The governing equations of a simple fluid

Abstract

In this chapter we derive formally the fundamental equations describing the transport of mass, momentum and energy of a one component, single phase fluid. Here, the balance equations are derived based on both an Eulerian and a Lagrangian approach. In the former, the conservation principles are enforced using a fixed volume element, as opposed to the Lagrangian approach, focused on a material volume element as it moves in time, with the fluid velocity along the fluid path lines. An easier, albeit less rigorous, derivation of the governing equations can be found in Appendix E, where an Eulerian approach is adopted, by performing the balance of mass, momentum and energy.