Foundations of Fluid Mechanics with Applications

1. Front Matter

   Pages i-xiv

   PDF

2. Definitions of Continuum Mechanics

   • Sergey P. Kiselev, Evgenii V. Vorozhtsov, Vasily M. Fomin

   Pages 1-74

3. Fundamental Principles and Laws of Continuum Mechanics

   • Sergey P. Kiselev, Evgenii V. Vorozhtsov, Vasily M. Fomin

   Pages 75-153

4. The Features of the Solutions of Continuum Mechanics Problems

   • Sergey P. Kiselev, Evgenii V. Vorozhtsov, Vasily M. Fomin

   Pages 155-185

5. Ideal Fluid

   • Sergey P. Kiselev, Evgenii V. Vorozhtsov, Vasily M. Fomin

   Pages 187-266

6. Viscous Fluid

   • Sergey P. Kiselev, Evgenii V. Vorozhtsov, Vasily M. Fomin

   Pages 267-310

7. Gas Dynamics

   • Sergey P. Kiselev, Evgenii V. Vorozhtsov, Vasily M. Fomin

   Pages 311-400

8. Multiphase Media

   • Sergey P. Kiselev, Evgenii V. Vorozhtsov, Vasily M. Fomin

   Pages 401-525

9. Back Matter

   Pages 526-575

   PDF

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.

• Profil
• aerodynamics
• algorithm
• continuum mechanics
• development
• differential equation
• dynamics
• fluid mechanics
• mechanics
• model
• partial differential equation
• physics
• problem solving
• science
• thermodynamics

"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

• Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

  Sergey P. Kiselev, Evgenii V. Vorozhtsov, Vasily M. Fomin

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