Similarity and Dimensional Methods in Mechanics (eBook)

Front Cover 1
Similarity and Dimensional Methods in Mechanics 4
Copyright Page 5
Table of Contents 16
Editor's Foreword 6
Author's Foreword to the English Translation 8
Foreword to First Edition 10
Foreword to Third Edition 12
Foreword to Fourth Edition 14
CHAPTER I. General Dimensional Theory 18
1. INTRODUCTION 18
2. DIMENSIONAL AND NONDIMENSIONAL QUANTITIES 19
3. FUNDAMENTAL AND DERIVED UNITS OF MEASUREMENT 20
4. DIMENSIONAL FORMULAS 25
5. ON NEWTON'S SECOND LAW 27
6. NATURE OF THE FUNCTIONAL RELATIONS BETWEEN PHYSICAL 
33 
7. PARAMETERS DEFINING A CLASS OF PHENOMENA 37
CHAPTER II. Similarity, Modelling and Various Examples of the Application 
41 
1. MOTION OF A SIMPLE PENDULUM 41
2. FLOW OF A HEAVY FLUID THROUGH A SPILLWAY 44
3. FLUID MOTION IN PIPES 45
4. MOTION OF A BODY IN A FLUID 50
5. HEAT TRANSFER FROM A BODY IN A FLUID FLOW FIELD 57
6. DYNAMIC SIMILARITY AND MODELLING OF PHENOMENA 60
7. STEADY MOTION OF A SOLID BODY IN A COMPRESSIBLE FLUID 71
8. UNSTEADY MOTION OF A FLUID 77
9. SHIP MOTION 82
10. PLANING OVER THE WATER SURFACE 90
11. IMPACT ON WATER 96
12. ENTRY OF A CONE AND WEDGE AT CONSTANT SPEED INTO A FLUID 104
14. THREE DIMENSIONAL SELF-SIMILAR MOTIONS OF COMPRESSIBLE 
114 
CHAPTER III. Application to the Theory of Motion of a Viscous Fluid and to 
118 
§1. 
118 
§2. EXACT SOLUTIONS OF THE EQUATIONS OF MOTION OF A VISCOUS INCOMPRESSIBLE 
120 
§3. 
127 
§4. 
131 
§5. 
154 
CHAPTER IV. One-Dimensional Unsteady Motion of a Gas 167
§1. 
167 
§2. ORDINARY DIFFERENTIAL EQUATIONS AND THE SHOCK CONDITIONS FOR SELF-SIMILAR MOTIONS 176
§3. 
187 
§4. 
195 
§5. 
198 
§6. 
208 
§7. 
212 
§8. 
214 
§9. 
221 
§10. 
227 
§11. 
231 
§12. 
261 
§13. 
274 
§14. 
283 
§15. 
294 
§16. 
304 
§17. ASYMPTOTIC 
318 
CHAPTER V. Application to Astrophysical Problems 328
§1. 
328 
§2. 
338 
§3. 
344 
§4. 
348 
§5. 
354 
§6. 
357 
References 378
Author Index 382
Subject Index 384