Dimensional analysis is the basis for the determination of laws that allow the experimental results obtained on a model to be transposed to the fluid system at full scale (a prototype). The similarity in fluid mechanics then allows for better redefinition of the analysis by removing dimensionless elements. This book deals with these two tools, with a focus on the Rayleigh method and the Vaschy-Buckingham method. It deals with the homogeneity of the equations and the conversion between the systems of units SI and CGS, and presents the dimensional analysis approach, before addressing the similarity of flows. Dimensional Analysis and Similarity in Fluid Mechanics proposes a scale model and presents numerous exercises combining these two methods. It is accessible to students from their first year of a bachelor's degree.
Table of Contents
- Cover
- Title page
- Copyright
- Foreword
- Preface
- Introduction
- 1 Homogeneity of Relationships and Conversion of Units
- 1.1. Introduction
- 1.2. Definitions of the basic SI units
- 1.3. Additional quantities and SI derived quantities
- 1.4. Rules for the use of units
- 1.5. Exercises
- 2 Dimensional Analysis: Rayleigh Method and Vaschy-Buckingham Method
- 2.1. Introduction
- 2.2. Definition of dimensional analysis
- 2.3. The Rayleigh method
- 2.4. Vaschy-Buckingham method or method of π
- 2.5. Exercises: homogeneity method or Rayleigh method
- 2.6. Exercises: Vaschy-Buckingham method or method of π
- 3 Similarity of Flows
- 3.1. Definition and principle of similarity
- 3.2. Exercises: similarity of flows
- Appendices
- Appendix 1: Some Dimensionless Numbers Used in Fluid Mechanics
- Appendix 2: Coefficients of Conversion to the International System or to the English System
- References
- Index
- End User License Agreement