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SOLVE
COLEBROOK
INSIDE YOUR EXCEL SPREADSHEET
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Notes
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The ability to simplify means
to eliminate the unnecessary,
so that
the necessary can speak
-Hans Hofmann
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69 Pages
COPYRIGHT STATEMENT
Published by:
M Anil Kumar, M.Sc., M.S (IIT)
539/5 A N Nivas- Kadirur
Tellicherry, Kerala 670642
India
© M Anil Kumar
This book contains information researched by us/ obtained from authentic and highly
regarded sources. Reasonable efforts have been made to publish reliable data and
information, but the author and the publisher cannot assume responsibility for the validity of
all materials or for the consequences of their use. The user of information
No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by
any electronic, mechanical, or other means, now known or hereafter invented, including
photocopying, microfilming, and recording, or in any information storage or retrieval
system, without written permission from the publishers.
Trademark Notice: Product or corporate names mentioned in this book may be trademarks
or registered trademarks, and are used only for identification and explanation without intent
to infringe.
This nook is licensed to:
FRPdesigns Consultants Publication Div.
www.ColebrookEquation.com
INDIA 670642
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CONTENTS
Preface
10
1 Spread Sheet Fundamentals
1. Introduction
2. Spreadsheets
3. Worksheet
4. Cells
5. Cell Stability
6. Advantages of Spreadsheet Programming
7. VBA in Excel
12
2 Numerical Capabilities of Spreadsheets
1. Precision
2. Excel Limits and Limitations
3. Scientific/Engineering Limits
4. Engineers and Scientists Can Relax!
16
3 Excel Basics
1. References
i. Entering Formulas
ii. Reference by Range
iii. Reference by Cell/Range Names
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2. Operators
i. Arithmetic Operators
ii. Comparison Operators
3. Functions
4 IF Logical Function
1. Introduction
2. Conditions
3. A Simple IF equation
4. Simple IF with references
5. Nested IF
6. Maximum Number of Nests
7. Information Functions as Conditions within IF
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24
5 Information Functions
1. ISERROR Function
2. Major Error Types
3. #Div/0! Error
4. #### Error
5. #REF! Error
28
6 Circular References
1. Examples
2. Activating Circular Reference
3. A “Working” Circular Reference
4. Maximum Iteration
5. Maximum Change
30
7 Advanced Worksheet Iterations
1. Applications
2. Simple Iteration
3. Understanding the Convergence
4. Variations of Same Equation
5. Mechanism of Iteration
6. Time Consumed for Iteration
7. Optimum Number of Iterative Cycles
34
8 Controls for Advanced Iterations
1. Concepts
a. Iterating Cells
b. Seed
c. Counter
d. Control Cell
e. ON and OFF Control
f. Reset Control
g. Iteration Cycles
h. Indicator
2. Creating Seed
3. Introducing ON/OFF Control
4. Creating a Counter
5. Creating a Indicator
a. 15 digit precision
40
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b. 5 digit precision
6. Creating ON/OFF/RESET Control
9 Solving of Colebrook Equations
1. Darcy-Weisbach Equation
2. Moody Diagram
3. Colebrook Equation
4. Relative Roughness
5. Solving Colebrook Equation
52
10 Fixed Point Iteration- Basics
1. Introduction
2. Examples
3. Solution
4. Iteration
5. Fixed Point
6. Fixed Point with Colebrook Equation
7. Divergence Conditions
56
11 Colebrook Equation – Important Points To Be Remembered
61
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Blank Page
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PREFACE
Many books exist to elaborate application of Excel for engineers and
scientists. Every engineers and scientist use Excel or other worksheet for
their professional calculations.
FORTRAN, which was a sequential programming tool, became unpopular
for general engineering tasks because it needed sequential intervention and
any error in feeding the inputs required that everything is executed again.
Excel being a special calculation tool provides advantages like special data
and inputs (instead of sequential in FORTRAN). Any error in input can be
corrected in a click.
A recent survey indicated that majority of Excel users does not like to use
VBA or Macros because of several reasons. The spatial feel (sense of space
that we have in our life) and the comfort is lost. Many have no time to learn
macros or rather not consider it worthy. Some fear also exists that macros
can erase data and equations or enter values in wrong cells if a minor error
occurs in program. I always look for doing things well within worksheet! It
is like we always wish to do things within than sourcing from outside!
Implicit equations in the form x = g (x) exist everywhere in engineering,
especially in transport phenomena (heat, momentum and mass transfer),
chemical kinetics, and in certain area of physics at many occasions.
We consulted many famous books like Excel Scientific and Engineering
Cookbook (by David M. Bourg), Excel for Scientists and Engineers –
Numerical Methods (by E Joseph Billo), Excel 2007 for Scientists (by Dr.
Gerard M. Verschuuren) etc. to name a few to know how Excel can solve
these equations. There is no treatment of iterative solutions within worksheet
seen in any reference books we could examine.
Engineers need a method to solve thousands of instances within our
worksheet comfortably. We worked a great deal on iterations within
worksheet, how to introduce a iteration, to seed an initial approximation, to
control and to limit number of iterations to a specified times – without using
VBA or Macros or solver or goal seek. We succeeded and this book share
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you the findings.
This book describes necessary fundamentals for chemical engineers, piping
designers, refrigeration experts, ducting engineers, HVAC experts etc. to
enable them solve their implicit equations in great easy and comfort of
spreadsheet.
ACKNOLEDGEMENTS
Our immense thanks to Dr Kumar, (Industrial Consultant, Former Associate
Professor, University of Malaysia), for suggestions to improve this book.
Encouragements extended by family members and friends are immense and
are remembered thankfully.
-M. Anil Kumar
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