Fundamentals of Dimensional Analysis - Theory and Applications in Metallurgy
This is the first book which systematically describes an integral approach on dimensional analysis. The amount of textbooks on dimensional analysis is huge, however most of the books start with the definition of the relevant variables. When the variables are given to the reader without prior knowled...
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| Main Author | |
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| Format | eBook |
| Language | English |
| Published |
Singapore
Springer Nature
2021
Springer Springer Singapore |
| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9789811616013 9811616019 |
| DOI | 10.1007/978-981-16-1602-0 |
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| Abstract | This is the first book which systematically describes an integral approach on dimensional analysis. The amount of textbooks on dimensional analysis is huge, however most of the books start with the definition of the relevant variables. When the variables are given to the reader without prior knowledge on each problem it has serious consequences: the usefulness of dimensional analysis is not appreciated, is not possible to understand the real challenges of this subject and the result, which is a general relationship with dimensionless groups is useless. This book closes the hole in previous books because in addition to describe step by step how to reach the general relationship with dimensionless groups, which creates solid basis of different metallurgical problems to understand the role of the relevant variables. It provides a full description on how to obtain the experimental data and applies the experimental data to transform the general relationship in a particular solution. Once the reader learns how to design the experimental work and uses that information to define the particular solution, it is possible to asses if the selection of variables was adequate or not. The book is useful for both undergraduate and graduate students. |
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| AbstractList | This is the first book which systematically describes an integral approach on dimensional analysis. The amount of textbooks on dimensional analysis is huge, however most of the books start with the definition of the relevant variables. When the variables are given to the reader without prior knowledge on each problem it has serious consequences: the usefulness of dimensional analysis is not appreciated, is not possible to understand the real challenges of this subject and the result, which is a general relationship with dimensionless groups is useless. This book closes the hole in previous books because in addition to describe step by step how to reach the general relationship with dimensionless groups, which creates solid basis of different metallurgical problems to understand the role of the relevant variables. It provides a full description on how to obtain the experimental data and applies the experimental data to transform the general relationship in a particular solution. Once the reader learns how to design the experimental work and uses that information to define the particular solution, it is possible to asses if the selection of variables was adequate or not. The book is useful for both undergraduate and graduate students. This is the first book which systematically describes an integral approach on dimensional analysis. The amount of textbooks on dimensional analysis is huge, however most of the books start with the definition of the relevant variables. When the variables are given to the reader without prior knowledge on each problem it has serious consequences: the usefulness of dimensional analysis is not appreciated, is not possible to understand the real challenges of this subject and the result, which is a general relationship with dimensionless groups is useless. This book closes the hole in previous books because in addition to describe step by step how to reach the general relationship with dimensionless groups, which creates solid basis of different metallurgical problems to understand the role of the relevant variables. It provides a full description on how to obtain the experimental data and applies the experimental data to transform the general relationship in a particular solution. Once the reader learns how to design the experimental work and uses that information to define the particular solution, it is possible to asses if the selection of variables was adequate or not. The book is useful for both undergraduate and graduate students. This is the first book which systematically describes an integral approach on dimensional analysis.The amount of textbooks on dimensional analysis is huge, however most of the books start with the definition of the relevant variables. |
| Author | Conejo Alberto N |
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| Copyright | 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 |
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| DOI | 10.1007/978-981-16-1602-0 |
