ABSTRACT
In Chapter 6, we discussed potential flows, which are ideal fluid flows with constant density and zero viscosity. Although a fluid flow with constant density is physically possible, one with zero viscosity is not. Nevertheless, one of the major contributions of the potential flow theory, which forms most of classical fluid mechanics, has been to provide a good insight into how a lift force is generated on a body. Euler’s equations governing potential flows provide a system of partial differential equations whose numerical solutions (using a CFD method) yield three-dimensional results in complex geometries. These solutions, without the wall boundary layers found in real flows, provide a good insight into these flows with their reasonably accurate static pressure distributions. A logical next step in our journey to understand real fluid flows is to introduce constant fluid viscosity in the mathematical modeling of these flows. The resulting governing partial differential equations are the Navier-Stokes equations, which are discussed at some length in this chapter along with their few exact solutions under special situations of fully developed two-dimensional laminar flows.
