Fluid Mechanics for Chemical Engineering

Chapter 1

Local Equations of Fluid Mechanics

In this chapter, to begin with, we recall the Navier–Stokes equations that govern the flow of a Newtonian fluid. These equations explain the behavior of common fluids such as water or air. For a given force field and boundary conditions, the solution of Navier–Stokes equations controls both the flow velocity and pressure at any point and at any time in the domain under consideration. The Navier–Stokes equations are the most commonly used equations in fluid mechanics; they provide the knowledge of the flow of Newtonian fluids at the local level.

The solutions to Navier–Stokes equations are typically very difficult to arrive at. This fact is attested to by the extraordinary development of numerical computation in fluid mechanics. Only a few exact analytical solutions are known for Navier– Stokes equations. We present in this chapter some laminar flow solutions whose interpretation per se is essential in this regard. We then introduce the boundary layer concept. We conclude the chapter with a discussion on the uniqueness of solutions to Navier–Stokes equations, with special reference to the phenomenon of turbulence.

This being the introductory chapter, we have not included a prolonged discussion on continuum mechanics. The derivation of Navier–Stokes equations is available in other continuum mechanics or fluid mechanics books.¹ We have consciously avoided concentrating on the derivational aspects of Navier–Stokes equations as we are convinced ...