Dimensional Analysis: Examples of the Use of Symmetry

Dimensional Analysis: Examples of the Use of Symmetry

by Hans G Hornung
Dimensional Analysis: Examples of the Use of Symmetry

Dimensional Analysis: Examples of the Use of Symmetry

by Hans G Hornung

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Overview

Derived from a course in fluid mechanics, this text for advanced undergraduates and beginning graduate students employs symmetry arguments to demonstrate the principles of dimensional analysis. The examples provided illustrate the effectiveness of symmetry arguments in obtaining the mathematical form of the functions yielded by dimensional analysis. Students will find these methods applicable to a wide field of interests.
After discussing several examples of method, the text examines pipe flow, material properties, gasdynamical examples, body in nonuniform flow, and turbulent flow. Additional topics include waves on a free liquid surface, examples with other fluid properties, and ideal gas equations of state. Figures appear throughout the text, which concludes with a bibliography.

Product Details

ISBN-13: 9780486446059
Publisher: Dover Publications
Publication date: 01/14/2006
Series: Dover Books on Physics Series
Pages: 80
Product dimensions: 5.30(w) x 8.30(h) x 0.30(d)

Table of Contents

Preface
1 Introduction
2 Example of method
  2.1 Restriction of range of interest
  2.2 Application
  2.3 Symmetry arguments
3 Pipe flow
  3.1 Dimensionless variables
  3.2 Symmetry at Re --> 0
  3.3 Symmetry at Re --> infinity
4 Material properties
  4.1 Constitutive equations
  4.2 Simple shear flow
5 Gasdynamical examples
  5.1 Shock waves
    5.1.1 The case [U/square root of (p/rho)] --> 0, weak wave
    5.1.2 The case [U/square root of (p/rho)] --> infinity, strong shock wave
    5.1.3 Gas explosions
  5.2 Space-time analogy, boundary layer
  5.3 Compressible flow with friction and heat transfer
6 Body in nonuniform flow
  6.1 Shear flow
  6.2 Channel flow
  6.3 Inviscid flow with shear
7 Turbulent flow
  7.1 Wall-bounded flow
  7.2 Free shear layer
8 Waves on a free liquid surface
  8.1 Very deep water
  8.2 Shallow water
  8.3 Damping of surface waves
9 Examples with other fluid properties
  9.1 Thermocapillary flow
    9.1.1 Liquid drop in horizontal temperature gradient
    9.1.2 Liquid drop in vertical temperature gradient
  9.2 Viscoelastic flow
10 Ideal gas equations of state
  10.1 Non-relativistic limit
    10.1.1 Ideal Boltzmann gas
    10.1.2 The small entropy regime
  10.2 Black body radiation
Bibliography
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