Kt factors for larger diameter pipes

[marcoh]

I am looking at the pressure loss for a 500mm diameters pipe system and the loss coefficient chart indicated that the pressure drop for a 45 degree bend is greater than a 90 degree bend?

The table give Kt values as follows:

90 deg , 45 deg
100mm: 0.21 , 0.18
150mm: 0.17 , 0.17
200mm: 0.15 , 0.16
300mm: 0.12 , 0.15
400mm: 0.10 , 0.15
500mm: 0.09 , 0.14

For smaller diameters it predicts that a 90 degree bend will have a larger pressure drop then a 45 degree bend, but the opposite on larger pipes. I would have thought a 45 degree bend would always have a lower pressure loss so am I missing something or is there an error in the table? All other tables I have managed to find only go up to 300mm dia.

 

[katmar]

This trend certainly surprised me. I went to my usual sources of data, and I've found some clues.

Crane TP410 is always the first place to look, but it does not give any data for 45 degree bends (other than threaded elbows). Crane does give a formula for calculating bends of arbitrary angle as a fraction of a 90 degree bend, and this would imply that a 45 degree bend would always have a resistance less than an equivalent 90 degree bend.

My next step is usually Simpson (Chem Eng, April 3, 1978) and at least here I found the source of your confusion. Simpson gives data from various sources and the data you have given is referenced to Hydraulic Institute "Pipe Friction Manual" 3rd Ed, New York, 1961. This data is plotted as K vs ID by Simpson and clearly shows the slope is much flatter for the 45 deg bend than for the 90 deg bend, and that K is higher for 45 deg bends for ID's greater than 200mm. However, on the same graphs, Simpson plots the data attributed to Miller ("Internal Flow", British Hydromechanics Research Association, Cranfield, England, 1971) which shows the more expected behaviour of the 90 deg K always being higher than that for the same size 45 deg bend.

The most recent reference I have is the 3-K method by Darby (Chem Eng, April 2001). Darby gives a formula which results in the 90 deg bend always being higher than the 45 deg bend. He also references the Hydraulic Institute and Miller, but both of these publications are dated 1990 and are presumably updated from the data available to Simpson in 1978.

A disadvantage of Darby's data is that he does not give data for flanged 90 deg elbows with r/d=1.5, although this is probably the most frequently used bend in industry. Also, the data give by Darby for 45 deg elbows is unclear whether he intends it for threaded, flanged (or both) types. Anyway, with a bit of interpolation I have set up some software based on Darby which gives the following data for 500 mm bends with a Reynolds of 1,000,000 and r/d = 1.5
90 deg : K = 0.17
45 deg : K = 0.12

I suspect that the table you have is based on some rogue data from 1961, but hopefully someone who has access to both the 1961 and 1991 Hydraulic Institute publications can tell us whether the data was revised.


Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[BigInch]

Don't know what diagram you're looking at, but the Hydraulic Institute says it should look something like this,

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[katmar]

BigInch, is the graphic you posted specific to 500 mm pipe, or is it for all sizes? I couldn't see any pipe size on it. This graphic would support the numbers I gave earlier for 500 ID pipe, but it would give low numbers for small pipes when compared with other references.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[BigInch]

HI Chart makes no size distinction, only the bend radius, as noted.

Other's do and don't as well, for example
Fith Edition of Piping Handbook has a nomograph that yields equivalent lengths for 45º Ells equal from 60 to 75% of those for a 90º, with the larger diameters (48") towards the 60%, 12" and below towards the 75%.

Bend radius seems more intuitive ot me, as geometic similarities should take precedence over a simple variation of D. In any case the difference is slight and using the average or the most conservative would more often than not do little harm, given the relatively few 45s used in any given system. I'm calling it 70%.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[BigInch]

Addinfo,
This used to be on a Purdue Soils server, but now appears as a broken link.

Table 29. Bend loss coefficients (Schwab et al.,1981)

Bend coefficient, Kb

R/D 45º 90º
0.5 0.7 1.0
1 0.4 0.5
2 0.3 0.4
5 0.2 0.3

I've calculated the % of 90 as,
---------------------
R/D 45º %of 90º
0.5 0.7 70%
1 0.4 80%
2 0.3 75%
5 0.2 67%
---------------------

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[Mech85]

Figure 9.2 "Loss Coefficients, Kb for circular cross-section bends (Re = 10^6)" from the Internal Flow Systems book by BHRA gives the following data for a Reynolds No. of 1,000,000 and r/d = 1.5

90 deg : K = 0.18
45 deg : K = 0.09

Table 32(a) "Typical Resistance Coefficients for Valves and Fittings" from the HI Engineering Databook indicates that a "long Radius Flanged 45 deg Ell" has a K value of just less than 0.1 for a 20 inch diameter pipe - The small log chart is diffuclt to read for the larger pipe diameters. For comparison, a 10 inch pipe has a K value of just over 0.1.

Hope this helps.