Coordinate transformation of the Navier Stokes equation

Thread starter hcpysicist
Start date Dec 10, 2023
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Coordinate transformations Fluid dynamics Navier stokes equation

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The discussion focuses on the transformation of the Navier-Stokes equations, specifically the continuity equation, which has been successfully transformed by the user. However, challenges arise with the momentum equation, particularly in transforming the right-hand side. The user seeks assistance in this area, requesting guidance on the appropriate transformation methods. The need for clarity in the momentum equation transformation highlights the complexities involved in fluid dynamics. Overall, the thread emphasizes the importance of coordinate transformations in solving Navier-Stokes equations.

Dec 10, 2023

hcpysicist

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 .

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

Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW

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