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Similarity and Dimensional Methods in Mechanics - 1st Edition - ISBN: 9781483200880, 9781483225913

Similarity and Dimensional Methods in Mechanics

1st Edition

Author: L. I. Sedov
eBook ISBN: 9781483225913
Imprint: Academic Press
Published Date: 1st January 1959
Page Count: 380
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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.

Table of Contents

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

1. Motion of a Simple Pendulum

2. Flow of a Heavy Liquid through a Spillway

3. Fluid Motion in Pipes

4. Motion of a Body in a Fluid

5. Heat Transfer from a Body in a Fluid Flow Field

6. Dynamic Similarity and Modelling of Phenomena

7. Steady Motion of a Solid Body in a Compressible Fluid

8. Unsteady Motion of a Fluid

9. Ship Motion

10. Planing Over the Water Surface

11. Impact on Water

12. Entry of a Cone and Wedge at Constant Speed into a Fluid

13. Shallow Waves on the Surface of an Incompressible Fluid

14. 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

1. Diffusion of Vorticity in a Viscous Fluid

2. Exact Solutions of the Equations of Motion of a Viscous Incompressible Fluid

3. Boundary Layer in the Flow of a Viscous Fluid Past a Flat Plate

4. Isotropic Turbulent Motion of an Incompressible Fluid

5. Steady Turbulent Motion

IV. One-Dimensional Unsteady Motion of a Gas

1. Self-Similar Motion of Spherical, Cylindrical and Plane Waves in a Gas

2. Ordinary Differential Equations and the Shock Conditions for Self-Similar Motions

3. Algebraic Integrals for Self-Similar Motions

4. Motions which are Self-Similar in the Limit

5. Investigation of the Family of Integral Curves in the z, V Plane

6. The Piston Problem

7. Problem of Implosion and Explosion at a Point

8. Spherical Detonation

9. Flame Propagation

10. Collapse of an Arbitrary Discontinuity in a Combustible Mixture

11. The Problem of an Intense Explosion

12. Point Explosion Taking Counter Pressure into Account

13. On Simulation and on Formulas for the Peak Pressure and Impulse in Explosions

14. Problem of an Intense Explosion in a Medium with Variable Density

15. Unsteady Motion of a Gas, when the Velocity is Proportional to Distance from the Centre of Symmetry

16. On the General Theory of One-Dimensional Motion of a Gas

17. Asymptotic Laws of Shock Wave Decay

V. Application to Astrophysical Problems

1. Certain Observational Results

2. On the Equations of Equilibrium and Motion of a Gaseous Mass Simulating a Star

3. Theoretical Formulas Relating Luminosity with Mass and Radius with Mass

4. Certain Simple Solutions of the System of Equations of Stellar Equilibrium

5. On the Relation Between the Period of Variation of the Brightness and the Average Density for Cepheids

6. On the Theory of the Flare-Ups of Novae and Supernovae


Author Index

Subject Index


No. of pages:
© Academic Press 1959
1st January 1959
Academic Press
eBook ISBN:

About the Author

L. I. Sedov

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