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# Applied Dimensional Analysis and Modeling,

**Thomas Szirtes**

ISBN **0123706203**

Pages **856**

Description

Applied Dimensional Analysis and Modeling provides the full mathematical background and step-by-step procedures for employing dimensional analyses, along with a wide range of applications to problems in engineering and applied science, such as fluid dynamics, heat flow, electromagnetics, astronomy and economics. This new edition offers additional worked-out examples in mechanics, physics, geometry, hydrodynamics, and biometry.

Contents

Chapter 1: Mathematical Preliminaries by Pál Rózsa 1.1 Matrices and Determinants 1.2 Operations with Matrices 1.3 The Rank of a Matrix 1.4 Systems of Linear Equations 1.4.1 Homogeneous Case 1.4.2 Nonhomogeneous Case 1.5 List of Selected Publications Dealing with Linear Algebra and Matrices Chapter 2: Formats and Classification 2.1 Formats for Physical Relations 2.1.1 Numeric Format 2.1.2 Symbolic Format 2.1.3 Mixed Format 2.2 Classification of Physical Quantities 2.2.1 Variability 2.2.2 Dimensionality Chapter 3: Dimensional Systems 3.1 General Statements 3.1.1 Monodimensional System 3.1.2 Omnidimensional System 3.1.3 Multidimensional System 3.2 Classification 3.3 The SI 3.3.1 Preliminary Remarks 3.3.2 Structure (a) Fundamental Dimensions (b) Derived Dimensionless Units (c) Derived Dimensional Units with Specific Names (d) Derived Dimensional Units without Specific Names (e) Non-SI Units Permanently Permitted to be Used with SI (f) Non-SI Units Temporarily Permitted to be Used with SI (g) Prohibited Units 3.3.3 Prefixes 3.3.4 Rules of Etiquette in Writing Dimensions 3.3.4.1 Problems 3.4 Other Than SI Dimensional Systems 3.4.1 Metric, Mass-based Systems (a) CGS System (b) SI (for reference only) 3.4.2 Metric, Force-based System 3.4.3 American/British Force (Engineering) System 3.4.4 American/British Mass (Scientific) System 3.5 A Note on the Classification of Dimensional Systems Chapter 4: Transformation of Dimensions 4.1 Numerical Equivalences 4.2 Technique 4.3 Examples 4.4 Problems Chapter 5: Arithmetic of Dimensions Chapter 6: Dimensional Homogeneity 6.1 Equations 6.2 Graphs 6.3 Problems Chapter 7: Structure of Physical Relations 7.1 Monomial Power Form 7.2 The Dimensional Matrix 7.3 Generating Products of Variables of Desired Dimension 7.4 Number of Independent Sets of Products of Given Dimension (I) 7.5 Completeness of the Set of Products of Variables 7.6 Special Case: Matrix A is Singular 7.7 Number of Independent Sets of Products of Given Dimension (II); Buckingham’s Theorem 7.8 Selectable and Nonselectable Dimensions in a Product of Variables 7.9 Minimum Number of Independent Products of Variables of Given Dimension 7.10 Constancy of the Sole Dimensionless Product 7.11 Number of Dimensions Equals or Exceeds the Number of Variables 7.11.1 Number of Dimensions Equals the Number of Variables 7.11.2 Number of Dimensions Exceeds the Number of Variables 7.12 Problems Chapter 8: Systematic Determination of Complete Set of Products of Variables 8.1 Dimensional Set; Derivation of Products of Variables of a Given Dimension 8.2 Checking the Results 8.3 The Fundamental Formula Chapter 9: Transformations 9.1 Theorems Related to Some Specific Transformations 9.2 Transformation between Systems of Different D Matrices 9.3 Transformation between Dimensional Sets 9.4 Independence of Dimensionless Products of the Dimensional System Used Chapter 10: Number of Sets of Dimensionless Products of Variables 10.1 Distinct and Equivalent Sets 10.2 Changes in a Dimensional Set Not Affecting the Dimensionless Variables 10.3 Prohibited Changes in a Dimensional Set 10.3.1 Duplications 10.4 Number of Distinct Sets 10.5 Exceptions 10.5.1 Dimensionally Irrelevant Variable 10.5.2 In Matrix C, One Row is a Multiple of Another Row 10.6 Problems Chapter 11: Relevancy of Variables 11.1 Dimensional Irrelevancy 11.1.1 Condition 11.1.2 Adding a Dimensionally Irrelevant Variable to a Set of Relevant Variables 11.1.3 The Cascading Effect 11.2 Physical Irrelevancy 11.2.1 Condition 11.2.2 Techniques to Identify a Physically Irrelevant Variable Common Sense Existence of Dimensional Irrelevancy Heuristic Reasoning Tests Combined with Deft Interpretation of Results 11.3 Problems Chapter 12: Economy of Graphical Presentation 12.1 Number of Curves and Charts 12.2 Problems Chapter 13: Forms of Dimensionless Relations 13.1 General Classification 13.2 Monomial is Mandatory 13.3 Monomial is Impossible—Proven 13.4 Monomial is Impossible—Not Proven 13.5 Reconstructions 13.5.1 Determination of Exponents of Monomials The Measurement Method The Analytic Method The Heuristic Reasoning Method 13.5.2 Determination of Some Nonmonomials 13.6 Problems Chapter 14: Sequence of Variables in the Dimensional Set 14.1 Dimensionless Physical Variable is Present 14.2 Physical Variables of Identical Dimensions are Present 14.3 Independent and Dependent Variables 14.4 Problems Chapter 15: Alternate Dimensions Chapter 16: Methods of Reducing the Number of Dimensionless Variables 16.1 Reduction of the Number of Physical Variables 16.2 Fusion of Dimensionless Variables 16.3 Increasing the Number of Dimensions 16.3.1 Dimension Splitting 16.3.2 Importation of New Dimensions 16.3.3 Using Both Mass and Force Dimensions 16.4 Problems Chapter 17: Dimensional Modeling 17.1 Introductory Remarks 17.2 Homology 17.3 Specific Similarities 17.3.1 Geometric Similarity 17.3.2 Kinematic Similarity 17.3.3 Dynamic Similarity 17.3.4 Thermal (or Thermic) Similarity 17.4 Dimensional Similarity 17.4.1 Scale Factors 17.4.2 Model Law 17.4.3 Categories and Relations Categories Relations 17.4.4 Modeling Data Table 17.5 Scale Effects 17.6 Problems Chapter 18: Forty-three Additional Applications References Numerical Order Alphabetical Order (by Authors???Surname) Appendices