Introduction

One approach in teaching introductory fluid mechanics is to avoid the presentation of complex fluid dynamic equations. This is done for very good reasons, including the lack of preparation in partial differential equations and the overall complexity of the problem. Although avoiding the introduction of complex equations is welcome by the average student, the negative and long-term outcome of this approach is that there is no clear rationale and a connecting string among the various chapters that follow. Therefore students are asked to be patient and “suffer quietly” at the beginning and the benefits of a clear roadmap will surface with the systematic approach that follows.

The mechanisms controlling fluid motion may include elements of basic mechanics, heat transfer, phase change, chemical reactions, and even molecular mechanics. Limiting the discussion to the simple mechanics of fluids, usually leads to principles such as the conservation of mass momentum and energy. In this text, however, we concentrate on the conservation of mass (continuity equation) and the conservation of momentum and assume a simple Newtonian fluid without heat transfer. Hence our objective in this chapter is to derive these two conservation laws, the conservation of mass and momentum.