How to convert the Reynolds equation from Cartesian coordinate (equation1) to polar coordinate (equation2)? by showing the steps?

Question

∂/∂x ((ρh^3)/12μ ∂p/∂x) + ∂/∂z ((ρh^3)/12μ ∂p/∂z) = ∂/∂x (ρh (U_1+U_2)/2) + ∂/∂z (ρh (W_1+W_2)/2) + (∂(ρh))/∂t (1)

1/r ∂/∂r (r (ρh^3)/12μ ∂p/∂r) + 1/r ∂/∂θ ((ρh^3)/12μ ∂p/r∂θ) = rω/2 ∂(ρh)/r∂θ + (∂(ρh))/∂t (2)

Answer 1

Hi Rakan,

I was able to get the left hand side changed over, but did not get to the final form for the RHS. At any rate, I hope you can use some of the information in here even if the question wasn't completely answered. Good luck! Let me know if you'd like to set up a tutoring session to go over any of these topics (purely math related since I'm not as familiar with the actual fluid dynamics involved here).