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2017 | Book

Some Fundamentals of Dimensional Analysis Read chapter Read first chapter

Dimensional Analysis for Engineers

Authors: Volker Simon, Bernhard Weigand, Hassan Gomaa

Publisher: Springer International Publishing

Book Series : Mathematical Engineering

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

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About this book

This monograph provides the fundamentals of dimensional analysis and illustrates the method by numerous examples for a wide spectrum of applications in engineering. The book covers thoroughly the fundamental definitions and the Buckingham theorem, as well as the choice of the system of basic units. The authors also include a presentation of model theory and similarity solutions. The target audience primarily comprises researchers and practitioners but the book may also be suitable as a textbook at university level.

Table of Contents

Frontmatter
Chapter 1. Some Fundamentals of Dimensional Analysis
Abstract
This chapter provides an introduction into the topic of dimensional analysis. Terms and definitions are given. It is shown what a physical quantity, a base quantity and a quantity system is. Then physical equations and dimensional constants are explained. The Buckingham-Theorem (Pi-Theorem) is derived and explained. Here it is shown that the introduction of non-dimensional quantities reduces the number of dependent variables. This is visualized by a simple example. At the end of Chapter 1 the choice of the base system is discussed and the implications of that choice are highlighted for some examples.
Volker Simon, Bernhard Weigand, Hassan Gomaa
Chapter 2. Model Theory
Abstract
This chapter explains the fundamental of model theory which can be used for obtaining scaled experiments in a laboratory.
Volker Simon, Bernhard Weigand, Hassan Gomaa
Chapter 3. Illustrative Examples
Abstract
This chapter provides several illustrative examples on how to use dimensional analysis in order to obtain the structure of a solution for problems of various areas. The method is applied in this chapter for examples from mechanics, fluid mechanics, thermodynamics, electrical machines, biology,… This shows nicely how powerful and general dimensional analysis can be applied.
Volker Simon, Bernhard Weigand, Hassan Gomaa
Chapter 4. Similarity Solutions
Abstract
As already mentioned, dimensional analytical considerations provide exact results. The solution of a problem is considerably simplified, however in most cases the result must be complemented by experimental evidence or by solving the differential equations describing the problem.
Volker Simon, Bernhard Weigand, Hassan Gomaa
Backmatter
Metadata
Title
Dimensional Analysis for Engineers
Authors
Volker Simon
Bernhard Weigand
Hassan Gomaa
Copyright Year
2017
Electronic ISBN
978-3-319-52028-5
Print ISBN
978-3-319-52026-1
DOI
https://doi.org/10.1007/978-3-319-52028-5

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