In this post, we will see the book Similarity And Dimensional Methods In Mechanics by L.I. Sedov.

# About the book

This book contains a complete development of the fundamental concepts of Dimensional Analysis and Similarity Methods, illustrated by applications to a wide variety of problems in mechanics, and particularly in fluid dynamics. The subject is developed from first principles and can be understood with the aid of an elementary knowledge of mathematical analysis and fluid dynamics. More advanced physical concepts are explained in the book itself. The first three chapters describe the basic ideas of the subject with illustrations from familiar problems in mechanics. The last two chapters show the power of Dimensional and Similarity Methods in solving new problems in the theory of explosions and astrophysics.

The book should be of interest to students who wish to learn dimensional analysis and similarity methods for the first time and to students of fluid dynamics who should gain further insight into the subject by following the presentation given here. The book as a whole and particularly the application to recent problems should appeal to all those connected with the many present-day aspects of gas dynamics including astrophysics, space technology and atomic energy.

The basic ideas behind Similarity and Dimensional Methods are given in the first chapter, which is general and descriptive in character. The second chapter consists of a series of examples of application of the methods, to familiar problems such as the motion of a simple pendulum, modelling in ship design, and the many scaling effects which arise in wind tunnel or water tank testing. Chapter III shows the use of Similarity and Dimensional Analysis in developing fundamental contributions to viscous fluid theory, such as the Blasius flat plate solution, and the various theories of isotropic turbulence.

The book was translated from Russian by Morris Friedman and edited by Maurice Holt and was published in 1959.

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You can get the book here.

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# Contents

## I. General Dimensional Theory 1

1. Introduction 1

2. Dimensional and Nondimensional Quantities 2

3. Fundamental and Derived Units of Measurement 3

4. Dimensional Formulas 8

5. On Newton’s Second Law 10

6. Nature of the Functional Relations between Physical Quantities 16

7. Parameters defining a Class of Phenomena 20

## II. Similarity, Modelling and Examples of the Application of Dimensional Analysis 24

1. Motion of a Simple Pendulum 24

2. Flow of a Heavy Liquid through a Spillway 27

3. Fluid Motion in Pipes 28

4. Motion of a Body in a Fluid 33

5. Heat Transfer from a Body in a Fluid Flow Field 40

6. Dynamic Similarity and Modelling of Phenomena 43

7. Steady Motion of a Solid Body in a Compressible Fluid 52

8. Unsteady Motion of a Fluid 56

9. Ship Motion 61

10. Planing over the Water Surface 69

11. Impact on Water 75

12. Entry of a Cone and Wedge at Constant Speed into a Fluid 83

13. Shallow Waves on the Surface of an Incompressible Fluid 85

14. Three-dimensional Self-Similar Motions of Compressible

Median 93

## III. Application to the Theory of Motion of a Viscous Fluid and to the Theory of Turbulence 97

1. Diffusion of Vorticity in a Viscous Fluid 97

2. Exact Solutions of the Equations of Motion of a Viscous Incompressible Fluid 99

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

Plate 106

4. Isotropic Turbulent Motion of an Incompressible Fluid 110

5. Steady Turbulent Motion 133

## IV. One-Dimensional Unsteady Motion of a Gas 146

1. Self-similar Motion of Spherical, Cylindrical and Plane Waves in a Gas 146

2. Ordinary Differential Equations and the Shock Conditions for Self-similar Motions 155

3. Algebraic Integrals for Self-similar Motions 166

4. Motions which are Self-similar in the Limit 174

5. Investigation of the Family of Integral Curves in the z, V Plane 177

6. The Piston Problem 187

7. Problem of Implosion and Explosion at a Point 191

8. Spherical Detonation 193

9. Flame Propagation 200

10. Collapse of an Arbitrary Discontinuity in a Combustible Mixture 206

11. The Problem of an Intense Explosion 210

12. Point Explosion taking Counter Pressure into Account 238

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 260

15. Unsteady Motion of a Gas, when the Velocity is Proportional to Distance from the Centre of Symmetry 271

16. On the General Theory of One-dimensional Motion of a Gas 281

17. Asymptotic Laws of Shock Wave Decay 295

## V. Application to Astrophysical Problems 305

1. Certain Observational Results 305

2. On the Equations of Equilibrium and Motion of a Gaseous Mass Simulating a Star 315

3. Theoretical Formulas relating Luminosity with Mass and Radius with Mass 321

4. Certain Simple Solutions of the System of Equations of Stellar Equilibrium 325

5. On the Relation between the Period of Variation of the Brightness and the Average Density for Cepheids 331

6. On the Theory of the Flare-Ups of Novae and Supernovae 334

REFERENCES 355

AUTHOR INDEX 359

SUBJECT: INDEX 361

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