Simon, Volker
Dimensional analysis for engineers Volker Simon, Bernhard Weigand, Hassan Gomaa - Cham : Springer, 2017. - xiv, 133 p. : ill. ; 23 cm. - Mathematical engineering . - Mathematical engineering .
Preface; Contents; Symbols; 1 Some Fundamentals of Dimensional Analysis; 1.1 Some Preliminary Remarks; 1.2 Terms and Definitions; 1.2.1 Physical Quantities; 1.2.2 Entities, Base Quantities, Derived Quantities and Quantity System; 1.2.3 Dimension, Dimensional Formula and Bridgman Equation; 1.2.4 Units, Unit System and Unit of Measurement; 1.2.5 Change of the Unit System; 1.2.6 Physical Equations and Dimensional Constants; 1.3 Buckingham-Theorem (Pi-Theorem); 1.4 Choice of the Base System; 1.4.1 The [LMFT]-System; 1.4.2 The [LMT\varTheta]-System; 2 Model Theory; 2.1 General Model Theory. 2.2 Complete Similarity2.3 Incomplete Similarity; 3 Illustrative Examples; 3.1 Examples from Mechanics; 3.1.1 Large Elastic Deformations; 3.1.2 Small Elastic Deformations; 3.1.3 Deformation of an Elastic Beam; 3.1.4 Critical Load and Buckling of a Beam; 3.1.5 Natural Frequency of an Elastic Rod; 3.2 Examples from Fluid Mechanics; 3.2.1 Surface Waves; 3.2.2 Ship Waves; 3.2.3 Chimney Flow; 3.2.4 Hydraulic Machines; 3.3 Examples from Thermodynamics; 3.3.1 Thermal Equation of State for Ideal Gases; 3.3.2 Strong Explosion; 3.3.3 Unsteady Heat Transfer; 3.4 Examples from Nature. 3.4.1 The Dynamics of Planetary Rings3.4.2 The Flight Velocity of Birds; 3.4.3 The Run-off from a Watershed; 3.5 Examples from Classical Electrodynamics; 3.5.1 The Governing Equations; 3.5.2 Electrodynamic Quantities in the SI-Unit-System; 3.5.3 Implication of the SI-Unit-System; 3.5.4 Electrical Circuits; 4 Similarity Solutions; 4.1 Transient Temperature Distribution in a Semi-infinite Body; 4.2 Flow Along a Stretched Sheet; 4.3 Natural Convection Along a Vertical Plate; 4.4 Natural Convection Along a Horizontal Cylinder; 4.5 Laminar Free Jet; 4.6 Laminar Buoyant Jet. Appendix A: Selected ProblemsAppendix B: Solutions to the Problems; References; Index.
This monograph provides the fundamentals of dimensional analysis and illustrates the method by numerous examples for a wide spectrum of applications in engineering. The book covers thoroughly the fundamental definitions and the Buckingham theorem, as well as the choice of the system of basic units. The authors also include a presentation of model theory and similarity solutions. The target audience primarily comprises researchers and practitioners but the book may also be suitable as a textbook at university level.
9783319520285 3319520288 9783319520261
Dimensional analysis
Engineering mathematics
530.8 SI DI
Dimensional analysis for engineers Volker Simon, Bernhard Weigand, Hassan Gomaa - Cham : Springer, 2017. - xiv, 133 p. : ill. ; 23 cm. - Mathematical engineering . - Mathematical engineering .
Preface; Contents; Symbols; 1 Some Fundamentals of Dimensional Analysis; 1.1 Some Preliminary Remarks; 1.2 Terms and Definitions; 1.2.1 Physical Quantities; 1.2.2 Entities, Base Quantities, Derived Quantities and Quantity System; 1.2.3 Dimension, Dimensional Formula and Bridgman Equation; 1.2.4 Units, Unit System and Unit of Measurement; 1.2.5 Change of the Unit System; 1.2.6 Physical Equations and Dimensional Constants; 1.3 Buckingham-Theorem (Pi-Theorem); 1.4 Choice of the Base System; 1.4.1 The [LMFT]-System; 1.4.2 The [LMT\varTheta]-System; 2 Model Theory; 2.1 General Model Theory. 2.2 Complete Similarity2.3 Incomplete Similarity; 3 Illustrative Examples; 3.1 Examples from Mechanics; 3.1.1 Large Elastic Deformations; 3.1.2 Small Elastic Deformations; 3.1.3 Deformation of an Elastic Beam; 3.1.4 Critical Load and Buckling of a Beam; 3.1.5 Natural Frequency of an Elastic Rod; 3.2 Examples from Fluid Mechanics; 3.2.1 Surface Waves; 3.2.2 Ship Waves; 3.2.3 Chimney Flow; 3.2.4 Hydraulic Machines; 3.3 Examples from Thermodynamics; 3.3.1 Thermal Equation of State for Ideal Gases; 3.3.2 Strong Explosion; 3.3.3 Unsteady Heat Transfer; 3.4 Examples from Nature. 3.4.1 The Dynamics of Planetary Rings3.4.2 The Flight Velocity of Birds; 3.4.3 The Run-off from a Watershed; 3.5 Examples from Classical Electrodynamics; 3.5.1 The Governing Equations; 3.5.2 Electrodynamic Quantities in the SI-Unit-System; 3.5.3 Implication of the SI-Unit-System; 3.5.4 Electrical Circuits; 4 Similarity Solutions; 4.1 Transient Temperature Distribution in a Semi-infinite Body; 4.2 Flow Along a Stretched Sheet; 4.3 Natural Convection Along a Vertical Plate; 4.4 Natural Convection Along a Horizontal Cylinder; 4.5 Laminar Free Jet; 4.6 Laminar Buoyant Jet. Appendix A: Selected ProblemsAppendix B: Solutions to the Problems; References; Index.
This monograph provides the fundamentals of dimensional analysis and illustrates the method by numerous examples for a wide spectrum of applications in engineering. The book covers thoroughly the fundamental definitions and the Buckingham theorem, as well as the choice of the system of basic units. The authors also include a presentation of model theory and similarity solutions. The target audience primarily comprises researchers and practitioners but the book may also be suitable as a textbook at university level.
9783319520285 3319520288 9783319520261
Dimensional analysis
Engineering mathematics
530.8 SI DI