Deriving navier stokes in polar

[ericm1234]

Can anyone point me to a derivation of the navier stokes equations in polar? I don't see where the single derivative in theta terms are coming from in the first 2 components.

 

[Andy Resnick]

http://www.its.caltech.edu/~mefm/me19b/handouts/Equations.pdf

 

[ericm1234]

the equations are not derived in the link you gave; my own derivation fails to see where the last terms in those 2nd and 3rd equations in that link are coming from.

 

[Chestermiller]

the equations are not derived in the link you gave; my own derivation fails to see where the last terms in those 2nd and 3rd equations in that link are coming from.

Check out the set of equations for the stress tensor, which have these same terms in them. You can probably figure this out by first writing out your derivation in terms of the components of the stress tensor. You can check your derivation of the differential force balance equations in terms of the stress tensor in cylindrical coordinates in most fluid mechanics books. Check out Transport Phenomena by Bird, Stewart, and Lightfoot (but note that their presentation treats positive stress as compressive, so that their τ's are equal to our -σ's).