The essential purpose of this chapter is to derive the set of equations that results from invoking the physical laws of conservation of mass, momentum, and energy. In order to realize this objective, it is necessary to discuss certain preliminary topics. The ‡rst topic of discussion is the two basic ways in which the conservation equations may be derived: the statistical method and the continuum method. Having selected the basic method to be used in deriving the equations, one is then faced with the choice of reference frame to be employed, Eulerian or Lagrangian. Next, a general theorem, called Reynolds’ transport theorem, is derived, since this theorem relates derivatives in the Lagrangian framework to derivatives in the Eulerian framework.