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2011 | Book | 1. edition

Introduction Read chapter Read first chapter

Dimensional Analysis

Author: Qing-Ming Tan

Publisher: Springer Berlin Heidelberg

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

Dimensional analysis is an essential scientific method and a powerful tool for solving problems in physics and engineering. This book starts by introducing the Pi Theorem, which is the theoretical foundation of dimensional analysis. It also provides ample and detailed examples of how dimensional analysis is applied to solving problems in various branches of mechanics. The book covers the extensive findings on explosion mechanics and impact dynamics contributed by the author’s research group over the past forty years at the Chinese Academy of Sciences.

The book is intended for research scientists and engineers working in the fields of physics and engineering, as well as graduate students and advanced undergraduates of the related fields.

Qing-Ming Tan is a former Professor at the Institute of Mechanics, the Chinese Academy of Sciences, China.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
A physical law or principle is determined through experiment or theoretical work. Through analysis and synthesis, quantities related to physical problems are examined, classified, and related. Correctness is verified according to whether or not the deduction conforms to experiments and observations.
Qing-Ming Tan
Chapter 2. Fundamental Principles of Dimensional Analysis
Abstract
The operation must have a unified measurement unit system. To permit operation related to physical quantities, multiple unit systems must convert to a single unit system
Qing-Ming Tan
Chapter 3. Problems in Fluid Mechanics
Abstract
Application of dimensional analysis to typical problems in fluid mechanics is introduced by using a case study approach, that consists of three steps: 1. analysis of basic physical principles involved in the problem, 2. introduction of governing parameters, and 3. making useful conclusions. Some commonly used similarity criterion numbers derived through mathematical formulation of fluid flow problems are identified. Other similarity criterion numbers for some special problems are given. Flow problems are classified according to flow conditions and corresponding similarity criterion numbers are identified.
Qing-Ming Tan
Chapter 4. Problems in Solid Mechanics
Abstract
Dimensional analysis can be applied to the distribution of deformation and stress in simple structures like elastic beams or plates, to three-dimensional elastic bodies as well as to the stability criterion of an Eulerian column under compression
Qing-Ming Tan
Chapter 5. Heat Conduction and Thermal Stress in Solids
Abstract
Many problems involve effects that interconnect in particular ways and interfere with each other to form distinctive coupling. In other problems, coexisting effects can be considered to be decoupled. This chapter discusses problems related to heat conduction and thermal stress in solids. Generally, effects of heat conduction and thermal stress can be decoupled because the orders of magnitude of characteristic times for these effects differ considerably. The chapter discusses heat conduction, introduces a thermal stress–strain relationship and discusses the similarity law for thermal stress in solids.
Qing-Ming Tan
Chapter 6. Problems of Coupling Fluid Motion and Solid Deformation
Abstract
Some natural phenomena or engineering problems relate to fluid–solid interaction that involves coupling of fluid motion and solid deformation. Typical examples are water hammers and fluttering airfoils; more complex examples include deformation of blood vessels, blood flow, and pulse phenomena in the human body. This chapter uses dimensional analysis to discuss cases related to a water hammer, elastic bearings, fluttering airfoils and vortex-excited vibration of heat exchangers.
Qing-Ming Tan
Chapter 7. Hydro-Elasto-Plastic Modeling
Abstract
A hydro-elasto-plastic model shows fluid-like behavior and solid-like behavior of a body subjected to intense dynamic loading and deformation. Governing parameters and similarity parameters useful in solving real problems of explosion and high velocity impact are given 
Qing-Ming Tan
Chapter 8. Similarity Laws for Explosions
Abstract
This chapter discusses propagation laws of explosion waves and fundamental principles and similarity laws of explosions in engineering technology applications that mainly concern explosive forming, explosive welding and blasting.
Qing-Ming Tan
Chapter 9. Similarity Laws for High Velocity Impacts
Abstract
The antitank rod projectile came into service in the 1960s. Compared with conventional projectile length–diameter ratio of about 4, the rod projectile has length–diameter ratio of about 15 and projectile velocity of about 1.7 km/s, nearly twice the velocity of about 0.8 km/s of conventional projectiles. Rod projectile penetration depth exceeds that of conventional projectiles by as much as 1.7 times.
Qing-Ming Tan
Chapter 10. Normalization in Mathematical Simulations
Abstract
This chapter discusses normalization of functions, algebraic equations, ordinary differential equations and partial differential equations. Examples demonstrate principles and applications of normalization, showing some treatments that seem to be right but are actually wrong and other treatments that are reasonable and effective.
Qing-Ming Tan
Chapter 11. Errata to: Dimensional Analysis
Qing-Ming Tan
Backmatter
Metadata
Title
Dimensional Analysis
Author
Qing-Ming Tan
Copyright Year
2011
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-19234-0
Print ISBN
978-3-642-19233-3
DOI
https://doi.org/10.1007/978-3-642-19234-0

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