Chemical Engineering March 2012 - 55

branches: W-1 and W0, where the latter
is the principal branch. The evolution
of the W function began with
ideas proposed by J.H. Lambert in
1758 and the function was refined
by L. Euler over the subsequent two
decades. Only part of the principal
branch of the Lambert W function
will be used for solving the Colebrook
equation. The equation can be written
in explicit form in an exact mathematical
way without any approximation
involved (Equation 7):
could find application in commercial
software packages.
The Lambert W function is implemented
in many mathematical
systems, such as Mathematica by
Wolfram Research, under the name
ProductLog, or Matlab by MathWorks,
under the name Lambert [30].
Regarding the name of the Cole(7)
Where
x = Re·ln(10)/5.02. Also, procedures
to arrive at the solution of the
reformulated Lambert W function
brook equation, it is sometimes alternately
known as the Colebrook-White
equation, or the CW equation [31].Cedric
White was not actually a coauthor
of the paper where the equation was
presented, but Cyril Frank Colebrook
made a special point of acknowledging
the important contribution of White
for the development of the equation.
So the letter W has additional symbolic
value in the reformulated Colebrook
equation.
Summary of uses
In solving the Colebrook equation approximately,
the trial-and-error method
is obsolete, and the graphical solution
approach is useful only as an orientation.
A spreadsheet solver, such as
Excel, can generate accurate iterative
solutions to the implicit Colebrook equation.
The numerous explicit approximations
available are also very accurate
for solution to the equation. Finally, the
new approach using the Lambert W
function can be useful [32-34].
■
Edited by Scott Jenkins
Author
Dejan Brkić (Strumička
88, 11050 Beograd, Serbia;
Phone: +38 16425 43668;
Email: dejanrgf@tesla.rcub.
bg.ac.rs) received his doctoral
degree in petroleum
and natural engineering from
University of Belgrade (Serbia)
in 2010. He also holds
M.S. degrees in petroleum
engineering (2002) and in the
treatment and transport of
fluids (2005), both from the University of Belgrade.
Brkić has published 15 research papers
in international journals. His research interests
include hydraulics and natural gas. Brkić is
currently searching for a post-doctoral position
abroad.
Circle 10 on p. 70 or go to adlinks.che.com/40265-10
CHEMICAL ENGINEERING WWW.CHE.COM MARCH 2012 39

http://adlinks.che.com/40265-10 http://WWW.CHE.COM

Chemical Engineering March 2012

Table of Contents for the Digital Edition of Chemical Engineering March 2012

Contents
Chemical Engineering March 2012 - Cover1
Chemical Engineering March 2012 - Cover2
Chemical Engineering March 2012 - Contents
Chemical Engineering March 2012 - 2
Chemical Engineering March 2012 - 3
Chemical Engineering March 2012 - 4
Chemical Engineering March 2012 - 5
Chemical Engineering March 2012 - 6
Chemical Engineering March 2012 - 7
Chemical Engineering March 2012 - 8
Chemical Engineering March 2012 - 9
Chemical Engineering March 2012 - 10
Chemical Engineering March 2012 - 11
Chemical Engineering March 2012 - 12
Chemical Engineering March 2012 - 13
Chemical Engineering March 2012 - 14
Chemical Engineering March 2012 - 15
Chemical Engineering March 2012 - 16
Chemical Engineering March 2012 - 17
Chemical Engineering March 2012 - 18
Chemical Engineering March 2012 - 19
Chemical Engineering March 2012 - 20
Chemical Engineering March 2012 - 21
Chemical Engineering March 2012 - 22
Chemical Engineering March 2012 - 23
Chemical Engineering March 2012 - 24
Chemical Engineering March 2012 - 25
Chemical Engineering March 2012 - 26
Chemical Engineering March 2012 - 27
Chemical Engineering March 2012 - 28
Chemical Engineering March 2012 - 29
Chemical Engineering March 2012 - 30
Chemical Engineering March 2012 - 31
Chemical Engineering March 2012 - 32
Chemical Engineering March 2012 - 33
Chemical Engineering March 2012 - 34
Chemical Engineering March 2012 - 35
Chemical Engineering March 2012 - 36
Chemical Engineering March 2012 - 37
Chemical Engineering March 2012 - 38
Chemical Engineering March 2012 - 39
Chemical Engineering March 2012 - 40
Chemical Engineering March 2012 - 41
Chemical Engineering March 2012 - 42
Chemical Engineering March 2012 - 43
Chemical Engineering March 2012 - 44
Chemical Engineering March 2012 - 45
Chemical Engineering March 2012 - 46
Chemical Engineering March 2012 - 47
Chemical Engineering March 2012 - 48
Chemical Engineering March 2012 - 49
Chemical Engineering March 2012 - 50
Chemical Engineering March 2012 - 51
Chemical Engineering March 2012 - 52
Chemical Engineering March 2012 - 53
Chemical Engineering March 2012 - 54
Chemical Engineering March 2012 - 55
Chemical Engineering March 2012 - 56
Chemical Engineering March 2012 - 57
Chemical Engineering March 2012 - 58
Chemical Engineering March 2012 - 59
Chemical Engineering March 2012 - 60
Chemical Engineering March 2012 - 61
Chemical Engineering March 2012 - 62
Chemical Engineering March 2012 - 63
Chemical Engineering March 2012 - 64
Chemical Engineering March 2012 - 65
Chemical Engineering March 2012 - 66
Chemical Engineering March 2012 - 67
Chemical Engineering March 2012 - 68
Chemical Engineering March 2012 - 69
Chemical Engineering March 2012 - 70
Chemical Engineering March 2012 - 71
Chemical Engineering March 2012 - 72
Chemical Engineering March 2012 - 73
Chemical Engineering March 2012 - 74
Chemical Engineering March 2012 - 75
Chemical Engineering March 2012 - 76
Chemical Engineering March 2012 - 77
Chemical Engineering March 2012 - 78
Chemical Engineering March 2012 - 79
Chemical Engineering March 2012 - 80
Chemical Engineering March 2012 - 81
Chemical Engineering March 2012 - 82
Chemical Engineering March 2012 - 83
Chemical Engineering March 2012 - 84
Chemical Engineering March 2012 - 85
Chemical Engineering March 2012 - 86
Chemical Engineering March 2012 - 87
Chemical Engineering March 2012 - 88
Chemical Engineering March 2012 - Cover3
Chemical Engineering March 2012 - Cover4
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/che_may-2024
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/che_april-2024
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/che_march-2024
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/che_february-2024
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/che_january-2024
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/che_november-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/che_december-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering_october-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2023
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-intl-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-intl-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-intl-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-intl-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2022
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2021
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2020
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2019
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2018
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2017
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2016
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2015
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2014
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2013
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2012
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-april-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-march-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-february-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-january-2011
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-december-2010
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-november-2010
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-october-2010
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-september-2010
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-august-2010
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-july-2010
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-june-2010
https://www.nxtbook.com/accessintelligence/ChemicalEngineering/chemical-engineering-may-2010
https://www.nxtbookmedia.com