Chapter 13 - Continuity and Navier-Stokes equation in different coordinate systems

Abstract

By now we have derived the fundamental equations which allow us to solve for the field variables. Until now, we have primarily worked with equations in Cartesian coordinates. For many applications, this is the preferred coordinate system. However, there are several applications which are better solved in a different coordinate system. In this section, we will derive versions of these equations in different coordinate systems. We have introduced the most important coordinate systems in section 7. In section 7.6 we have derived the different operators in these coordinate systems. In this section, we will use these operators to note down the modified versions of the fundamental equations in the respective coordinate systems. As we will see, these equations will come in handy later when solving, e.g., the Navier-Stokes equation in cylindrical flow profiles.