Basic Equations of Fluid Dynamics

Abstract

In this chapter, the basic equations of fluid dynamics are derived and their physical significances are discussed in depth and in examples. Both integral and differential forms of the continuity equation, momentum equation, and energy equation are derived. In addition, Bernoulli’s equation, angular momentum equation, enthalpy equation and entropy equation are also introduced. Finally, several analytical solutions of these governing equations are shown, and the mathematical properties of the equations are discussed. Besides the fundamental equations, some important concepts are explained in this chapter, such as the shaft work in integral energy equation and its origin in differential equations, the viscous dissipation term in the differential energy equation and its relation with stress and deformation, and the method to increase total enthalpy of a fluid isentropically.