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| Snippet | This is the first book which systematically describes an integral approach on dimensional analysis. The amount of textbooks on dimensional analysis is huge,... This is the first book which systematically describes an integral approach on dimensional analysis.The amount of textbooks on dimensional analysis is huge,... |
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| SubjectTerms | Applications of Mathematics Classical Mechanics Dimensional analysis Engineering General References Materials Science Metals & Metallurgy Structural Materials |
| TableOfContents | Title Page
Preface
Table of Contents
1. Introduction
2. Origin and Historic Evolution of Dimensional Analysis
3. Units, Dimensions and Dimensional Homogeneity
4. Dimensionless Numbers
5. Rayleigh's Method
6. Buckingham's π Theorem
7. Step by Step Method (Ipsen's Method)
8. Matrix Method
9. Inspection Method
10. Engineering Problems with and without Experimental Data
11. Applications of Dimensional Analysis in Metallurgy
12. Scaling and Similarity
13. Non-Dimensionalization of Differential Equations
Epilogue Intro -- Preface -- Contents -- About the Author -- 1 Introduction -- 1.1 Nature Is Dimensionless -- 1.2 Advantages and Disadvantages of Dimensional Analysis -- References -- 2 Origin and Historic Evolution of Dimensional Analysis -- 2.1 Origins of Dimensional Analysis -- 2.2 Historic Evolution of Dimensional Analysis -- References -- 3 Units, Dimensions and Dimensional Homogeneity -- 3.1 Units -- 3.1.1 Origin and Evolution of Units -- 3.1.2 Metric System, Base Units and SI -- 3.1.3 New Developments on the Definition of Units -- 3.1.4 Previous Systems of Units -- 3.1.5 Derived Units -- 3.2 Dimensions -- 3.3 Principle of Dimensional Homogeneity -- 3.3.1 Derivation of the Principle of Dimensional Homogeneity [16, 17] -- References -- 4 Dimensionless Numbers -- 4.1 Concept of a Dimensionless Number -- 4.2 Common Dimensionless Numbers -- References -- 5 Rayleigh's Method -- 5.1 John William Strutt [1-4] -- 5.2 Rayleigh's Method -- 5.3 Examples of Application of Rayleigh's Method -- References -- 6 Buckingham's π Theorem -- 6.1 Edgar Buckingham -- 6.2 General π-Theorem -- 6.3 Examples of Application of π-Theorem -- References -- 7 Step by Step Method (Ipsen's Method) -- 7.1 Step by Step Method -- 7.2 Examples of Application of the Step by Step Method -- References -- 8 Matrix Method -- 8.1 Matrix Algebra -- 8.2 Matrix Method -- 8.3 Examples of Application of Matrix Method -- References -- 9 Inspection Method -- 9.1 Inspection Method -- 9.2 Examples of Application of the Inspection Method -- Reference -- 10 Engineering Problems with and without Experimental Data -- 10.1 General Engineering Problems with and without Experimental Data -- 10.1.1 Bubble Shape Dynamics Rising in a Liquid -- 10.1.2 Motion of Non-Metallic Inclusions in Liquid Metals -- 10.1.3 Thermal Stresses in Continuous Casting -- 10.1.4 Mass Transfer Coefficient Under Natural Convection 13.2 Scaling Differential Equations -- 13.3 How to Decrease the Number of Dimensionless Groups -- 13.4 Discriminated Dimensional Analysis (DDA) -- References -- Epilogue 10.1.5 Blast Furnace Raceway Dimensions -- 10.2 Engineering Problems with Experimental Data -- 10.2.1 Deformation of an Elastic Ball Striking a Wall -- 10.2.2 Pressure Drop of a Fluid in a Long Circular Pipe -- References -- 11 Applications of Dimensional Analysis in Metallurgy -- 11.1 Slag Foaming -- 11.1.1 Introduction to the Problem -- 11.1.2 Experimental Data on Foaming Index from Fruehan et al.: [1-9] -- 11.1.3 Experimental Data Including the Effect of Bubble Diameter from Fruehan et al. [4, 5] -- 11.1.4 Experimental Data Including the Effect of Bubble Diameter from Ghag et al. [16, 17] -- 11.1.5 Experimental Database from Pilon et al. [18-22] -- 11.2 Slag Open Eye Area -- 11.2.1 Introduction to the Problem -- 11.2.2 Experimental Data from Yonezawa and Schwerdtfeger [24] -- 11.2.3 Experimental Data from Peranandhanthan and Mazumdar [25] -- 11.2.4 Ladle Eye as a Function of Nozzle Radial Position -- 11.3 Mixing Time in the Ladle Furnace -- 11.3.1 Experimental Data from Pan et al. [32] -- 11.3.2 Experimental Data from Mandal and Mazumdar [33, 34] -- 11.4 Entrainment of Iron Droplets at Liquid/Liquid Interfaces Due to Rising Gas Bubbles -- 11.5 Tundish Open Slag Eye (TOSE) -- 11.6 Liquid Steel Discharge from a Ladle to the Tundish Using a Protective Shroud [57-62] -- 11.7 Teeming of Liquid Steel -- 11.7.1 Experimental Work from Kuwana [65] -- 11.7.2 Experimental Work from Kamaraj et al. [66] -- 11.8 Rate of Consumption of Mold Fluxes -- 11.9 Penetration of a High-Velocity Gas Jet Through a Liquid Surface -- References -- 12 Scaling and Similarity -- 12.1 Introduction -- 12.2 Similarity Criteria -- 12.2.1 Geometric Similarity -- 12.2.2 Materials Similarity -- 12.2.3 Mechanical Similarity -- 12.2.4 Thermal Similarity -- 12.2.5 Chemical Similarity -- References -- 13 Non-dimensionalization of Differential Equations -- 13.1 Introduction |
| Title | Fundamentals of Dimensional Analysis - Theory and Applications in Metallurgy |
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