The present work aims to revisit the simplifications made in the Navier-Stokes equations for the flow between two cylinders with a small thickness of lubricating oil film. Through a dimensionless analysis, the terms of these equations are mapped and ordered by importance for the hydrodynamic bearing application. An effective parameterization of the geometry is proposed, enabling a more detailed description of the problem and its adaptation to other contexts. At the end, an elliptical partial differential equation is reached and solved by the centered finite difference method, whose solution is the pressure field between the cylinders. To illustrate the effectiveness of the proposed approach, the model is applied to hydrodynamic bearings, where the pressure field and some parameters resulting from it, such as stiffness and damping coefficients, are computed. Based on the facilities offered by the parameterization of the geometry, two different configurations are presented: (1) elliptical and (2) worn bearings. Their responses are evaluated and a comparative analysis is performed. The modeling exposed in this text, as well as all its simulations were developed to integrate Ross-Rotordynamics, an open library in Python, available on the GitHub platform.