1. Fluid Mechanics Based on Continuum Assumption

The study of flow problem is very important for many applications and the approach varies across disciplines. The widely used theory is based on the continuum assumption by using macroscopic quantities (e.g., flow velocity, density, pressure and temperature) that can be conveniently measured and are close to our ordinary concepts about the flow problem. Its derivation could be classified into the Eulerian and Lagrangian descriptions, and the later can be presented in a neat mathematical form with clear implementations of the basic physical laws (e.g., mass, momentum and energy conservations) to a closed fluid parcel composed of fixed material particles, as introduced in this chapter. The obtained system of governing equations will be closed by introducing the constitutive equations, which are valid for ordinary flow problems but become inaccurate as the characteristic scale of flow problem or the density of gas media decreases, where the kinetic theory based on a statistical description at the molecular scale can be used as discussed at the end of this chapter. Additionally, the governing equations will be changed in non-inertial reference frame and the component form in orthogonal curvilinear coordinate will be different from that in the Cartesian coordinate, which are also discussed.