Teaching a first course in fluid mechanics is always challenging because of the numerous new concepts that were not used in previous engineering courses. The source of the problem is in the highly nonlinear nature of the governing equations, which cannot be solved analytically for a general case. Over the years, various flow regimes were treated by neglecting large portions of the governing equations, leading to approximate solutions, which are unique to that limited problem. Consequently, many introductory fluid mechanics courses focus on surveying those localized solutions and not dealing directly with the governing equations. This approach perhaps is less mathematically intense, but it may confuse the novice student who cannot connect the various partial solutions to construct a more comprehensive understanding of the fluid mechanics discipline.

The present approach is aimed at easing the learning process by providing an early overview of the field and identifying a roadmap for understanding the different flow regimes. This is accomplished by presenting the governing equations (in their simplest laminar form) early on. In each of the following chapters, students are reminded how the particular subject of the chapter relates to the original roadmap (i.e., hydrostatics is a case in which the velocity in the governing equations is zero). Another benefit is that some similar cases are combined and students do not feel that each case needs a new and different mathematical approach.