Transformation of Reynolds Equation from Cartesian to cylindrical

[rakan]

TL;DR Summary

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

∂/∂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)

 

[Dr.D]

Rather than attempt a conversion, why not review the steps in the Cartesian derivation, and then attempt to repeat the equivalent steps in cylindrical coordinates? I think that is the way I would approach this problem.