How do I convert the Reynolds equation from Cartesian to Cylindrical (polar) coordinates?

Answer 1

The easiest way is to write it using vector operators like div( (h³/12ν) grad(p) ) + ... (fill in the rest of it) and then write each operator using cylindrical coordinates.

Another way is to transform each piece separately using the chain rule from Cartesian to cylindrical. That method is a lot more painful.