Physical Laws for Motion of a System
Throughout the discussions in this chapter, we use the simplifications available by application of the modeling ideas discussed in Chapter 2. Thus, the medium is taken to be composed of a continuum of contiguous fluid particles rather than individual molecules. Because we are interested in the dynamics of fluid flow, it is natural to express each physical law describing the motion of these particles as a rate of change of a physical variable required to characterize the material. As examples, we may be interested in the rate at which mass flows across a cross section of a duct, how fluid particles are accelerated by external forces, and the rate at which work is done on the fluid by pressure forces.
All of the physical effects needed in representing the fluid motion can be given in rate form for a system of particles. To aid in visualization of what we are modeling, consider a flow of fluid in which we identify at some arbitrary initial time a distinct “glob” of air consisting of many individual particles. Imagine that the glob can be marked by coloring it with dye. Then, as it moves downstream, it is stretched and deformed by its interaction with the surroundings and by forces acting among the constituent particles. The identity is preserved although its shape, size, and other characteristics may be altered by the motion, by forces applied at its boundaries, or by body forces (e. g., gravity or magnetic force) that act on the entire system, or by energy flowing into or out of the surroundings. Henceforth, we refer to this marked glob as the system.
Each of the required physical laws is expressed in system form. These should be already familiar to students from the study of basic physics and thermodynamics.