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By Thomas Szirtes, Ph.D, P.E., Thomas Szirtes and Associates, Inc.
Toronto, Ontario
Canada
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.
Audience
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
Contents Chapter 1: Mathematical Preliminaries by Pal Rozsa
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
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