Foundations of Fluid Mechanics with Applications

Fluid mechanics (FM) is a branch of science dealing with the investi gation of flows of continua under the action of external forces. The fundamentals of FM were laid in the works of the famous scientists, such as L. Euler, M. V. Lomonosov, D. Bernoulli, J. L. Lagrange, A. Cauchy, L. Navier, S. D. Poisson, and other classics of science. Fluid mechanics underwent a rapid development during the past two centuries, and it now includes, along with the above branches, aerodynamics, hydrodynamics, rarefied gas dynamics, mechanics of multi phase and reactive media, etc. The FM application domains were expanded, and new investigation methods were developed. Certain concepts introduced by the classics of science, however, are still of primary importance and will apparently be of importance in the future. The Lagrangian and Eulerian descriptions of a continuum, tensors of strains and stresses, conservation laws for mass, momentum, moment of momentum, and energy are the examples of such concepts and results. This list should be augmented by the first and second laws of thermodynamics, which determine the character and direction of processes at a given point of a continuum. The availability of the conservation laws is conditioned by the homogeneity and isotrop icity properties of the Euclidean space, and the form of these laws is related to the Newton's laws. The laws of thermodynamics have their foundation in the statistical physics.

Includes supplementary material: sn.pub/extras

Texte du rabat

Fluid mechanics (FM) is a branch of science dealing with the investi­ gation of flows of continua under the action of external forces. The fundamentals of FM were laid in the works of the famous scientists, such as L. Euler, M. V. Lomonosov, D. Bernoulli, J. L. Lagrange, A. Cauchy, L. Navier, S. D. Poisson, and other classics of science. Fluid mechanics underwent a rapid development during the past two centuries, and it now includes, along with the above branches, aerodynamics, hydrodynamics, rarefied gas dynamics, mechanics of multi phase and reactive media, etc. The FM application domains were expanded, and new investigation methods were developed. Certain concepts introduced by the classics of science, however, are still of primary importance and will apparently be of importance in the future. The Lagrangian and Eulerian descriptions of a continuum, tensors of strains and stresses, conservation laws for mass, momentum, moment of momentum, and energy are the examples of such concepts and results. This list should be augmented by the first and second laws of thermodynamics, which determine the character and direction of processes at a given point of a continuum. The availability of the conservation laws is conditioned by the homogeneity and isotrop­ icity properties of the Euclidean space, and the form of these laws is related to the Newton's laws. The laws of thermodynamics have their foundation in the statistical physics.

Résumé

"This is a self-contained book that systematically takes the reader from basic principles to the most advanced topics of fluid mechanics... Every concept is rigorously derived and proof is provided for theorems and equations... This reviewer has found the combination of fluid mechanics with computer algebra very useful since it allows one to 'wet the hands' with simple programs thus making the learning process more interactive... The book is well written, and every topic has a rigorous treatment from the mathematical point of view. It is very easy to move through the book since an initial index and a good final subject index are given... This reviewer certainly recommends the purchase of [this book], since it contains a lot of interesting material not commonly found in usual textbooks."

-Applied Mechanics Review

"This new text/reference presents the basic concepts and methods of fluid mechanics, including Lagrangian and Eulerian descriptions, tensors of stresses and strains, continuity, momentum, energy, thermodynamics laws, and similarity theory. The models and their solutions are presented within a new context of the mechanics of multiphase media. The treatment fully utilizes the computer algebra and software system Mathematica (to both develop concepts and help the reader to master modern methods of solving problems in fluid mechanics).

Foundations of Fluid Mechanics with Applications is a complete and accessible text/reference for graduates and professionals in mechanics, applied mathematics, physical sciences, materials science, and engineering. It is an essential resource for the study and use of modern solution methods for problems in fluid mechanics and the underlying mathematical models."

-Analele Stiintifice

Contenu
1 Definitions of Continuum Mechanics.- 1.1 Vectors and Tensors.- 1.2 Eulerian and Lagrangian Description of a Continuum: Strain Tensor.- 1.3 Stress Tensor.- References.- 2 Fundamental Principles and Laws of Continuum Mechanics.- 2.1 Equations of Continuity, Motion, and Energy for a Continuum.- 2.2 The HamiltonOstrogradsky's Variational Principle in Continuum Mechanics.- 2.3 Conservation Laws for Energy and Momentum in Continuum Mechanics.- References.- 3 The Features of the Solutions of Continuum Mechanics Problems.- 3.1 Similarity and Dimension Theory in Continuum Mechanics.- 3.2 The Characteristics of Partial Differential Equations..- 3.3 Discontinuity Surfaces in Continuum Mechanics.- References.- 4 Ideal Fluid.- 4.1 Integrals of Motion Equations of Ideal Fluid and Gas.- 4.2 Planar Irrotational Steady Motions of an Ideal Incompressible Fluid.- 4.3 Axisymmetric and Three-Dimensional Potential Ideal Incompressible Fluid Flows.- 4.4 Nonstationary Motion of a Solid in the Fluid.- 4.5 Vortical Motions of Ideal Fluid.- References.- 5 Viscous Fluid.- 5.1 General Equations of Viscous Incompressible Fluid.- 5.2 Viscous Fluid Flows at Small Reynolds Numbers.- 5.3 Viscous Fluid Flows at Large Reynolds Numbers.- 5.4 Turbulent Fluid Flows.- References.- 6 Gas Dynamics.- 6.1 One-Dimensional Stationary Gas Flows.- 6.2 Nonstationary One-Dimensional Flows of Ideal Gas.- 6.3 Planar Irrotational Ideal Gas Motion (Linear Approximation).- 6.4 Planar Irrotational Stationary Ideal Gas Flow (General Case).- 6.5 The Fundamentals of the Gasdynamic Design Technology.- References.- 7 Multiphase Media.- 7.1 Mathematical Models of Multiphase Media.- 7.2 Correctness of the Cauchy Problem: Relations at Discontinuities in Multiphase Media.- 7.3 Quasi-One-Dimensional Flows of a Gas-ParticleMixture in Laval Nozzles.- 7.4 The Continual-Discrete Model and Caustics in the Pseudogas of Particles.- 7.5 Nonstationary Processes in Gas-Particle Mixtures.- 7.6 The Flows of Heterogeneous Media without Regard for Inertial Effects.- 7.7 Wave Processes in Bubbly Liquids.- References.- Appendix B: Glossary of Programs.