Lemons, Don S.
A student's guide to dimensional analysis Don S. Lemons - New York : Cambridge University Press, c2017. - xii, 102 p. : ill. ; 24 cm.
Cover; Half-title ; Title page ; Copyright information ; Table of contents ; Preface ; Acknowledgments ; 1 Introduction ; 1.1 Dimensional Homogeneity ; Symmetry under Change of Units ; 1.2 Dimensionless Products ; Dimensional Analysis ; 1.3 Dimensional Formulae.
1.4 The Rayleigh Algorithm A Marble on the Interior Surface of a Cone ; Rayleigh's Algorithm ; The Rayleigh Algorithm Modified ; 1.5 The Buckingham pp Theorem ; 1.6 The Number of Dimensions ; 1.7 The Number of Dimensionless Products ; 1.8 Example: Pressure of an Ideal Gas.
1.9 A Mistake to Avoid The Mistake of Not Minimizing the Number of Dimensional Variables and Constants ; Essential Ideas ; Problems ; 2 Mechanics ; 2.1 Kinematics and Dynamics ; 2.2 Effective Dimensions ; The Number of Effective Dimensions ; 2.3 Imposed Dimensions.
2.4 Example: Hanging Spring-Mass System 2.5 Example: Hanging, Stretched Cable ; 2.6 Asymptotic Behavior ; 2.7 Example: Speed of Sound ; 2.8 Example: Side Window Buffeting ; 2.9 Example: Two-Body Orbits ; Essential Ideas ; Problems ; 3 Hydrodynamics ; 3.1 Fluid Variables.
3.2 Example: Water Waves 3.3 Surface Tension ; Capillary Waves ; 3.4 Example: Largest Water Drop ; 3.5 Viscosity ; Terminal Speed ; Stokes' Law ; 3.6 Example: Hydraulic Jump ; Reynolds Number ; 3.7 Example: Equilibrium Pipe Flow ; 3.8 Example: Non-Equilibrium Pipe Flow ; 3.9 Scale Models.
This introduction to dimensional analysis covers the methods, history and formalisation of the field, and provides physics and engineering applications. Covering topics from mechanics, hydro- and electrodynamics to thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis. Introducing basic physics and fluid engineering topics through the mathematical methods of dimensional analysis, this book is perfect for students in physics, engineering and mathematics. Explaining potentially unfamiliar concepts such as viscosity and diffusivity, the text includes worked examples and end-of-chapter problems with answers provided in an accompanying appendix, which help make it ideal for self-study. Long-standing methodological problems arising in popular presentations of dimensional analysis are also identified and solved, making the book a useful text for advanced students and professionals.
9781107161153
Dimensional analysis
Electrodynamics
530.8 LE ST
A student's guide to dimensional analysis Don S. Lemons - New York : Cambridge University Press, c2017. - xii, 102 p. : ill. ; 24 cm.
Cover; Half-title ; Title page ; Copyright information ; Table of contents ; Preface ; Acknowledgments ; 1 Introduction ; 1.1 Dimensional Homogeneity ; Symmetry under Change of Units ; 1.2 Dimensionless Products ; Dimensional Analysis ; 1.3 Dimensional Formulae.
1.4 The Rayleigh Algorithm A Marble on the Interior Surface of a Cone ; Rayleigh's Algorithm ; The Rayleigh Algorithm Modified ; 1.5 The Buckingham pp Theorem ; 1.6 The Number of Dimensions ; 1.7 The Number of Dimensionless Products ; 1.8 Example: Pressure of an Ideal Gas.
1.9 A Mistake to Avoid The Mistake of Not Minimizing the Number of Dimensional Variables and Constants ; Essential Ideas ; Problems ; 2 Mechanics ; 2.1 Kinematics and Dynamics ; 2.2 Effective Dimensions ; The Number of Effective Dimensions ; 2.3 Imposed Dimensions.
2.4 Example: Hanging Spring-Mass System 2.5 Example: Hanging, Stretched Cable ; 2.6 Asymptotic Behavior ; 2.7 Example: Speed of Sound ; 2.8 Example: Side Window Buffeting ; 2.9 Example: Two-Body Orbits ; Essential Ideas ; Problems ; 3 Hydrodynamics ; 3.1 Fluid Variables.
3.2 Example: Water Waves 3.3 Surface Tension ; Capillary Waves ; 3.4 Example: Largest Water Drop ; 3.5 Viscosity ; Terminal Speed ; Stokes' Law ; 3.6 Example: Hydraulic Jump ; Reynolds Number ; 3.7 Example: Equilibrium Pipe Flow ; 3.8 Example: Non-Equilibrium Pipe Flow ; 3.9 Scale Models.
This introduction to dimensional analysis covers the methods, history and formalisation of the field, and provides physics and engineering applications. Covering topics from mechanics, hydro- and electrodynamics to thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis. Introducing basic physics and fluid engineering topics through the mathematical methods of dimensional analysis, this book is perfect for students in physics, engineering and mathematics. Explaining potentially unfamiliar concepts such as viscosity and diffusivity, the text includes worked examples and end-of-chapter problems with answers provided in an accompanying appendix, which help make it ideal for self-study. Long-standing methodological problems arising in popular presentations of dimensional analysis are also identified and solved, making the book a useful text for advanced students and professionals.
9781107161153
Dimensional analysis
Electrodynamics
530.8 LE ST