دانلود کتاب مکانیک سیالات نظری -مقدمه‌ای کاربردی با مشتقات دقیق

Among graduates of scientific disciplines, particularly mathematicians, only a relatively small proportion go into applied research, which is traditionally dominated by engineers. One of the reasons is the gap between theoretically oriented education and the demands of practice. Like other theories that have developed over centuries, fluid mechanics also contains a wealth of important details that can hardly be accommodated in a short textbook. When choosing the necessary abridgements, each specialist is guided by their target audience. Mathematicians tend to shorten or omit the discussion of applications, while engineers shorten certain mathematical details on the way to the results, especially as they can be compensated for by computer calculations. With this compromise, there is a risk that some aspects will be lost from view. This book aims to help overcome this barrier. It is primarily aimed at students and lecturers of university colleges in the mathematical scientific field. At the same time, it should be useful for engineers who are interested in the derivation of the formulas and backgrounds. Unlike other modern presentations that assume greater familiarity with the subject and its methods, it gently guides the beginner through the theory to practical examples. Definitions and central concepts are highlighted in the text. To motivate the theory, the applications covered in the corresponding sections are briefly introduced at the beginning and discussed in detail after the formulas are provided. An introductory chapter is used to practice the necessary calculation techniques that are only marginally covered in the basic mathematics lectures. If the derivations are rarely found in standard textbooks, they are given here. Otherwise we refer to them. The main part begins with the derivation of the basic equations of fluid mechanics. The explanation of aerodynamic lift is very extensive and is only touched upon in introductory texts. Therefore, it is in the foreground here. After a discussion of the boundary layer as the main location of vortex formation, we present Prandl’s three-dimensional lift theory. This allows the relevant forces for specific wing profiles to be calculated in the low _light speed range. Finally, we present some applications from hydrodynamics that show different facets of the Navier-Stokes model and are characterized by particular clarity. As a mathematical background, basic knowledge from four semesters of analysis is required. To appeal to a broader audience, numerous small and sometimes tiring calculation steps are not left to the reader, but formulated as problems that are fully recalculated in the solution part. Thus, the more experienced reader can follow the presentation in a condensed form, while the beginner continues reading after a glance at the solution part. Details of mathematical derivations, which are used less frequently and exceed the scope of the main text, are moved to the appendix “Formulas, Tables and Supplements.” To simplify readability, the concrete enumeration of mathematical prerequisites such as smoothness of curves and areas, differentiability and integrability of functions is largely dispensed with. As far as possible, we assume that the corresponding requirements are met. These details are indispensable for mathematical existence and uniqueness proofs, while they are less often needed for understanding physical mechanisms. A prominent exception is the trailing edge of an aerofoil, which is of essential importance for aerodynamic lift. To avoid erroneous copyright infringements, I have decided to create most of the illustrations myself. For this reason, the book contains some pencil sketches instead of photos. The manuscript received significant corrections from Prof. Thomas P. Witelski and additions from Prof. Maximilian Platzer, who pointed out important aspects of aerodynamic lift. Excellent cooperation with Springer Spectrum was ensured by the editors Veronika Erdmann and Iris Ruhmann, whose criticism contributed to a better understanding of the text. However, my special thanks go to two people. First to my wife Olga, who patiently and persistently stood by my side during long work phases. I am also deeply indebted to Prof. em. Albert Fässler. He not only provided valuable suggestions but also gave me the strength and support to complete the project at a critical moment.