Applied Dimensional Analysis and Modeling

Applied Dimensional Analysis and Modeling

2nd Edition - November 27, 2006

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  • Author: Thomas Szirtes
  • eBook ISBN: 9780080555454
  • Hardcover ISBN: 9780123706201

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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.

Key Features

  • 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

Table of 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 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
    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
    17.4.4 Modeling Data Table
    17.5 Scale Effects
    17.6 Problems

    Chapter 18: Forty-three Additional Applications

    Numerical Order
    Alphabetical Order (by Authors’ Surname)

Product details

  • No. of pages: 856
  • Language: English
  • Copyright: © Butterworth-Heinemann 2006
  • Published: November 27, 2006
  • Imprint: Butterworth-Heinemann
  • eBook ISBN: 9780080555454
  • Hardcover ISBN: 9780123706201

About the Author

Thomas Szirtes

Affiliations and Expertise

Thomas Szirtes and Associates, Inc. Toronto, Ontario Canada

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