Coefficients for Missing Fittings - Darby 3-K Pressure Drop Formulas

[gwalkerb]

I'm implementing pressure drop calculations in a number of internal sizing tools using the Darby 3-K method. However, a problem I'm running into is finding appropriate coefficients for the actual fittings that we use.

Does anyone know if there are any published coefficients other than what I currently have? My current reference is Table 7.3 from 'Chemical Engineering Fluid Mechanics - 3rd Edition, (Darby, Chhabra)'. But it seems like it is missing details for some of the B16.9 fittings that we commonly use. Any of the data I've found online also seems to just be a summary of this table. For BW 90 degree elbows, it provides data for r/D of 1, 2, 4, & 6 - my intent was to determine the actual r/D for any given B16.9 BW elbow (whether SR or LR), and linearly interpolate between the provided coefficients as needed. The r/D ratio is 1.5 for a LR elbow, but this is based on nominal size, not actual OD, and given that actual diameters are dissimilar from nominal diameters at sizes less than NPS14, the ratio is never actually going to be 1.5. I'm not sure if this is the best method, as the Ki and Kd coefficients are not monotonic across the r/D range, but I'm not sure how else to approach it. As well, because the Kf formula references nominal pipe diameter, and not actual pipe diameter, I'm wondering if that's what I should use for elbow definition.

For 45 degree elbows, it only provides information for threaded and mitered elbows. My understanding is that the Kf value for a 45 degree elbow is not the same as half of a 90 degree elbow, as the pressure recovery characteristics are different, but unless there's coefficients for BW 45 degree elbows out there somewhere, that's how I'll need to proceed.

For tees, the table lists threaded and flanged, but not BW. I am assuming that I can use the flanged coefficients for BW tees, as the design of a flanged tee is basically a BW tee with flanges attached. It's not clear how to approach reducing tees however. Should I calculate it as a non-reducing tee of the larger or the smaller size? Or is there a different approach? This would affect how I calculate my Reynolds number - I'm leaning towards using the smaller of the two sizes, as this is consistent with recommendations in the book when looking at reductions or expansions, but a reducing tee isn't quite the same as a straight reducer.

 

[1503-44]

I don't think that they are missing. I believe that they do not exist in the 3K domain.
Suggest that you default to the KV^2/(2g) method.

Higher accuracy is not usually needed in most cases as clients are afraid of pipe friction loss calculations and always want to increase overall friction loss by at least 10% (or 10 miles for pipelines) anyway. If you have so many fittings that the KV^2 method appears to be insufficient for your needs, you should probably spend more time straightening out your system. Any such calculated differences between fitting friction methods should not be allowed to affect overall system design. Meaning that if there was some difference that indicated you should select ANSI 600# rather than 300#, you would be far better off by selecting the most conservative result or having a serious review of the pipe layout, or perhaps even the original design concept.

“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"

 

[gwalkerb]

Isn't the 3-K method just a more refined method to find the K coefficient? If I'm not using 3-K, I still need to determine a value for K, whether that's the f*L/d from TP410, or one of the 2-K or 3-K methods. The majority of the pressure drop calculations I'll be doing are for gas flow (with some less critical liquid applications), but this is for shop fabricated equipment, not pipelines, so we still use Darcy's formula for incompressible flow, following the limitations outlined in TP410 (i.e. if calculated pressure drop is > 10% of inlet pressure, more refinement is needed). Given that we are looking for system design that limits pressure drop to a minimal value, the 10% limit is not a problem. So 3-K might not provide too much benefit over f*L/d for the conditions I'm looking at, but if there's a method that's more accurate under some conditions, I would prefer to use it even if it's more complicated, as I'm not doing hand calcs here.

I've read many of the previous posts on this site about Crane vs 2-K vs 3-K, including many by Katmar (who seems to be the local expert), but none of them really seem to touch on my questions here. I can just fall back to TP410 equivalent length methods where 3-K data isn't available, it just seemed odd to me that there wasn't data for such common fittings.

