Macroscopic balances

Abstract

In fluid mechanics, conservation of mass, momentum and energy lead to the so-called continuity and Navier-Stokes equations. These equations can be written in either integral or differential form. In this chapter, we consider their integral formulation, which is applicable to a finite mass offluid in motion. The more rigorous differential treatment will be the subject of Chap. 6. Here, setting up macroscopic balances and, at first, neglecting all diffusive effects, we derive the continuity equation in Sect. 4.1, the Bernoulli equation in Sect. 4.2, and the Euler equation in Sect. 4.3. Then, in Sects. 4.4, 4.5 and 4.6, the corrections to the Bernoulli equation are analyzed, discussing the pressure losses due to friction forces, in particular for the cases of flows within pipes and around submerged objects.