Coordinate transformation of the Navier Stokes equation

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SUMMARY

The discussion focuses on the coordinate transformation of the Navier-Stokes equations, specifically the continuity and momentum equations. The user successfully transformed the continuity equation but encountered difficulties with the momentum equation. They requested assistance with the transformation of the right-hand side of the momentum equation, indicating a need for clarity on this specific mathematical process.

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  • Understanding of the Navier-Stokes equations
  • Familiarity with coordinate transformations in fluid dynamics
  • Knowledge of differential equations
  • Proficiency in mathematical notation and terminology
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  • Research the coordinate transformation techniques for the Navier-Stokes equations
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Fluid dynamics researchers, applied mathematicians, and engineers working on computational fluid dynamics or related fields will benefit from this discussion.

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Homework Statement
Given navier stokes equation in certisian form ,it is asked to use coordinate transformation equation to derive navier stokes equation in cylindrical coordinates .
Relevant Equations
x=rcos(theta),
y=rsin(theta)
z=z
i have successfully transformed the continuity equation using coordinate transform,but having trouble with the momentum equation .
1702232831115.png

can someone kindly provide the transformation of the right hand sight of equation of the image i have attached.
 

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