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Applied Dimensional Analysis and Modeling

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ISBN-10: 0123706203

ISBN-13: 9780123706201

Edition: 2nd 2007

Authors: Thomas Szirtes, Pal Rozsa, P. Rozsa

List price: $170.00
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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. Divided into 4 convenient parts: principle 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…    
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Book details

List price: $170.00
Edition: 2nd
Copyright year: 2007
Publisher: Elsevier Science & Technology
Publication date: 4/27/2007
Binding: Hardcover
Pages: 856
Size: 5.98" wide x 9.02" long x 0.66" tall
Weight: 2.728
Language: English

List of Titled Examples and Problems
Foreword to the First Edition
Foreword to the Second Edition
Preface to the First Edition
Preface to the Second Edition
Organization, Notation, and Conventions
Mathematical Preliminaries
Matrices and Determinants
Operations with Matrices
The Rank of a Matrix
Systems of Linear Equations
Homogeneous Case
Nonhomogeneous Case
List of Selected Publications Dealing with Linear Algebra and Matrices
Formats and Classification
Formats for Physical Relations
Numeric Format
Symbolic Format
Mixed Format
Classification of Physical Quantities
Dimensional Systems
General Statements
Monodimensional System
Omnidimensional System
Multidimensional System
The SI
Preliminary Remarks
Fundamental Dimensions
Derived Dimensionless Units
Derived Dimensional Units with Specific Names
Derived Dimensional Units without Specific Names
Non-SI Units Permanently Permitted to be Used with SI
Non-SI Units Temporarily Permitted to be Used with SI
Prohibited Units
Rules of Etiquette in Writing Dimensions
Other Than SI Dimensional Systems
Metric, Mass-based Systems
CGS System
SI (for reference only)
Metric, Force-based System
American/British Force (Engineering) System
American/British Mass (Scientific) System
A Note on the Classification of Dimensional Systems
Transformation of Dimensions
Numerical Equivalences
Arithmetic of Dimensions
Dimensional Homogeneity
Structure of Physical Relations
Monomial Power Form
The Dimensional Matrix
Generating Products of Variables of Desired Dimension
Number of Independent Sets of Products of Given Dimension (I)
Completeness of the Set of Products of Variables
Special Case: Matrix A is Singular
Number of Independent Sets of Products of Given Dimension (II); Buckingham's Theorem
Selectable and Nonselectable Dimensions in a Product of Variables
Minimum Number of Independent Products of Variables of Given Dimension
Constancy of the Sole Dimensionless Product
Number of Dimensions Equals or Exceeds the Number of Variables
Number of Dimensions Equals the Number of Variables
Number of Dimensions Exceeds the Number of Variables
Systematic Determination of Complete Set of Products of Variables
Dimensional Set; Derivation of Products of Variables of a Given Dimension
Checking the Results
The Fundamental Formula
Theorems Related to Some Specific Transformations
Transformation Between Systems of Different D Matrices
Transformation Between Dimensional Sets
Independence of Dimensionless Products of the Dimensional System Used
Number of Sets of Dimensionless Products of Variables
Distinct and Equivalent Sets
Changes in a Dimensional Set Not Affecting the Dimensionless Variables
Prohibited Changes in a Dimensional Set
Number of Distinct Sets
Dimensionally Irrelevant Variable
In Matrix C, One Row is a Multiple of Another Row
Relevancy of Variables
Dimensional Irrelevancy
Adding a Dimensionally Irrelevant Variable to a Set of Relevant Variables
The Cascading Effect
Physical Irrelevancy
Techniques to Identify a Physically Irrelevant Variable
Common Sense
Existence of Dimensional Irrelevancy
Heuristic Reasoning
Tests Combined with Deft Interpretation of Results
Economy of Graphical Presentation
Number of Curves and Charts
Forms of Dimensionless Relations
General Classification
Monomial is Mandatory
Monomial is Impossible-Proven
Monomial is Impossible-Not Proven
Determination of Exponents of Monomials
The Measurement Method
The Analytic Method
The Heuristic Reasoning Method
Determination of Some Nonmonomials
Sequence of Variables in the Dimensional Set
Dimensionless Physical Variable is Present
Physical Variables of Identical Dimensions are Present
Independent and Dependent Variables
Alternate Dimensions
Methods of Reducing the Number of Dimensionless Variables
Reduction of the Number of Physical Variables
Fusion of Dimensionless Variables
Increasing the Number of Dimensions
Dimension Splitting
Importation of New Dimensions
Using Both Mass and Force Dimensions
Dimensional Modeling
Introductory Remarks
Specific Similarities
Geometric Similarity
Kinematic Similarity
Dynamic Similarity
Thermal or (Thermic) Similarity
Dimensional Similarity
Scale Factors
Model Law
Categories and Relations
Modeling Data Table
Scale Effects
Fifty-two Additional Applications
Numerical Order
Alphabetical Order of Authors' Surnames
Recommended Names and Symbols for Some Physical Quantities
Some More-Important Physical Constants
Some More-Important Named Dimensionless Variables
Notes Attached to Figures
Solutions of Problems
Proofs of Selected Theorems and Equations
Blank Modeling Data Table
Subject Index
Surname Index