7/25/2014 Solutions Of Colebrook & White Equation ~ My
Engineering World

http://www.myengineeringworld.net/2011/05/solutions-of-colebrook-white-equation.html
1/7

Solutions Of Colebrook & White EquationWritten by Christos
Samaras on Thursday, 19 May 2011 at 19:26

Problem description

Colebrook & White equation is widely used for calculating
the friction factor in turbulent flows. The equation is difficult
to

be solved by hand, but with nowadays computers we can overcome
this difficulty very fast. The equation is written

below:

Where:

f: friction factor [-]

: roughness [m]

Dh: hydraulic diameter - for pipes is equal to the internal
diameter [m]

Re: Reynolds number [-]

The Reynolds number is calculated by the following formula:

RSS Feed Twitter Google Plus

My Engineering World

+ 48

Follow +1

Follow @MyEnginWorld

Your e-mail address... Submit

Please Join Our New Linkedin Group

Professional Excel Development

Search this blog...

Top 10 Stories

Water Flow Meterbrinstrumentation.in/Enquire_Now

Leading Manufacturer & Supplier of

Water Flow Meter at Best Price.

Hydraulic VanePump

veljandenisondealer.com/Enquire_Now

Wide Range Of Hydraulic Vane

Pumps At Best Price. Corrosion

Resistant.

Tweet

0

1

0

Home Blog Contents About Work With Me ERTAT Add-In Advertise
Here Suggested Books Disclaimer

7/25/2014 Solutions Of Colebrook & White Equation ~ My
Engineering World

http://www.myengineeringworld.net/2011/05/solutions-of-colebrook-white-equation.html
2/7

Where:

V: mean velocity of the flow in the pipe [m/s]

L: pipe length [m]

: dynamic viscosity of the fluid [kg/(ms)]

: kinematic viscosity ( = /) [m/s]

: density of the fluid (kg/m)

Solutions

Here we will discuss about five different approaches to the
above equation. The degree of accuracy differs for each

approach, as well as the level of difficulty.

1. Iteration process

If we rewrite the above equation, it will look like this:

By changing the values of friction factor we can find the
solution using the trial and error method. However, this can

easily be done in an Excel worksheet using goal seek.

2. Swamee Jains equation

The Swamee Jains equation is used in order to find directly the
friction factor in a full-flowing circular pipe. It is an

approximation of the Colebrook & Whites equation.

3. Haaland's equation

Haaland in 1983 simplified the Colebrook & Whites equation
to the following equation:

4. Serghides' equations

The last two solutions are more complicated since they approach
the problem with a set of equations. Serghides'

solution was based on Steffensen's method. The solution involves
the calculation of three intermediate values first and

then substituting those values into a final equation.

Excel VBA Read And Write Text Files

VBA Macro To Open A PDF File

VBA Macro To Convert PDF Files Into Different Format

Draw A Polyline In AutoCAD Using Excel VBA

Numerical Integration In Excel Using The Trapezoidal

Rule

Welding Discontinuities X-ray Films

Open A Google Earth File (kmz) With Google Maps

Fatigue Analysis In Turbomachinery

Open A PDF File With VBA

7/25/2014 Solutions Of Colebrook & White Equation ~ My
Engineering World

http://www.myengineeringworld.net/2011/05/solutions-of-colebrook-white-equation.html
3/7

5. Goudar Sonnad's equations

Goudar Sonnads set of equations is the most complicated of all
the solutions since there are a lot of intermediate

values that should be calculated before the final equation. This
set of equations is given below:

Considering that the iteration process gives the most accurate
results, I have developed an Excel workbook in order to

experiment on the other four solutions/methods. So, with this
workbook you can try it yourself and see which approach

gives results that are closer to the iteration process
results.

How to use it

7/25/2014 Solutions Of Colebrook & White Equation ~ My
Engineering World

http://www.myengineeringworld.net/2011/05/solutions-of-colebrook-white-equation.html
4/7

In the first sheet (named Solutions) fill all the green cells
and press the Solve Equation button. If the flow in the pipe

is turbulent, the sheet will automatically calculate the
friction factor with the five different methods that described
above.

If you press one of the buttons named Roughness, Diameter,
Velocity or Viscosity you will be transferred to the

corresponding sheet. There you can play (loop calculation) with
the corresponding parameter and see how the results

of five methods are affected from the parameters change.
Furthermore, in each sheet there is also a chart which

depicts the results of your loops.

Downloads

This file can be opened with Excel 2007 or newer. For best
results, go to File -> Options -> Formulas tab and put

Maximum Iteration = 30000 (max value is 32767) and Maximum
Change = 0.00001 (or even smaller).

Read also

10 + 1 Ways To Find The Friction Factor In Pipes

Pressure Losses In Piping Systems

Friction Factor Function

Head And Pressure Losses In Pipes

Did you like this post? If yes, then share it with your friends.
Thank you!

