Solving a Difficult Math Problem

[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!

 

[gabbagabbahey]

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))=

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

 

[alexmarison]

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

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

 

[gabbagabbahey]

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

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

 

[alexmarison]

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

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.

 

[alexmarison]

I've been still looking at the problem too, and I think I noticed that in the example solution I gave:
ω_z = (1/r) ∂/∂r (ru_φ ) = (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)=nx^n-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:
ω_z = C^1/2/2rr^1/2?