geometry. It's definition has nothing to do with physics. Jul10 comment Convert PDE for Navier equation to cylindrical As Nick points out in his answer, $v_x$ is just $\frac{\partial x}{\partial t}$, so if you replace x with it's representation in terms of cylindrical coordinates, you can just do the math from there. Remember $v_r=\frac{\partial \theta}{\partial t}$ and similarly for $v_\theta$. Jul10 comment Convert PDE for Navier equation to cylindrical Oh and by the way, it's likely that as you work through this and apply it to your NS equation, it will get messy with lots of terms... then they should start to cancel, or many may be zero, and you should eventually get where you want to be. Just might be a bit of a bumpy road. Jul10 comment Convert PDE for Navier equation to cylindrical What have you tried? Should just be a change of variables, I assume you've at least got as far as $x=f(r,\theta,z)$, $y=$, $z=$ and so on. Don't forget the chain rule for the derivatives... If you can show specifically where you're getting hung up, you're much more likely to get an answer. Also, I cleaned up the math in your post. Have a look and make sure it's still as intended, and try and use the math markup on future posts.