Tweet 0 1

Categories: Articles

7/25/2014 Solutions Of Colebrook & White Equation ~ My
Engineering World

http://www.myengineeringworld.net/2011/05/solutions-of-colebrook-white-equation.html
5/7

Newer Post Older Post

Christos Samaras

Mechanical Engineer (Ph.D. cand.), M.Sc. Cranfield University,
Dipl.-Ing. Aristotle University, Thessaloniki - Greece.

Communication: tel. +30-6973513308, e-mail , Facebook , Twitter
, Google+ and Linkedin. Full CV here.

Home

16 Comments My Engineering World Login

Sort by Newest Share

Join the discussion

Reply

Eugene Fang 4 months ago

Thank you very much for this excel sheet

Reply

Christos Samaras 4 months agoAdmin Eugene Fang

You 're welcome, my friend!

Reply

Otieno Otieno D 9 months ago

This is a nice one, it has helped me alot. Thanks alot
Christos.

Reply

Christos Samaras 9 months agoAdmin Otieno Otieno D

You 're welcome, Otieno! It's good to know that it was useful to
someone.

Best Regards,

Christos

Reply

Bkash 9 months ago

Thanks mate... Much appreciated

Reply

Christos Samaras 9 months agoAdmin Bkash

You 're welcome, my friend!

Kind Regards,

Christos

Reply

mike a year ago

how to solve the colebrook equation by just hand calculating? i
find no way. any idea?

thanks.

Reply

Christos Samaras a year agoAdmin mike

Mike, all these equations, as well the equations on the other
post are in reality

approximations of Coolebrook-White formula. You cannot solve
Coolebrook-

White formula by hand, but you can solve the other formulas by
hand. And as

Wikipedia writes The Colebrook equation used to be solved
numerically due to

its apparent implicit nature.

Reply

Vincent Carpenter 6 months ago Christos Samaras

Christos. Kindly note you can solve CW by hand, it just takes a
while.

Typically three iterations are required if the first guesstimate
is

reasonable.

Christos Samaras 6 months agoAdmin Vincent Carpenter

Vincent, thats true, but, what I was implying in the
previous

answer is that there is no DIRECT solution; its not like f

=something, it is friction factor as a function of friction
factor (both

sides of equation include the unknown parameter f). So, of
course

Favorite

Share

Share

Share

Share

Share

Share

Share

Share

Share

7/25/2014 Solutions Of Colebrook & White Equation ~ My
Engineering World

http://www.myengineeringworld.net/2011/05/solutions-of-colebrook-white-equation.html
6/7

Drawing Circles n AutoCAD UsingExcel & VBA

2 comments 5 months ago

Christos Samaras Hi keneshi,The

application that you want to build what will

do?It will design a ductile pipe or

Read DBF Files Using VBA

6 comments 10 months ago

Christos Samaras Good to hear that

your problem was solved!

QWT 2 Get The Unique Values FromAn Excel List

6 comments 11 months ago

Petros Chatzipantazis Christos Thanks

for wrapping up the year with a useful

tip.My favorite tools are:1) Remove

Custom Elevation Function (VBA &Google API)

7 comments 11 months ago

Muhammed Ali AYDIN Thanks Christos

ALSO ON MY ENGINEERING WORLD

Reply

you can do the iterations by hand and get an acceptable
accuracy

after 3-4 iterations, but, again, you can use any of the
alternative

equations

Reply

jack a year ago

thanks for the great work

best regards

Reply

Christos Samaras a year agoAdmin jack

Jack. thank you very much for your kind comment!

Reply

jack a year ago

hi chris

I just want know why Colebrook equation is the most

1

Reply

Christos Samaras a year agoAdmin jack

Hi Jack,

Sorry, but I cannot understand the question. Your comment was
somehow cut in

the middle.

Reply

Christos Samaras a year ago

Hi ma65p,

A short answer will be that the most accurate equation depends
on the input

parameters.

I think that the iterative process gives the best results. Then
are probably the Goudar

Sonnad and Serghides' equations. Excluding the iterative
process, the results are

strongly depended on input parameters (roughness, diameter,
fluid velocity etc.), so in

some cases maybe the Goudar Sonnad is better, while on others
the Serghides.

Because this is unclear, you can run the other sheets of this
workbook in order to

perform a parametric analysis and see which equation is better
for your case.

You can check also this workbook that has more equations.

Kind Regards,

Christos

Reply

ma65p a year ago

Thank you for the spreadsheet. However, what was your conclusion
as to which

approximation was the most accurate?

WHAT'S THIS?

Subscribe Add Disqus to your site

Share

Share

Share

Share

Share

Share

Share

7/25/2014 Solutions Of Colebrook & White Equation ~ My
Engineering World

http://www.myengineeringworld.net/2011/05/solutions-of-colebrook-white-equation.html
7/7

Copyright 2011 - 2014: Christos Samaras Follow us on Facebook ,
Google+ , Twitter & Linkedin