Dimensional analysis beyond the pi theorem /

Dimensional analysis beyond the pi theorem /

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Bibliographic Details
Author / Creator:Zohuri, Bahman.
Imprint:Cham, Switzerland : Springer, [2017]
Description:1 online resource
Language:English
Subject:
Dimensional analysis.
Dimensional analysis.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11268842
Hidden Bibliographic Details
ISBN:3319457268
9783319457260
331945725X
9783319457253
Digital file characteristics:text file PDF
Notes:Includes bibliographical references and index.
Summary:Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham's Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First and Second kind. Such solutions are not newly discovered; they have been identified and named by Zel'dovich, a famous Russian Mathematician in 1956. They have been used in the context of a variety of problems, such as shock waves in gas dynamics, and filtration through elasto-plastic materials. Self-Similarity has simplified computations and the representation of the properties of phenomena under investigation. It handles experimental data, reduces what would be a random cloud of empirical points to lie on a single curve or surface, and constructs procedures that are self-similar. Variables can be specifically chosen for the calculations.
Other form:Print version: Zohuri, Bahman. Dimensional analysis beyond the pi theorem. Cham, Switzerland : Springer, 2016, ©20107 331945725X 9783319457253
Standard no.:10.1007/978-3-319-45726-0
Table of Contents:
  • About the Author; Preface; Acknowledgments; About This Document; Contents; Chapter 1: Principles of the Dimensional Analysis; 1.1 Introduction; Units of Force and Mass; 1.2 Dimensional Analysis and Scaling Concept; 1.2.1 Fractal Dimension; 1.3 Scaling Analysis and Modeling; 1.4 Mathematical Basis for Scaling Analysis; Lie Group; 1.5 Dimensions, Dimensional Homogeneity, and Independent Dimensions; 1.6 Basics of Buckinghamś pi (Pi) Theorem; Theory; 1.6.1 Some Examples of Buckinghamś pi (Pi) Theorem; 1.7 Oscillations of a Star; 1.8 Gravity Waves on Water.
  • 1.9 Dimensional Analysis Correlation for Cooking a Turkey1.10 Energy in a Nuclear Explosion; The Method of Least Squares; 1.10.1 The Basic Scaling Argument in a Nuclear Explosion; Derivation of Eq. 1.25; 1.10.2 Calculating the Differential Equations of Expanding Gas of Nuclear Explosion; 1.10.3 Solving the Differential Equations of Expanding Gas of Nuclear Explosion; 1.11 Energy in a High Intense Implosion; Note; 1.12 Similarity and Estimating; 1.13 Self-Similarity; Blasius Boundary Layer; 1.14 General Results of Similarity; 1.14.1 Principles of Similarity; 1.15 Scaling Argument.
  • 1.16 Self-Similar Solutions of the First and Second KindNote; 1.17 Conclusion; References; Chapter 2: Dimensional Analysis: Similarity and Self-Similarity; 2.1 Lagrangian and Eulerian Coordinate Systems; 2.1.1 Arbitrary Lagrangian-Eulerian (ALE) Systems; 2.2 Similar and Self-Similar Definitions; 2.3 Compressible and Incompressible Flows; 2.3.1 Limiting Condition for Compressibility; 2.4 Mathematical and Thermodynamic Aspect of Gas Dynamics; 2.4.1 First Law of Thermodynamics; 2.4.2 The Concept of Enthalpy; 2.4.3 Specific Heats; 2.4.4 Speed of Sound; 2.4.5 Temperature Rise.
  • 2.4.6 The Second Law of Thermodynamics2.4.7 The Concept of Entropy; 2.4.8 Gas Dynamics Equations in Integral Form; 2.4.9 Gas Dynamics Equations in Differential Form; 2.4.10 Perfect Gas Equation of State; 2.5 Unsteady Motion of Continuous Media and Self-Similarity Methods; 2.5.1 Fundamental Equations of Gas Dynamics in the Eulerian Form; 2.5.2 Fundamental Equations of Gas Dynamics in the Lagrangian Form; 2.6 Study of Shock Waves and Normal Shock Waves; 2.6.1 Shock Diffraction and Reflection Processes; References; Chapter 3: Shock Wave and High-Pressure Phenomena.
  • 3.1 Introduction to Blast Waves and Shock Waves3.2 Self-Similarity and Sedov-Taylor Problem; 3.3 Self-Similarity and Guderley Problem; 3.4 Physics of Nuclear Device Explosion; 3.4.1 Little Boy Uranium Bomb; 3.4.2 Fat Man Plutonium Bomb; 3.4.3 Problem of Implosion and Explosion; 3.4.4 Critical Mass and Neutron Initiator for Nuclear Devices; 3.5 Physics of Thermonuclear Explosion; 3.6 Nuclear Isomer and Self-Similar Approaches; 3.7 Pellet Implosion-Driven Fusion Energy and Self-Similar Approaches; 3.7.1 Linear Stability of Self-Similar Flow in D-T Pellet Implosion.

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