Dimensional analysis and self-similarity methods for engineers and scientists

Dimensional analysis is routinely used to check the plausibility of derived equations and computations and to form reasonable hypotheses about complex physical situations. Providing a concise and accessible overview of key concepts in dimensional analysis, this book uses engineering and science cases and examples to show the practical use of dimensional analysis and self-similarity methods in solving complex problems. The text presents all of the mathematical steps along with the main equations. The appendix includes two detailed case studies. In addition, the author integrates numerous part figures as well as photos with the examples and cases.

Dimensional Analysis
Introduction
Dimensional Analysis and Scaling Concept
Scaling Analysis and Modeling
Mathematical Basis for Scaling Analysis
Dimensions, Dimensional Homogeneity, and Independent Dimensions
Buckingham's - (Pi) Theorem
Oscillations of a Star
Gravity Waves on Water
Dimensional Analysis Correlation for Cooking a Turkey
Energy in a Nuclear Explosion
Energy in a High-Intensity Implosion
Similarity and Estimating
Self-Similarity
General Results of Similarity
Scaling Argument
Self-Similarity Solutions of the First and Second Kind
Conclusion
References

Similitude Theory and Applications
Introduction
Dimensional Analysis and Physical Similarity
Typical Applications
Dimensional Analysis to Obtain Similarity Parameters
Dimensional Analysis and Similarity
Buckingham Pi Theorem
Determination of Pi Terms
Determination of Pi Terms by Inspection
Common Dimensionless Groups
Purposes and Usefulness of Dimensional Analysis
Development of Prediction Equations
Similarity and Similar System
Dissimilarity and Dissimilar System
Scaling and Scaling Process
Modeling and Similitude
Distorted Models
Nondimensionalization
References

Dimensional Analysis and Intermediate Asymptotics
Introduction
Similarity Solutions for Partial and Differential Equations
Asymptotic Analysis and Singular Perturbation Theory
References

Similarity Methods for Nonlinear Problems
Similarity Solutions for Partial and Differential Equations
Fundamental Solutions of the Diffusion Equation Using Similarity Method
Fundamental Solutions of the Diffusion Equation: Global Affinity
Solution of the Boundary-Layer Equations for Flow over a Flat Plate
Solving First-Order Partial Differential Equations Using Similarity Method
Exact Similarity Solutions on Nonlinear Partial Differential Equations
Asymptotic Solutions by Balancing Arguments
References

Similarity Methods and Dimensional Analysis in Engineering Dynamics
Introduction to Similarity and Analogy
Infinite Dimensional Analysis
Unsteady Motion of Continuous Media and Self-Similarity Methods
Dimensional Analysis and Physical Similarity of Lossy Electromagnetic Systems
Extended Self-Similarity in Geophysical and Geological Applications
Visual Similarity-Based Three-Dimensional Model
References

Appendix A: Simple Harmonic Motion
Appendix B: Pendulum Problem
Appendix C: Some Examples of Dimensional Analysis and Similitude
Appendix D: Similarity Solution Methods for Partial Differential Equations (PDEs), George W. Bluman and J. D. Cole
Appendix E: Some Common Liquids Information