The mass- and momentum-balance techniques described in Chapters 3–5 are general and apply to any control volume (CV). We apply those techniques to a general microscopic control volume in Chapter 6 and use the microscopic balances in Chapters 7 and 8. Microscopic-control-volume calculations yield the equations that govern three-dimensional velocity and stress fields. If the equations can be solved, the information that microscopic balances provide is complete. Solving the microscopic balances is difficult, however, because the continuity equation and the Navier-Stokes equation are a set of four nonlinear, coupled, partial differential equations (PDEs).
For many fluids problems, the information sought is relatively large scale and flow details are not very important. For these problems—such as the calculation of the total force on a wall; overall flow rate in a device; and the total work performed by a pump, a turbine, or a mixer-balancing on a larger CV can be a fast and simple way to arrive at quantities of interest. Macroscopic CV balances are mathematically easier to calculate than microscopic CV balances, although they generally require information that must be determined experimentally.
In this chapter, we derive and learn to use the macroscopic mass, momentum, and energy balances, including the mechanical energy balance (MEB), which is discussed in Chapter 1.