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Equivalent Length Calculations For Pipe Fittings And Valves




November 16, 2011 is kind of a momentous day in my life. 25 years ago on this very day a young girl joined hands with me and both of us pledged our love and devotion to each other till death do us apart. This woman has stood by me through all the ups and downs in this long journey of 25 years. She has primarily been responsible for our children growing up as responsible citizens of this society. Today's blog entry is dedicated to my wife Anu and for our silver jubilee anniversary.

Enough of the sentimental stuff. Let's get down to the topic in hand. Equivalent length of pipe fittings and valves has been a topic often debated on engineeering forums and there is a lot of information available freely availbale on the internet related to the subject. In fact our own forum has a very wonderful article devoted to the subject at the following link:

http://www.cheresour.../eqlength.shtml

Crane Technical Paper No: 410, "Flow of Fluids through Valves, Fittings and Pipe" has been the primary source for determining the equivalent length for pipe fittings and valves over the years specifically when you are dealing with turbulent flow and utilizing the Moody Friction factor chart. Crane Paper 410 can be considered a kind of pioneering work in the field of fluid flow and I would recommend all chemical engineers to go throught this "treatise" on fluid flow. The concept of the resistance coefficient 'K' for valves and ffitings was in fact introduced through this paper. One of the limitations of the Crane method for determining the equivalent length was the equivalent lengths for pipe fittings and valves in laminar flow regime. The Hooper 2-K method and the Darby 3-K method could address the calculation of the equivalent lengths in the laminar flow regime by essentially co-relating equivalent lengths as a function of the Reynolds number for a given pipe diameter. For a great discussion on the 2-K method readers can refer the following link:

http://www.cheresour...1882#entry31882

Despite all the hoopla-hoo about the new 2-K and 3-K methods for providing more accurate equivalent length calculations the Crane method for determining the equivalent length still remains universally accepted. Many standard chemical engineering books have utilized the principles of the Crane paper to develop charts for the resistance coefficient 'K' for various fittings and valves which when multiplied with the pipe diameter gives the equivalent length for the particualr pipe fitting or valve. One of the most popular books in the oil and gas field "GPSA Engineering Databook", 11th edition, SI units provides a chart (Fig 17-4) in Section 17, "Fluid Flow & Piping" for the equivalent lengths of the commonly used fittings and valves as a function of the resistance coefficient and the nominal pipe diameter. It however misses out on pipe reduction and pipe exapnsion through concentric reducers / expanders and sudden contraction / expansion.

The main intention of today's blog entry was to provide an excel spreadsheet for equivalent length calculations for pipe fittings and valves using the combination of the GPSA Engineering Databook and the Crane Technical Paper No: 410. The contraction / expansion of pipe has been considered from the Crane Paper 410, since it provides a very comprehensive discussion on how to determine equivalent length for pipe contraction and expansion. For concentric reducers / expanders the actual dimensions are considered for various standard reducers based on ASME B16.9 - "Factory-Made Wrought Buttweld Fittings".

The excel workbook is attached with this blog entry. Hope all of you will enjoy reading this blog entry and find the excel workbook useful. Looking forward to comments from the readers and members of "Cheresources".

MS Excel file available in the Download section at:
http://www.cheresour...pes-and-valves/

Regards,
Ankur.




Hearty wishes for your silver jubilee anniversary. Nice compilation and very useful as a quick reference.
Thanks
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S.Chittibabu
Nov 18 2011 12:25 AM
May all happiness prevails in your life.
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elaheh.ghasemi
Nov 19 2011 03:46 AM
Hi.Have a good life with your wife.
Below is another interesting discussion on the subject:
http://www.chemwork....Correlation.pdf
Thank you for your useful spreadsheet, handy indeed!
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sidibouziane
Dec 03 2011 10:11 AM
you are a blessed gentleman. please continue your devotion, the world still remembers you.

regards
Hi Ankur,
It is very late to say wishes for your silver jubilee anniversary.
Any way nice article.
Thanks,
Manikumar
Hi,
Piping on a process plant does more than run in a straight line. Pipe runs consist of straight lengths of pipe punctuated by any number of fittings - including bends, valves and T-pieces. These impose a pressure drop as they:
  • Change the fluid flow direction
  • Change the size of the cross-sectional flow path, causing the fluid to either accelerate or de-accelerate.
  • Present an obstruction in the flow path.
  • The equivalent equation for pipe fittings is
    Posted Image
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wingsofdreams
Jan 25 2012 04:50 AM
hi...Mr Ankur....

