Chapter 12 Foundations of Fluid Dynamics

Having studied elasticity theory, we now turn to a second branch of continuum mechanics: uid dynamics. Three of the four states of matter (gases, liquids and plasmas) can be regarded as uids and so it is not surprising that interesting uid phenomena surround us in our everyday lives. Fluid dynamics is an experimental discipline and much of what has been learned has come in response to laboratory investigations. Fluid dynamics nds experimental application in engineering, physics, biophysics, chemistry and many other elds. The observational sciences of oceanography, meteorology, astrophysics and geophysics, in which experiments are less frequently performed, are also heavily reliant upon uid dynamics. Many of these elds have enhanced our appreciation of uid dynamics by presenting ows under conditions that are inaccessible to laboratory study. Despite this rich diversity, the fundamental principles are common to all of these appli-cations. The fundamental assumption which underlies the governing equations that describe the motion of uid is that the length and time scales associated with the ow are long com-pared with the corresponding microscopic scales, so the continuum approximation can be invoked. In this chapter, we will derive and discuss these fundamental equations. They are