Mathematical physics was brought into existence by the development of mechanics. It originated in the study of the planetary motions and of the falling of heavy bodies, which led Newton to formulate the fundamental laws of mechanics, as early as 1687. Even though the mechanics of continuous media, first as solid mechanics, and later as fluid mechanics, is a more recent development, its roots can be found in Isaac Newton’s “Philosophiae naturalis principia mathematica” (Mathematical Principles of Natural Philosophy), several pages of which are dedicated to the falling streams of liquid.

Applications of fluid mechanics to irrigation problems date back to Antiquity, but the subject gained a key status during the industrial revolution. Energetics was vital to the development of knowledge-demanding, specialized industrial areas such as fluid supply, heat engineering, secondary energy production or propulsion. Either as a carrier of sensible heat or as the core of energy production processes, fluid is ubiquitous in all the high-technology industries of the century: aeronautics, aerospace, automotive, industrial combustion, thermal or hydroelectric power plants, processing industries, national defense, thermal and acoustic environment, etc.

Depending on the target audience, there are various approaches to fluid mechanics. Covering this diversity is what we are striving for in this book.

Whatever the degree of difficulty of the approached subject, it is important for the reader to reflect on it while being fully aware of the laws to be written in one form or another. Various approaches to fluid mechanics are illustrated by examples in this book.

First of all, the student will have the opportunity to handle simplified tools, providing him/her with a convenient first approach of the subject. On the other hand, the practitioner will be provided with elementary dimensioning means.

Other problems may justify or require a more complex approach, involving more significant theoretical knowledge, in particular of calculus. This is once again a point on which students and practitioners who already master these subjects can converge.

A third approach, which is essential for today’s physics, especially when dealing with problems that are too complex to be accurately solved by simple calculations, resorts to numerical methods. This book illustrates these remarks.

Problem resolution relies in each chapter on reviews of fundamental notions. These reviews are not exhaustive, and the reader may find it useful to go back to textbooks for knowledge consolidation. Nevertheless, certain proofs referring to important points are resumed. As already mentioned, what matters is that the reader has a good grasp of what he/she writes.

Given that we target wide audiences, the deduction or review of general equations can be found in the appendices, to avoid the book becoming too cumbersome.

The attempt to effectively address audiences with widely varied levels of knowledge, expertise or experience in the field may seem an impossible task.

Drawing on their experience of teaching all these categories of audiences, the authors felt motivated and encouraged to engage in this daring enterprise.

This volume gathers examples of relatively simple approaches to academic problems as well as practical ones. In principle, this work is accessible to all potential readers.

The first chapter recalls the basis of dynamics by focusing on the mechanics of point power. Both the state of fluidity, as well as the main properties of fluids are defined. The problems for writing force, surface and volume when applied to a fluid volume, are discussed. Finally, a strategy for resolving problems in mechanics is approached from a general point of view.

The second chapter covers fluid in equilibrium. The study of incompressible fluid statics under simple forces of gravity or hydrostatics, is completed by that of other forces derived from a potential, such as inertia forces. Compressible fluid statics are also covered.

The third chapter is dedicated to describing flows. The Eulerian vision is favored here. The geometric elements of kinematics are defined. The geometry of flows is established, based on the data of a flow’s Eulerian speed. This chapter also provides the opportunity for a first physics principle to be outlined and developed: the principle of continuity.

The first chapter examines the structure of surface forces. This is also where one will find a definition of perfect fluids where the action of viscosity can be overlooked. The fourth chapter is dedicated to processing these flows, in which the Bernoulli theorem is central. Although this theorem is limited by the underlying hypotheses, its strength is observed in how easily one can obtain pertinent orders of magnitude in a large range of phenomena.

When the speed of a fluid varies significantly in a confined space, which is an instance of the barrier between fluids and solids, viscosity becomes a major phenomenon. This is particularly found in pipelines and all components of a hydraulic circuit. In such a situation, one is often only concerned with the loss of mechanical energy that results from fluid friction. This ‘head loss’ will be calculated in the fifth chapter.

As a general rule, propulsion studies result from a momentum exchange between fluid and a wall. Euler’s theorems apply to both perfect flows and viscous fluids and allow one to determine, with a simple knowledge of kinematic fluid passing through boundaries, the resulting moments of a system of forces when applied to a fluid. The sixth chapter will demonstrate how this powerful tool can be applied to determine different types of thrusting.

This work is aimed at students enrolled in engineering schools and technical colleges or in University Bachelors or Masters programs. It is also meant to be useful to the professionals whose activity requires knowledge or mastery of tools related to fluid mechanics.

Michel LEDOUX

Abdelkhalak EL HAMI

November 2016