Dimensional Analysis and Similarity in Fluid Mechanics

ISBN-13: 9781786305961 / Angielski / Twarda / 2020 / 240 str.

Spis treści

Foreword ixPreface xiIntroduction xiiiChapter 1. Homogeneity of Relationships and Conversion of Units 11.1. Introduction 11.2. Definitions of the basic SI units 21.2.1. Definition of the meter as adopted in 1983 21.2.2. Definition of the kilogram 21.2.3. Definition of the second adopted in 1967 31.2.4. Definition of the ampere adopted in 1948 41.2.5. Definition of Kelvin adopted in 1967 41.2.6. Definition of a mole 51.2.7. Definition of the candela adopted in 1979 51.3. Additional quantities and SI derived quantities 51.4. Rules for the use of units 71.4.1. Unit name 71.4.2. Unit symbols 81.4.3. Compound symbols 81.5. Exercises 91.5.1. Exercise 1: calculation of dimensions 91.5.2. Exercise 2: homogeneity of relationships 151.5.3. Exercise 3: dimension of the constants of an equation 221.5.4. Exercise 4: equation for perfect gases 231.5.5. Exercise 5: unit conversions 24Chapter 2. Dimensional Analysis: Rayleigh Method and Vaschy-Buckingham Method 292.1. Introduction 292.2. Definition of dimensional analysis 302.3. The Rayleigh method 312.3.1. Example of application: the period of the swinging of a pendulum 312.4. Vaschy-Buckingham method or method of pi 342.4.1. The Vaschy-Buckingham theorem 352.4.2. Formation of terms in pi 362.4.3. Application example: linear pressure drop calculation 372.5. Exercises: homogeneity method or Rayleigh method 412.5.1. Exercise 1: Reynolds number 412.5.2. Exercise 2: the Weber number 442.5.3. Exercise 3: capillary number 462.5.4. Exercise 4: power of a propeller 472.5.5. Exercise 5: flow through an orifice with thin walls 502.5.6. Exercise 6: a linear pressure drop along a horizontal pipe 522.5.7. Exercise 7: force exerted by a fluid on a body 572.5.8. Exercise 8: oscillation of a liquid in a U-shaped tube 592.5.9. Exercise 9: a falling ball 612.5.10. Exercise 10: implosion time of an air bubble 662.5.11. Exercise 11: vibration of a drop of water 682.5.12. Exercise 12: drag force of water on a ship 702.6. Exercises: Vaschy-Buckingham method or method of pi 722.6.1. Exercise 13: pressure drop in a pipe of circular cross-section 722.6.2. Exercise 14: friction forces on a flat plate 752.6.3. Exercise 15: drag force exerted on a sphere 792.6.4. Exercise 16: hydraulic jump 842.6.5. Exercise 17: flow through a thin-walled spillway with a horizontal crested 862.6.6. Exercise 18: flow through a triangular weir 892.6.7. Exercise 19: volume of a bubble 922.6.8. Exercise 20: flow through an orifice 942.6.9. Exercise 21: sudden narrowing of a section 982.6.10. Exercise 22: capillary tube 1022.6.11. Exercise 23: deformation of a bubble 1062.6.12. Exercise 24: laminar dynamic boundary layer on a flat plate 1082.6.13. Exercise 25: power of a stirrer 115Chapter 3. Similarity of Flows 1193.1. Definition and principle of similarity 1193.1.1. Geometric similarity 1193.1.2. Kinematic similarity 1203.1.3. Dynamic similarity 1213.1.4. Similarity conditions for viscous, incompressible, non-heavy fluids (Reynolds similarity) 1243.1.5. Similarity conditions for non-viscous, incompressible, heavy fluids (Reech-Froude similarity) 1243.1.6. Similarity requirements for non-viscous, non-compressible, heavy fluids 1253.1.7. Conditions of similarity of turbulent flows 1263.1.8. Distortion of the model 1273.2. Exercises: similarity of flows 1273.2.1. Exercise 1: similarity between ships 1273.2.2. Exercise 2: similarity of centrifugal pumps. 1303.2.3. Exercise 3: volumetric pumps with small dimensions 1363.2.4. Exercise 4: characteristics of a centrifugal pump 1383.2.5. Exercise 5: test of an automobile in a wind tunnel 1403.2.6. Exercise 6: power ratios (p model / p prototype) of a pump 1423.2.7. Exercise 7: flow in a pipe 1453.2.8. Exercise 8: viscous force on a rotating disk 1463.2.9. Exercise 9: development study of a hydroelectric gallery 1513.2.10. Exercise 10: movement of solid matter by a water current 1553.2.11. Exercise 11: a tapered body 1593.2.12. Exercise 12: model of a seaplane 1623.2.13. Exercise 13: tide study 1643.2.14. Exercise 14: transient gas flow 1683.2.15. Exercise 15: model of a torpedo 1703.2.16. Exercise 16: movement of a ball in a fluid 1743.2.17. Exercise 17: similarity of the movement of an airship 1773.2.18. Exercise 18: resistance to the movement of a ship 1803.2.19. Exercise 19: mixing tank 1853.2.20. Exercise 20: friction on a prototype probe 192Appendices 195Appendix 1. Some Dimensionless Numbers Used in Fluid Mechanics 197Appendix 2. Coefficients of Conversion to the International System or to the English System 201References 205Index 207

O autorze

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.