CHAPTER 10 - EQUATIONS OF FLUID MECHANICS

Abstract

This chapter discusses a branch of continuum mechanics, the mechanics of nonviscous and Newtonian viscous fluids. Like the classical elasticity theory, this branch also uses linear constitutive equations. Many common fluids including water and air satisfy such constitutive equations. Therefore, nonviscous and Newtonian viscous fluids serve as excellent models for studying the mechanical behavior of a wide variety of common liquids and gases. The chapter presents the derivation of the governing equations for nonviscous and Newtonian viscous fluid flows and their immediate consequences. The fundamental characteristic property of a fluid, which distinguishes it from a solid, is its inability to sustain shear stresses when it is at rest or in uniform motion. More specifically, whereas shear stresses can occur in a solid even when the solid is in static equilibrium or in uniform motion, shear stresses cannot occur in a fluid unless it undergoes a nonuniform motion.