This chapter presents the derivation of the total mass conservation equation, species mass conservation equation, momentum equation (Navier–Stokes equation), and energy conservation equation. The derivations are presented by following a very simple method that involves the balance across an infinitesimal control volume, followed by the application of the partial derivative definition. The differential equations are therefore obtained in a straightforward manner. Moreover, the constitutive relations for the stress tensor are also derived. Tensor relations are used in this derivation, and more details are provided in the Appendix of the book. All the derivations are performed in the spherical coordinate system with the objective of showing the nuances of considering the interactions between unit orthogonal vectors in non-Cartesian (non-rectangular) coordinate systems. The derived equations are also presented in general vector form which makes it easy to write them in other coordinate systems. For example, the equations are also presented in cylindrical coordinate form and in Cartesian (rectangular) coordinate form.