CHAPTER II - VISCOUS FLUIDS

Abstract

This chapter discusses viscous fluids. When describing the motion of a viscous fluid, some additional terms need to be included in the equation of motion of an ideal fluid. The equation of continuity is equally valid for any fluid, whether viscous or not. Euler's equation, on the other hand, requires modification. The equation of motion of a viscous fluid may therefore be obtained by adding to the ideal momentum flux a term, - σ'ik, which gives the irreversible viscous transfer of momentum in the fluid. The boundary conditions on the equations of motion of a viscous fluid require that the fluid velocity should vanish at fixed solid surfaces. In studying the motion of viscous fluids, a number of important results can be obtained from simple arguments concerning the dimensions of various physical quantities so that if the shape of the body is given, it suffices to specify any one of its linear dimensions—such as the radius of a sphere or of a cylindrical pipe, one semi-axis of a spheroid with given eccentricity, and so on—to determine its dimensions completely.