Physical Laws in Control-Volume Form

Throughout the analyses in this chapter, we use the simplifications afforded by describing the fluid motion in Eulerian control-volume form rather than as a Lagrangian system of fixed identity. It is therefore necessary to transform the physical laws expressed in system form into a more convenient control-volume form. To do this, we change our focus from an identifiable glob of fluid to a region of space in which we are interested. There is really no need to follow the glob (i. e., the system) downstream. All we need to establish is the effect that its motion has on the local flow-field characteristics in the region, the control volume, that encompasses the part of the flow to be studied. Then, we must account for the passage of mass, momentum, energy, or other fluid properties through the boundaries of the control volume. The mathematical rule that facilitates the change from the system to the control-volume form often is called the Reynolds’ Transport Theorem.