Dimensional Analysis

Practical Guides in Chemical Engineering are a cluster of short texts that each provides a focused introductory view on a single subject. The full library spans the main topics in the chemical process industries that engineering professionals require a basic understanding of. They are ‘pocket publications’ that the professional engineer can easily carry with them or access electronically while working. Each text is highly practical and applied, and presents first principles for engineers who need to get up to speed in a new area fast. The focused facts provided in each guide will help you converse with experts in the field, attempt your own initial troubleshooting, check calculations, and solve rudimentary problems.

Dimensional Analysis provides the foundation for similitude and for up and downscaling. Aeronautical, Civil, and Mechanical Engineering have used Dimensional Analysis profitably for over one hundred years. Chemical Engineering has made limited use of it due to the complexity of chemical processes. However, Chemical Engineering can now employ Dimensional Analysis widely due to the free-for-use matrix calculators now available on the Internet. This book shows how to apply matrices to Dimensional Analysis.

• Practical, short, concise information on the basics will help you get an answer or teach yourself a new topic quickly
• Supported by industry examples to help you solve a real world problem
• Single subject volumes provide key facts for professionals

Practicing engineers (primarily chemical engineers).

Dedication

Chapter 1. Introduction

1.1 Process Development

1.2 Twentieth-Century Revolutions

1.3 Dimensional Analysis

1.4 Summary

Notes and References

Chapter 2. History of Dimensional Analysis

2.1 Pre Joseph Fourier

2.2 Post Joseph Fourier

2.3 Summary

Notes and References

Chapter 3. Dimensions and Systems of Units

3.1 Physical Concept and Physical Quantity

3.2 Physical Magnitude

3.3 Systems of Units

3.4 Heat and Temperature

3.5 Chemical Change

3.6 Summary

Notes and References

Chapter 4. Foundation of Dimensional Analysis

4.1 Introduction

4.2 Developing Dimensional Analysis

4.3 Foundation of Method of Indices

4.4 Dimensional Homogeneity

4.5 Matrix Formulation of Dimensional Analysis

4.6 Identifying Variables for Dimensional Analysis

4.7 Summary

References

Chapter 5. Mechanical/Physical Examples of Dimensional Analysis

5.1 Introduction

5.2 Point Moving in a Circular Orbit

5.3 Volumetric Flow Rate of a Fluid Through a Tube

5.4 Velocity on an Inclined Plane

5.5 Water Flow over a Weir

5.6 Determining Fluid Viscosity

5.7 Kepler’s Second Law

5.8 Fluid Flow in a Circular Pipe

5.9 Summary

References

Chapter 6. Thermal Examples of Dimensional Analysis

6.1 Introduction

6.2 Ideal Gas Law

6.3 Flowing Hot Water Heater (Boussinesq’s Problem)

6.4 Film Coefficient for Batch Mixer Heat Transfer

6.5 Steady State Heat Transfer in Bubble Columns

6.6 Heat Transfer Inside Tubes

6.7 Summary

References

Chapter 7. Mass Transfer and Reaction Examples of Dimensional Analysis

7.1 Introduction

7.2 First-Order, Homogeneous Batch Reaction

7.3 First-Order, Homogeneous Batch Reaction with Agitation

7.4 First-Order, Homogeneous Reaction in a Plug Flow Reactor

7.5 First-Order Reaction Using a Solid Supported Catalyst

7.6 Summary

References

Chapter 8. Dimensional Analysis and Scaling

8.1 Introduction

8.2 Modeling

8.3 Similarity

8.4 Theory of Models

8.5 Summary

References

Chapter 9. An Assessment of Dimensional Analysis

9.1 Scope of Dimensional Analysis

9.2 Uses for Dimensional Analysis

9.3 Limitations of Dimensional Analysis

9.4 Summary

References