It is very Informative....

Thanks a lot
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th.amitkumar
May 03 2012 11:57 PM
Sir Will you please tell me the criteria of sizing the bypass valve for a controll valve assembly & sizing procedure.

with regards
Amit Kumar
Could you please tell me where you sourced the equation for equivalent length: Le=K1/Ft*d*0.0254 ?

Great spreadsheet! Thanks

Could you please tell me where you sourced the equation for equivalent length: Le=K1/Ft*d*0.0254 ?

Great spreadsheet! Thanks


The equation is the specific modified form for fittings of the Darcy equation as given by equation 2-4 in Crane Technical Paper No: 410M for straight pipe. Equation 2-4 is given as

K = f*L / D --------Eqn 2-4 (Crane Technical Paper 410M)

Re-arranging we get

L = (K / f)*D

Where:

L = Length
K = resistance coefficient
f = friction factor
D = Diameter

The factor 0.0254 is the conversion for inches to meters.

Regards,
Ankur

Ankur,

 

Is the spreadsheet you uploaded with the Crane equations just for expansions and contractions associated with valves?  I am confused why the Crane equations are so different than the ones in the book "Pipe Flow - A Practical and Comprehensive Guide" by Donald Rennels and Hobart Hudson, which I downloaded to Kindle for $51.  There is a full chapter dedicated to expansions and another chapter dedicated to contractions, but to my suprise, the equations in Crane were not used.  Is my thought that the equations used in the book "Pipe Flow" are for expansions and contractions on pipes not associated with valves correct?

 

Trey

Trey,

 

No, the spreadsheet has been programmed for pipe expansion or enlargement and contraction or reduction. Valves have been dealt with separately including full bore and reduced bore with various types such as Gate, Globe, Ball, Check, Plug and Buttetrfly valves.

 

I do not have the book you have mentioned and hence cannot make a comment on the contents of the book.

 

Regards,

Ankur.

Ankur,

 

All the really good parts are not shown in this preview, but take a look and see if you are interested. 

http://books.google....n angle&f=false

Ankur,

 

The reason why I thought Crane's equations for expanders and reducers was only to be used when they are in combination with a valve is because, in the 1995 edition, the equations you used are in a section called "Formulas for Calculating K factors for Valves and Fittings with Reduced Port".  See the seven formulas on page 52.  However, in more modern editions, those equations are now in a section concerning pipe flow - but the equations are the same as in the 1995 edition.  Also, the Crane numbers did not match numbers from Idel'chik (1966 translation) as well as "Pipe Flow - A Practical and Comprehensive Guide" by Donald Rennels and Hobart Hudson (2012) did.  So, I am still confused as to which equations to trust.

Ankur,

 

I am still looking at "Pipe Flow - A Practical and Comprehensive Guide" by Donald Rennels and Hobart Hudson (2012) and one major difference I see is that the angles in your spreadsheet are smaller than the angles calculated in section 11.5 of the book.  Section 11.5 deals with ANSI Expansions.  The higher the angle, the greater the resistance; therefore, you may want to look into that as your angles are non-conservative.  Per the book, only 60% is a straight line and the other 40% is curvy; therefore, the angle will be higher than if a 100% straight line is assumed.

 

Trey

Ankur,

 

Disregard my last comment about the difference in the angles.  The angles turn out to be the same with your method versus the Rennels-Hudson method.

 

Trey

Wait, no - the angles are different!  If you keep the length as taken from ASME B16.9-2003 (page 17-18), then the angles in your spreadsheet are less steep.  When I said they were the same, I was recalculating the length for the conical (straight path) and not using the constant lengths from ASME.

I think for ANSI expansions, the angle should be calculated with this formula

 

=2*ATAN((larger diameter-smaller diameter)/(1.2*Length per ASME B16.9))*180/PI()

 

Also, the Rennels-Hudson method is generally more conservative when comparing apples to apples with the angle set the same.  However, the two methods are in the same ball park for expansions.

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