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…mehr
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.
Nord-Eddine Sad Chemloul is a teacher-researcher at the University of Tiaret in Algeria. He teaches fluid mechanics as well as related subjects, such as mass and heat transfer, heat exchangers, turbomachinery and propulsion mechanics.
Inhaltsangabe
Foreword ix
Preface xi
Introduction xiii
Chapter 1. Homogeneity of Relationships and Conversion of Units 1
1.1. Introduction 1
1.2. Definitions of the basic SI units 2
1.2.1. Definition of the meter as adopted in 1983 2
1.2.2. Definition of the kilogram 2
1.2.3. Definition of the second adopted in 1967 3
1.2.4. Definition of the ampere adopted in 1948 4
1.2.5. Definition of Kelvin adopted in 1967 4
1.2.6. Definition of a mole 5
1.2.7. Definition of the candela adopted in 1979 5
1.3. Additional quantities and SI derived quantities 5
1.4. Rules for the use of units 7
1.4.1. Unit name 7
1.4.2. Unit symbols 8
1.4.3. Compound symbols 8
1.5. Exercises 9
1.5.1. Exercise 1: calculation of dimensions 9
1.5.2. Exercise 2: homogeneity of relationships 15
1.5.3. Exercise 3: dimension of the constants of an equation 22
1.5.4. Exercise 4: equation for perfect gases 23
1.5.5. Exercise 5: unit conversions 24
Chapter 2. Dimensional Analysis: Rayleigh Method and Vaschy-Buckingham Method 29
2.1. Introduction 29
2.2. Definition of dimensional analysis 30
2.3. The Rayleigh method 31
2.3.1. Example of application: the period of the swinging of a pendulum 31
2.4. Vaschy-Buckingham method or method of pi 34
2.4.1. The Vaschy-Buckingham theorem 35
2.4.2. Formation of terms in pi 36
2.4.3. Application example: linear pressure drop calculation 37
2.5. Exercises: homogeneity method or Rayleigh method 41
2.5.1. Exercise 1: Reynolds number 41
2.5.2. Exercise 2: the Weber number 44
2.5.3. Exercise 3: capillary number 46
2.5.4. Exercise 4: power of a propeller 47
2.5.5. Exercise 5: flow through an orifice with thin walls 50
2.5.6. Exercise 6: a linear pressure drop along a horizontal pipe 52
2.5.7. Exercise 7: force exerted by a fluid on a body 57
2.5.8. Exercise 8: oscillation of a liquid in a U-shaped tube 59
2.5.9. Exercise 9: a falling ball 61
2.5.10. Exercise 10: implosion time of an air bubble 66
2.5.11. Exercise 11: vibration of a drop of water 68
2.5.12. Exercise 12: drag force of water on a ship 70
2.6. Exercises: Vaschy-Buckingham method or method of pi 72
2.6.1. Exercise 13: pressure drop in a pipe of circular cross-section 72
2.6.2. Exercise 14: friction forces on a flat plate 75
2.6.3. Exercise 15: drag force exerted on a sphere 79
2.6.4. Exercise 16: hydraulic jump 84
2.6.5. Exercise 17: flow through a thin-walled spillway with a horizontal crested 86
2.6.6. Exercise 18: flow through a triangular weir 89
2.6.7. Exercise 19: volume of a bubble 92
2.6.8. Exercise 20: flow through an orifice 94
2.6.9. Exercise 21: sudden narrowing of a section 98
2.6.10. Exercise 22: capillary tube 102
2.6.11. Exercise 23: deformation of a bubble 106
2.6.12. Exercise 24: laminar dynamic boundary layer on a flat plate 108
