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# Applied Dimensional Analysis and Modeling

- 2nd Edition - November 27, 2006
- Author: Thomas Szirtes
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 3 7 0 6 2 0 - 1
- eBook ISBN: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 app… Read more

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Request a sales quote*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

- No. of pages: 856
- Language: English
- Edition: 2
- 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
CanadaRead

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