Most of us learn the fundamentals of fluid mechanics using Cartesian coordinates. Specifically, derivations of the Navier-Stokes equations are done in a Cartesian reference system. This is a valid way for studying such a complicated set of equations as rectangular coordinates do not present us with the nuances of extra terms due to curvature or other effects that are present in curvilinear coordinates. The final form for the momentum equations is concisely written in vector notation for compactness and simplicity. This is given by
I would like to thank Prof. Gary Flandro of UTSI for promoting the use of this form.