Fundamentals of Fluid Dynamics

This chapter starts with a discussion of the continuum hypothesis and the conditions under which it can be used. The origin of the internal forces acting in moving fluids is then identified and the notion of the surface stress and the stress tensor are introduced, as is the rate-of-strain tensor. The constitutive equation, which relates the surface stress to the deformational motion of a fluid, is then derived. Newton’s Second Law and the law of conservation of energy are applied to deduce the equations governing fluid motion. These are known as the Navier–Stokes equations. They are derived for both incompressible fluid flows and compressible flows of a perfect gas. The chapter concludes with a demonstration of how the Navier–Stokes equations can be expressed in curvilinear coordinates.