Applied Dimensional Analysis and Modeling
- 2nd Edition - November 27, 2006
- Latest edition
- Author: Thomas Szirtes
- Language: English
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 app… Read more
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
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
- Edition: 2
- Latest edition
- Published: November 27, 2006
- Language: English
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Thomas Szirtes
Affiliations and expertise
Thomas Szirtes and Associates, Inc.
Toronto, Ontario
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