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Applied Dimensional Analysis and Modeling
2nd Edition - November 27, 2006
Author: Thomas Szirtes
Hardback ISBN:9780123706201
9 7 8 - 0 - 1 2 - 3 7 0 6 2 0 - 1
eBook ISBN:9780080555454
9 7 8 - 0 - 0 8 - 0 5 5 5 4 5 - 4
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… Read more
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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.
Covers 4 essential aspects and applications: principal characteristics of dimensional systems, applications of dimensional techniques in engineering, mathematics and geometry, applications in biosciences, biometry and economics, applications in astronomy and physics
Offers more than 250 worked-out examples and problems with solutions
Provides detailed descriptions of techniques of both dimensional analysis and dimensional modeling
Upper Undergraduate and First-year Graduate students in Mechanical, Civil, and Aerospace Engineering, students in Materials Engineering, Solid Mechanics, Engineering Mechanics, Professional Engineers in Mechanical, Civil and Aerospace Engineering, Manufacturers of primary structural materials, particularly structural metals like steel and aluminum, Manufacturing Engineers in the Aerospace, Aeronautical and Automotive industries
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
No. of pages: 856
Language: English
Published: November 27, 2006
Imprint: Butterworth-Heinemann
Hardback ISBN: 9780123706201
eBook ISBN: 9780080555454
TS
Thomas Szirtes
Affiliations and expertise
Thomas Szirtes and Associates, Inc.
Toronto, Ontario
Canada