Dimensional analysis for engineers

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....

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Bibliographic Details
Main Authors Simon, Volker (Author), Weigand, Bernhard, 1962- (Author), Gomaa, Hassan (Author)
Format Electronic eBook
LanguageEnglish
Published Cham, Switzerland : Springer, 2017.
SeriesMathematical engineering.
Subjects
Dimensional analysis.
Engineering mathematics.
elektronické knihy
electronic books
Online AccessFull text
ISBN9783319520285
9783319520261
Physical Description1 online resource

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Table of Contents:
  • 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.

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