Dimensional Analysis And Intelligent Experimentation

by Andrew Clennel Palmer

Overview

Dimensional analysis is a magical way of finding useful results with almost no effort. It makes it possible to bring together the results of experiments and computations in a concise but exact form, so that they can be used efficiently and economically to make predictions. It takes advantage of the fact that phenomena go their way independently of the units we measure them with, because the units have nothing to do with the underlying physics. This simple idea turns out to be unexpectedly powerful.Students often fail to gain from dimensional analysis, because bad teaching has led them to suppose it cannot be used to derive new results, and can only confirm results that have been secured by some other route. That notion is false. This book demonstrates what can be done with dimensional analysis through a series of examples, starting with Pythagoras' theorem and the simple pendulum, and going on to a number of practical examples, many from the author's experience in ocean engineering. In parallel, the book explains the underlying theory, starting with Vaschy's elegant treatment, whilst avoiding unnecessary complexity. It also explores the use and misuse of models, which can be useful but can also be seriously misleading.

Product Details

ISBN-13:	9789812708182
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	06/20/2008
Pages:	164
Product dimensions:	6.08(w) x 9.14(h) x 0.68(d)

Table of Contents

Introduction     1
Motivation: how to get something for nothing     1
Pythagoras' theorem     3
References     9
Numbers and Units in Engineering and Physics     10
Introduction     10
Labels     11
Scales     11
Measurement with units     12
Standardized units     13
Converting from one unit to another     14
Problems     17
References     19
Dimensions, Dimensionless Groups, and Variables     20
The concept of dimension     20
Dimensional consistency     22
Empirical relationships that are not dimensionally consistent     24
Dimensionless groups     26
Variables     28
Problems     30
References     37
Dimensional Analysis     38
Relations between dimensionless groups     38
Proof of Pi theorem     42
Revisiting the example of Sec. 4.2, starting from the Pi theorem     46
Choosing the dimensionless groups and fundamental dimensions in a different way     48
Resistance of ships     50
Heat transfer from pipelines     59
Problems     62
References     72
Similarity and Intelligent Experimentation     74
Similarity     74
Pressure drops in pipes     75
Plows in clay     82
Problems     88
References     91
Equations in Nondimensional Form     92
Motivation     92
Mass-spring systems     92
Laying underwater pipelines     101
Partial differential equations describing fluid flow     106
Problems     108
References     110
Physical Models     112
Introduction     112
Structural models     115
Aerodynamic models     120
Hydraulic models     123
Geotechnical models     128
Problems     130
References     132
Solutions to Problems     135
Introduction     135
Solutions to problems in Chapter 2     135
Solutions to problems in Chapter 3     137
Solutions to problems in Chapter 4     139
Solutions to problems in Chapter 5     147
Solutions to problems in Chapter 6     148
Solutions to problems in Chapter 7     151
References     154