Flow resistance in piping bends 5

[MadTech]

I've been comparing Fig 2-16 and the table on Page A29 in Crane Tech Paper 410 which both purport to show Kb versus r/d. The Fig 2-16 shows experimental data for Kb versus r/d which starts at values of Kb about 0.35 to 0.4, dips to about 0.2 at r/d = 4 and rises roughly to a plateau at r/d > say 16. This description is an eyeball fit to the data which has a lot of scatter. If you look at the table on A29, you get a curve which zooms off to a very large number at high r/d and does not show the plateau behavior from Fig 2-16. Note that the definition of Kb excludes resistance due to length alone. However, if you calculate the resistance due to length (KL) and subtract it from the data in A-29, you do now get a curve very similar to what I described above for Fig 2-16. I suspect that the data in A-29 includes resistance due to length as well as due to the flow bending but my problem is that the A-29 table is referred to as Kb not Kt = Kb + KL.

Has MadTech gone mad?

 

[katmar]

I suspect you are correct, and that A-29 includes the effect of the bend as well as the pipe length involved.

A similar discussion was involved in thread378-216873. If you follow my link in that thread to the graph published by Dennis Kirk it tends to confirm this and that the pipe length is a significant contributor to the overall pressure drop.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[MadTech]

I did some more work on this issue and compared in detail the experimental data given in Crane Fig 2-16 with the correlation in A-29 and can only conclude that A-29 is not derived from the data in Fig 2-16 even when we subtract the length effect. I suspect that A-29 comes from some entirely different formulation of bend resistance.

 

[greenche]

Although Figure 2-16 comes from Beij's paper, the data comes from several researchers. Only one of the data sets in Figure 2-16 is from Beij's flow study. It says the data on A-29 are based on the work of Beij. This could mean that there is additional Beij data that A-29 is based on that is not in Figure 2-16. I take Figure 2-16 to be illustrative of the trend rather than intending to provide numbers for practical use. Probably the only chance to really clear it up is to look at a copy of Beij's paper.

 

[DavidOC]

KB in A-29 includes resistance due to the length of the bend. See discussion on P 2-13. Also note the difference between Kb and KB.

 

[greenche]

I was curious so went to the local university library and read Beij's paper, which confirms that the data in Figure 2-16 are based on the curvature and tangent coefficients only and do not include losses due to length.

Beij defines loss in a bend as
H = H_s + [η] [·] U²/2g

where [η] is the sum of the curvature and tangent coefficients. It is [η] that is the y-axis of Figure 2-16 in Beij's paper. H_s is the loss due to pipe length and is defined as

H_s = [λ]_s [·] l/d [·] U²/2g

 

[katmar]

Excellent work greenche. It's great when we have some facts to work with and not just suppositions!

I have always regarded the most important bit of information displayed in Crane Fig 2-16 as being the variation between the different workers findings. The message I get from 2-16 is "don't get too hung up on the accuracy claimed by any one source". BigInch has often said he is happy to achieve a 10% accuracy in an hydraulic calc, and the accuracy on a single element such as a bend is probably much worse than that.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[MadTech]

Thanks all for your contributions! Greenche - what is the lamda term in the Beij paper? And, am I correct in assuming the "l" term is length of the bend (=pi.r/2)?

Is the Beij paper available electronically so I could purchase it?

Does Beij estimate how big are the relative contributions of the 'curvature' and 'tangential' elements of the loss? Crane makes a guess/assumption only (that the curvature and tangential losses in a 90 deg bend are about equal)

Thanks

MadTech

 

[greenche]

I wish a copy machine had been close by; the paper was only in hard copy in a journal. I did not make notes on the equation for H_s. Next time I am at the library I will look again.

 

[MadTech]

Greenche - thanks - if you could get that detail I would appreciate it

MadTech

 

[greenche]

H_s is defined as "the head loss with characteristic velocity distribution in a straight pipe of axial length equal to the distance between the points of pressure measurement."
[λ]_s is defined as "the coefficient of resistance for straight pipe with characteristic velocity distribution."
l is defined as "the length of pipe." From the paper, I take this to mean the length along the center line of the bend curvature.
d is defined as "the diameter of the pipe." From the paper this is further clarified as actual inside diameter.

Beij attempted to measure the loss in the tangent to determine it's contribution to the total but commented "it was found that accurate pressures could not be measured at the downstream end of the bend. It is believed that the disturbed flow and the rusting near or at the piezometer openings were the cause of the inconsistent pressure indications."

Nonetheless, there are separate tangent and deflection (curvature) coefficients tabulated. For bends with R/d <=8, the tangent coefficient is the same (0.18) and it is the deflection (curvature) coefficient that varies.

From the NIST web site, I believe that the paper may be in the public domain. See points 10 & 11 in the below linked FAQ.

http://nvl.nist.gov/nvl2.cfm?doc_id=59

 

[MadTech]

Greenche/Katmar:

I've looked though the internet and could not find a copy of Beij's article. Our local university library has the journal but not back to 1938. Any ideas on how I could get my hands on a copy?

Thanks ... MadTech

 

[greenche]

http://rapidshare.com/files/1703794...r_Fluid_Flow_in_90_Degree_Pipe_Bends.pdf.html

 

[MadTech]

Greenche - thank you very much indeed!

MadTech

 

[vpl]

greeneche ... or one of the 10 lucky people who were able to download the file ...

Would you mind posting it using Engineering.com? Rapidshare puts a limit of 10 downloads on free files.

Patricia Lougheed

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[katmar]

Patricia, it looks like greenche has started the holidays already and as I was one of the lucky 10 I will try to upload it to Engineering.com.

Harvey

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[davefitz]

In addition to the uncertainties from data scatter there is also the issue of the effect of upstream bends and pre-swirl on the pressure drop of the bend in question. If all bends are in the same plane then the pressure drop may be lower than the literature average, but if the upstream bend is out of plane then the bend loss will be larger than the literature average.

 

[vpl]

Thanks Katmar! A star for you.


Patricia Lougheed

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.