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SOLVING COLEBROOK COLEBROO K EQUA EQUATION TION FOR PIPING DESIGN AND SIZING CALCULATIONS
M Anil Kumar (MS Chemical, IIT Madras, Industrial Consultant)
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Notes
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The ability to simplify means to eliminate the unnecessary, unnecessary, so that the necessary can speak -Hans Hofmann
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COPYRIGHT STATEMENT STATEMENT Published by:
M Anil Kumar 539/5 A N Nivas- Kadirur Tellicherry, Kerala 670642 India © MAnil Kumar This This book book conta contains ins inform informati ation on resear research ched ed by us/ us/ obtai obtained ned from from authen authentic tic and highly highly regar regarde ded d sour source ces. s. Re Reas ason onab able le effo effort rtss have have been been made ade to publ publis ish h reli reliab able le data data and 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 to ensure the correctness and validity of the information or principles for his/her specific application. 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 photocop photocopying ying,, microfilm microfilming, ing, and recordin recording, g, or in any informati information on storage storage or retrieval retrieval system, without written permission from the publishers. Trademark Notice: Product or corporate names mentioned in this book may be trademarks or registered trademarks of the respective owners, and are used only for identification and explanation without intent to infringe.
www.ColebrookEquation.com 5
CONTENTS Preface
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1 Spread Sheet Fundamentals 1. Introduction 2. Spreadsheets 3. Worksheet 4. Cells 5. Cell St Stability 6. Advan Advantag tages es of Sprea Spreadsh dsheet eet Progra Programmi mming ng 7. VBA in Excel
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2 Numerical Capabilities of Spreadsheets 1. Precision 2. Exce Excell Lim Limits its and and Limi Limita tati tion onss 3. Sc Scie ient ntif ific ic/E /Eng ngine ineer erin ing g Limi Limits ts 4. Engi Engine neer erss and and Scie Scient ntis ists ts Can Can Rel Relax ax!! 3 Excel Basics
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19 1. References i. Ente Enterring ing Form rmul ulaas ii. Re Refe ferrence ence by Ra Rang ngee iii. iii. Re Refe fere renc ncee by Ce Cell ll/R /Ran ange ge Name Namess 2. Operators i. Arit Arithm hmet etic ic Oper Operaators tors ii. ii. Comp Compar aris ison on Oper Operat ator orss 3. Functions
4 IF Logical Function 1. Introduction 2. Conditions 3. A Simp Simple le IF equa equati tion on 4. Sim Simple ple IF IF with with re refe fere renc nces es 5. Nested IF 6. Maxi Maximu mum m Num Numbe berr of of Nes Nests ts 7. Inform Informati ation on Func Functio tions ns as as Condi Conditio tions ns within within IF 6
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5 Information Functions 1. ISER SERROR ROR Fun Function 2. Major jor Err Error or Types pes 3. #Div/0! Error 4. #### Error 5. #REF! Error
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6 Circular References 1. Examples 2. Acti Activa vati ting ng Circ Circul ular ar Re Refe fere renc ncee 3. A “Work “Working ing”” Circu Circular lar Refere Reference nce 4. Maximu ximum m Itera terati tio on 5. Maxim ximum Change
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7 Advanced Worksheet Iterations 1. Applications 2. Sim Simple ple Itera terati tio on 3. Unde Underst rstan andi ding ng the the Conv Conver erge genc ncee 4. Var aria iati tion onss of Sa Same me Equa Equati tion on 5. Mech Mechan anis ism m of of Itera terati tion on 6. Time ime Con Consu sume med d for for Iter Iterat atio ion n 7. Optim Optimum um Numb Number er of of Iter Iterat ativ ivee Cycl Cycles es
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8 Controlling Advanced Iterations 1. Concepts a. Itera teratting Cells lls b. Seed c. Counter d. Control Cell e. ON an and OF OFF Co Control f. Reset Control g. Itera terati tio on Cyc Cycles les h. Indicator 2. Creating Seed 3. Intr Introd oduc ucin ing g ON/O ON/OFF FF Cont Contro roll 4. Cr Crea eatting ing a Cou Coun nter ter 5. Cr Crea eatting ing a In Indic dicato ator a. 15 dig digiit pr precision
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b. 5 dig digiit pr precisi ision 6. Cr Crea eati ting ng ON/ ON/OF OFF/ F/RE RESE SET T Cont Contro rols ls 9 Solving of Colebrook Equations 1. Darcy Darcy-W -Wei eisb sbac ach h Equa Equati tion on 2. Moody Diagram 3. Cole Colebr broo ook k Equ Equaatio tion 4. Re Rela lati tive ve Roug oughne hness 5. Solv Solvin ing g Cole Colebr broo ook k Equa Equati tion on
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10 Fixed Point Iteration- Basics 1. Introduction 2. Examples 3. Solution 4. Iteration 5. Fixed Point 6. Fixe Fixed d Poin Pointt with with Col Coleb ebro rook ok Equ Equat atio ion n 7. Dive Diverrgenc gencee C Con ondi diti tion onss
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11 Colebrook Equation – Important Points To Note
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---NOTICE---
By purchasing this book, the purchaser is abide to international copy right rules 1) to pre prevent il illegal co copies of th this work work en entering iin n to to pub publi lic c domai domain n in any form form,, as co comp mput uter er file file or pr prin int t copy 2) To use this book if purchased as software copy (PDF) only in a single computer system
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PREFACE Many Many book bookss exis existt to elab elabor orat atee appl applic icat atio ion n of Exce Excell for for engi engine neer erss and 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 general engineering engineering tasks because because it needed needed sequential sequential intervention 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 in our life) and the comfort is lost. 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. program. I always look look for doing things things well within worksheet! 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 and most importantly in fluid dynamic dynamics. s. All scientists scientists and engineers engineers are not great mathematic mathematicians ians and thus finds it difficult to proceed with “complicated” equations where the parameter x appear on the either side of the equation. We consulted many famous books like Excel Scientific and Engineering Cook Cookbo book ok (by (by Davi David d M. Bour Bourg) g),, Exce Excell for for Sc Scie ient ntis ists ts and and Engi Engine neer erss – 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 as on the publication date.. Engi Engine neeers need need a me meth thod od to solv solvee thou thousa sand ndss of inst instan ance cess with within in thei theirr worksheet with a good degree of simplicity. We worked a great deal on
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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 solver or goal or goal seek. seek. We succeeded and this book share you the findings. This book describes necessary fundamentals for chemical engineers, piping designers, refrigeration experts, ducting engineers, HVAC experts etc. to enable them solve Colebrook equation (and other such implicit equations which converge) in the ease and comfort of a spreadsheet.
ACKNOWLEDGEMENTS Spec Specia iall than thanks ks to seni senior or coll collea eag gue of mine mine,, Mr Meha Mehabo boob ob P K, who remained with constant encouragement and motivations. Encouragements extended by friends and by family members and specially patience extended by my daughter Aradhana in the course of my experimentation and writings are always remembered. Your suggestions to improve this book -M. Anil Kumar
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