Deriving navier stokes in polar

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SUMMARY

The discussion focuses on deriving the Navier-Stokes equations in polar coordinates, specifically addressing the confusion surrounding the single derivative in theta terms in the first two components. Participants reference a link to a Caltech document that lacks the necessary derivation, leading to further inquiries about the origin of specific terms in the equations. The importance of the stress tensor in understanding these equations is emphasized, with recommendations to consult "Transport Phenomena" by Bird, Stewart, and Lightfoot for additional insights on stress representation.

PREREQUISITES
  • Understanding of Navier-Stokes equations
  • Familiarity with polar coordinates in fluid dynamics
  • Knowledge of stress tensor components
  • Basic principles of differential force balance in fluid mechanics
NEXT STEPS
  • Study the derivation of Navier-Stokes equations in polar coordinates
  • Review the stress tensor components in cylindrical coordinates
  • Examine "Transport Phenomena" by Bird, Stewart, and Lightfoot for stress representation
  • Explore differential force balance equations in fluid mechanics textbooks
USEFUL FOR

Students and professionals in fluid dynamics, particularly those focusing on the Navier-Stokes equations and stress tensor analysis in polar coordinates.

ericm1234
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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.
 
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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.
 
ericm1234 said:
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).
 

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