 

[1503-44]

Yes I think you can say 3K is a more refined version of the normal K factor, but as I say, I don't think the claimed extra accuracy is worth the wild goose chase in finding them.

For gas flow use the following General Gas Flow in Pipe Equation (for isothermal flow). You must include gas compressibility factor when it is appropriate to do so, (generally when pressure is over 99 psig, or if you are outside normal ambient temperature range) although with computers it doesn't cost a dime to use it all the time. For pipe flow around an equipment skid and fabricated vessels you shouldn't often have pressure drops that exceed 10% of highest pressure, P1, but if you do you can usually take the compressiblity factor at a
Pavg = 2/3*[P1+P2-(P1*P2)/(P1+P2)] to extend that range a bit more, or just break up a long pipe run into shorter pipe segmemts and string the results as you have already mentioned.

General Gas Pipe Flow Equation

Compressibility Factor

These links proclaim their use of Churchill friction factors for gas and liquid flow.
I have not checked their accuracy, but they should get you on your way to some kind of answers. Just be sure to check the results given are reasonable.
[link Pressure drop Excel calculation tool for compressible (= gas) flow, non choked]Churchill for Compressible Gas Flow[/url]
[link Pressure drop Excel calculation tool for incompressible (= liquid) flow]Compressible Liquid Flow[/url]

“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"

 

[1503-44]

Link didn't take so I'll just upload the file

Compressible flow

“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"

 

[1503-44]

Incompressible flow

“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"

 

[gwalkerb]

Thanks for the links! These will be helpful to validate whatever I come up with. Haha, in some ways, my search was driven by laziness originally - if I only had to implement 3-K factors, it would be simpler than implementing multiple K factor methods and choosing the most appropriate or available one.

We always require the use a of Z value when doing any gas calculations - even if it's ~0.99 or similar, requiring it reduces the need to decide if it is necessary or not, and avoids errors due to lack of application. It's almost always readily available from customers, process simulation software, or OEM software, and when that's not available, we use a solver I made based on the Redlich-Kwong equation of state, which agrees with the process simulator values close enough that I would expect that any minor variations in gas mixture would have a much greater effect.

For friction factor, we use an iterative Colebrook-White solver I wrote, but as your link includes a Moody friction factor, it's easy to ensure same inputs are used for checking.

 

[1503-44]

I also use the Redlich-Kwong equation of state and have always found it accurate enough for all my gas design needs, but now use Churhill's friction factor exclusively. Why iterate, even on a computer, when you don't have to plus you also don't have to stop and revert to alternate equations if you happen to wind up with laminar flow. Those advantages make Churchill far superior to the others.

“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"

 

[fel3]

gwalkerb...

Might this help?:

https://neutrium.net/fluid_flow/pressure-loss-from-fittings-3k-method/

============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

 

[georgeverghese]

Using the old fashioned trusty TP 410 method, note that the friction factor to be used for calculating fitting losses is not the Ft value for the flowing condition. It is the value at what Crane calls "fully turbulent conditions" - see Crane for what these values are for any pipe size. There is a formula in Perry for this turbulent flow Ft, but I have yet to check if values generated by this formula match those in Crane. Essentially, the fitting loss at any pipe size is only a function of density and velocity, but the "fully turbulent Ft value" remains the same no matter what your flowing Nre is.

 

[1503-44]

Isn't that Ft a multiplier that you're talking about applied to the pressure loss/unit length of straight pipe that you've already calculated? If so, then Ft may not be dependent on Nre, but the pressure loss/unit length of straight pipe certainly is, so then it follows that the ultimate result, the pressure loss of the fitting, is dependent on Nre. All that, even though as I understand it, losses from fittings are not so dependent on friction anyway, as even a large frictional loss per unit length of fitting x length of fitting wouldn't amount to much of anything.

“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"

 

[georgeverghese]

@axle, For fittings losses, the f value to be used in the f.L/d formula has nothing to do with the flowing f in the pipe. It is a fixed value related to pipe size only - you will see a graph for this in one of the appendices in Crane.