Similarity and Dimensional Methods in Mechanics

Similarity and Dimensional Methods in Mechanics provides a complete development of the basic concepts of dimensional analysis and similarity methods, illustrated by applications to a wide variety of problems in mechanics. This book shows the power of dimensional and similarity methods in solving problems in the theory of explosions and astrophysics.

Organized into five chapters, this book begins with an overview of the fundamental ideas behind similarity and dimensional methods. This text then provides a series of examples of application of the methods. Other chapters consider the use of similarity and dimensional analysis in developing fundamental contributions to viscous fluid theory. This book discusses as well the various theories of isotropic turbulence. The final chapter deals with the applications to the theory of the luminosity and internal structure of stars.

This book is a valuable resource for students who wish to learn dimensional analysis and similarity methods for the first time. Readers who are connected with the many aspects of gas dynamics, including space technology, astrophysics, and atomic energy will also find this book useful.

Contenu

Editor's Foreword
Author's Foreword to the English Translation
Foreword to the First Edition
Foreword to the Third Edition
Foreword to the Fourth Edition
Chapter I. General Dimensional Theory

1. Introduction
2. Dimensional and Nondimensional Quantities
3. Fundamental and Derived Units of Measurement
4. Dimensional Formulas
5. On Newton's Second Law
6. Nature of the Functional Relations Between Physical Quantities
7. Parameters Defining a Class of Phenomena
   II. Similarity, Modelling and Examples of the Application of Dimensional Analysis
8. Motion of a Simple Pendulum
9. Flow of a Heavy Liquid through a Spillway
10. Fluid Motion in Pipes
11. Motion of a Body in a Fluid
12. Heat Transfer from a Body in a Fluid Flow Field
13. Dynamic Similarity and Modelling of Phenomena
14. Steady Motion of a Solid Body in a Compressible Fluid
15. Unsteady Motion of a Fluid
16. Ship Motion
17. Planing Over the Water Surface
18. Impact on Water
19. Entry of a Cone and Wedge at Constant Speed into a Fluid
20. Shallow Waves on the Surface of an Incompressible Fluid
21. Three-Dimensional Self-Similar Motions of Compressible Media
    III. Application to the Theory of Motion of a Viscous Fluid and to the Theory of Turbulence
22. Diffusion of Vorticity in a Viscous Fluid
23. Exact Solutions of the Equations of Motion of a Viscous Incompressible Fluid
24. Boundary Layer in the Flow of a Viscous Fluid Past a Flat Plate
25. Isotropic Turbulent Motion of an Incompressible Fluid
26. Steady Turbulent Motion
    IV. One-Dimensional Unsteady Motion of a Gas
27. Self-Similar Motion of Spherical, Cylindrical and Plane Waves in a Gas
28. Ordinary Differential Equations and the Shock Conditions for Self-Similar Motions
29. Algebraic Integrals for Self-Similar Motions
30. Motions which are Self-Similar in the Limit
31. Investigation of the Family of Integral Curves in the z, V Plane
32. The Piston Problem
33. Problem of Implosion and Explosion at a Point
34. Spherical Detonation
35. Flame Propagation
36. Collapse of an Arbitrary Discontinuity in a Combustible Mixture
37. The Problem of an Intense Explosion
38. Point Explosion Taking Counter Pressure into Account
39. On Simulation and on Formulas for the Peak Pressure and Impulse in Explosions
40. Problem of an Intense Explosion in a Medium with Variable Density
41. Unsteady Motion of a Gas, when the Velocity is Proportional to Distance from the Centre of Symmetry
42. On the General Theory of One-Dimensional Motion of a Gas
43. Asymptotic Laws of Shock Wave Decay
    V. Application to Astrophysical Problems
44. Certain Observational Results
45. On the Equations of Equilibrium and Motion of a Gaseous Mass Simulating a Star
46. Theoretical Formulas Relating Luminosity with Mass and Radius with Mass
47. Certain Simple Solutions of the System of Equations of Stellar Equilibrium
48. On the Relation Between the Period of Variation of the Brightness and the Average Density for Cepheids
49. On the Theory of the Flare-Ups of Novae and Supernovae
    References
    Author Index
    Subject Index