# PDE solution

1. Aug 19, 2010

### alexmarison

Hi, I'm doing some research on my own, but my math is pretty bad and I am stuck trying to find the solution to this problem:
(1/r) ∂/∂r (r√(C/r))=

I've seen these solutions of similar-looking problems:
(1/r) ∂/∂r (r^2 (Ω))=2Ω
and
(1/r) ∂/∂r (r K/r)=0, except when r=0, in which case the solution is infinite.

Thank you very much!

2. Aug 19, 2010

### gabbagabbahey

Usually equations have something on both sides of the equal sign...

3. Aug 19, 2010

### alexmarison

Hi, sorry, guess the thing on the other side would matter. It happens to be vorticity or, in cylindrical coordinates, ω_z.

4. Aug 19, 2010

### gabbagabbahey

What coordinate variables does the vorticity depend on (i.e. does it depend on $r$,$\phi$ and/or$z$)?

5. Aug 19, 2010

### alexmarison

Out of the 3 cylindrical coordinates, there is only vortical motion wrt z, which motion is dependent on r, as the equation shows, I think.

Last edited: Aug 19, 2010
6. Aug 19, 2010

### alexmarison

I've been still looking at the problem too, and I think I noticed that in the example solution I gave:
ωz = (1/r) ∂/∂r (ruφ ) = (1/r) ∂/∂r (r2Ω) = 2Ω

it seems as though it was solved like a regular differential equation using only the rule for the derivative of powers:
If f(x)=xn, then f'(x)=nxn-1

Can I just do that to solve mine, too, in which case, I would get f'(x)=(1/2)r-1/2 to give me:
ωz = C1/2/2rr1/2?

Last edited: Aug 19, 2010