Classical Fluid Mechanics

This textbook primarily explains the construction of classical fluid model to readers in a holistic manner and the way it is constructed. Secondly, the book also demonstrates some possible modifications of the initial model which either make the model applicable in some special cases (viscous or turbulent fluids) or simplify it in accordance with peculiarity of a particular problem (hydrostatics, two-dimensional flows, boundary layers, etc.). The book explains theoretical concepts in two parts. The first part is dedicated to the derivation of the classical model of the perfect fluid. The second part of the book covers important modifications to the fluid model which account for calculations of momentum, force and the laws of energy conservation. Concepts in this section include the redefinition of the stress tensor in cases of viscous or turbulent flows and laminar and turbulent boundary layers. The text is supplemented by appropriate exercises and problems which may be used in practical classes. These additions serve to teach students how to work with complex systems governed by differential equations. Classical Fluid Mechanics is an ideal textbook for students undertaking semester courses on fluid physics and mechanics in undergraduate degree programs. This textbook primarily explains the construction of classical fluid model to readers in a holistic manner and the way it is constructed. Secondly, the book also demonstrates some possible modifications of the initial model which either make the model applicable in some special cases (viscous or turbulent fluids) or simplify it in accordance with peculiarity of a particular problem (hydrostatics, two-dimensional flows, boundary layers, etc.). The book explains theoretical concepts in two parts. The first part is dedicated to the derivation of the classical model of the perfect fluid. The second part of the book covers important modifications to the fluid model which account for calculations of momentum, force and the laws of energy conservation. Concepts in this section include the redefinition of the stress tensor in cases of viscous or turbulent flows and laminar and turbulent boundary layers. The text is supplemented by appropriate exercises and problems which may be used in practical classes. These additions serve to teach students how to work with complex systems governed by differential equations. Classical Fluid Mechanics is an ideal textbook for students undertaking semester courses on fluid physics and mechanics in undergraduate degree programs.

This is the first book in a four-part series designed to give a comprehensive and coherent description of Fluid Dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. The present Part 1 consists of four chapters. Chapter 1 begins with a discussion of Continuum Hypothesis, which is followed by an introduction to macroscopic functions, the velocity vector, pressure, density, and enthalpy. We then analyse the forces acting inside a fluid, and deduce the Navier-Stokes equations for incompressible and compressible fluids in Cartesian and curvilinear coordinates. In Chapter 2 we study the properties of a number of flows that are presented by the so-called exact solutions of the Navier-Stokes equations, including the Couette flow between two parallel plates, Hagen-Poiseuille flow through a pipe, and Karman flow above an infinite rotating disk. Chapter 3 is devoted to the inviscid incompressible flow theory, with particular focus on two-dimensional potential flows. These can be described in terms of the "complex potential", allowing the full power of the theory of functions of complex variables to be used. We discuss in detail the method of conformal mapping, which is then used to study various flows of interest, including the flows past Joukovskii aerofoils. The final Chapter 4 is concerned with compressible flows of perfect gas, including supersonic flows. Particular attention is given to the theory of characteristics, which is used, for example, to analyse the Prandtl-Meyer flow over a body surface bend and a corner. Significant attention is also devoted to the shock waves. The chapter concludes with analysis of unsteady flows, including the theory of blast waves.

This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.

Physics of Continuous Matter: Exotic and Everyday Phenomena in the Macroscopic World, Second Edition provides an introduction to the basic ideas of continuum physics and their application to a wealth of macroscopic phenomena. The text focuses on the many approximate methods that offer insight into the rich physics hidden in fundamental continuum mechanics equations. Like its acclaimed predecessor, this second edition introduces mathematical tools on a "need-to-know" basis. New to the Second Edition This edition includes three new chapters on elasticity of slender rods, energy, and entropy. It also offers more margin drawings and photographs and improved images of simulations. Along with reorganizing much of the material, the author has revised many of the physics arguments and mathematical presentations to improve clarity and consistency. The collection of problems at the end of each chapter has been expanded as well. These problems further develop the physical and mathematical concepts presented. With worked examples throughout, this book clearly illustrates both qualitative and quantitative physics reasoning. It emphasizes the importance in understanding the physical principles behind equations and the conditions underlying approximations. A companion website provides a host of ancillary materials, including software programs, color figures, and additional problems.

This text is designed to give a comprehensive and coherent description of classical fluid dynamics which is suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. Topics includeed in this text are: A discussion of Continuum Hypothesis, which is followed by an introduction to macroscopic functions, the velocity vector, pressure, density, and enthalpy ; Properties of a number of flows that are presented by the so-called exact solutions of the Navier-Stokes equations, including the Couette flow between two parallel plates, Hagen-Poiseuille flow through a pipe, and Karman flow above an infinite rotating disk ; Inviscid incompressible flow theory, with particular focus on two-dimensional potential flows ; Compressible flows of perfect gas, including supersonic flows.

Suitable for both a first or second course in fluid mechanics at the graduate or advanced undergraduate level, this book presents the study of how fluids behave and interact under various forces and in various applied situations - whether in the liquid or gaseous state or both.

Gregory's Classical Mechanics is a major new textbook for undergraduates in mathematics and physics. It is a thorough, self-contained and highly readable account of a subject many students find difficult. The author's clear and systematic style promotes a good understanding of the subject: each concept is motivated and illustrated by worked examples, while problem sets provide plenty of practice for understanding and technique. Computer assisted problems, some suitable for projects, are also included. The book is structured to make learning the subject easy; there is a natural progression from core topics to more advanced ones and hard topics are treated with particular care. A theme of the book is the importance of conservation principles. These appear first in vectorial mechanics where they are proved and applied to problem solving. They reappear in analytical mechanics, where they are shown to be related to symmetries of the Lagrangian, culminating in Noether's theorem.