Darby 3-K Method - impact of nominal diameter

[ceprab]

Hello All,

I am working on line sizing for the purpose of putting together a guideline and I have been looking at Darby's 3-K method as the 'latest and greatest'. Working out if it makes a significant impact over the various other methods is separate to this question I want to ask here.

The 3-K formula makes use of the Nominal pipe size i.e. round numbers ignoring wall thickness and inner diameter.
We do a lot of work in the Pharma sector and hence with ASME BPE pipe.
In this grade the inner diameter of smaller sizes 1/4 - 1" can be more similar to the ID of Schedule pipe of the next smaller line size. For 1/2" and 3/4" BPE these correspond reasonably neatly with the IDs for 1/4" and 1/2" Sch40 pipe. For 1" pipe the BPE ID is about halfway between Sch40 1/2" and 1". In the worst case I have bashed out of 1/2" BPE piping this would make approximately 17% difference in the fitting K value - potentially significant given how twisty pharma pipes can get after making sure critical falls are maintained.

Questions:
Is anyone aware of this aspect being considered for the BPE piping/3-K method combination?
Or alternatively, of the impact on the 3-K method of using actual ID instead of nominal ID?

Is this even relevant given that the purpose of this is to determine K values for valves, bends etc - does the Kd fitting value already take this into account?

And, since the Kd parameter was introduced to go from Hoopers 2-K to the Darby 3-K to better fit at larger pipe diameters, would the community recommend ignoring it and using 2K or Crane for these cases.

Phew - a lot of questions there Can anyone shed light?

 

[bimr]

Katmar discusses these issues in the paper on his website.

http://www.katmarsoftware.com/articles/pipe-fitting-pressure-drop.htm#accuracy

As noted in Katmar's paper, for piping sizes between 1" and 24" (typically pipe diamters used in process plants) the differences between these two methods are small and experimental data suggests that both these methods are slightly conservative.

 

[ceprab]

Hi bimr,

Thanks for the link to a useful review.

Unfortunately, the lower limit of that (1") is pretty much the upper limit of where my problems are - beyond that I am happy enough with the methods. As the table about halfway through that link shows, this size is where the 2K and 3K methods start to really diverge (90° bend example).

{Aside; interesting to note: the K values predicted by 3-K in that table are lower at higher pipe diameters than for 2-K, when 2-K (and other methods) underpredicting pressure drop is the main justification for the 3-K method}

Still hoping for any answers as to the justification for using nominal diameter and how to correct it for very different dimensions.

Ceprab

 

[bimr]

The reason for the 1-Inch pipe size cutoff is that these hydraulic equations are not accurate for analyzing flow in very small pipe sizes.

In small diameter pipes the internal roughness can have a major influence on the friction factor. Smaller pipe also causes a greater proportion of the liquid to be in contact with the pipe, which causes higher friction loss. Laminar flow generally happens when dealing with small pipes and low flow velocities. Fluids at low velocities tend to flow without lateral mixing,and adjacent layers slide past one another like playing cards. There are neither cross currents nor eddies. Laminar flow can be regarded as a series of liquid cylinders in the pipe, where the innermost parts flow the fastest, and the cylinder touching the pipe isn't moving at all.

 

[ceprab]

I have contacted Professor Darby to clarify the basis.

The correlation is based on DN because that fits the data better, and goes down to 1/2" Schedule 40 pipe.

As the fluid behaviour will be based on what the fluid 'sees' i.e. the I.D. AND on the dimensions of the fitting I am heading towards the conclusion that I need to look at the pipe r/D ratios to determine the appropriate correlation i.e. as 3/4" BPE spec has the same ID (almost) as Sched 40 1/2" the 3-K method calculation should be used but with a DN value of 0.5 instead of 0.75.

I think the correlation is then unreliable below 1/2" Sched 40 equivalent simply because the data it is based upon (which I haven't seen) don't go there.

So I feel that now I have a view of what I know and don't know and am going to do some cases (laminar, turbulent) for 2-K, 3-K, Crane and 3-K-reducing-the-pipe-size-for-the-calculation as I suggest above. I'm hoping that pushing it to the 1/4" DN (1/2" BPE) looks suitably conservative in these as this will give me a relatively neat 'how to modify 3-K to do small Pharma tube' section in my guideline. It's a pain to have to write that section at all, but it looks like the best option.

The 3-K correlation should take care of laminar flow for the fittings and the e/D ratio should deal with the relative roughness in the pipe.

In general, I would hope to largely avoid pressure drop calculations for such small pipes, but given the Pharma industry scale it is unlikely so I am happier with having had the chance to discuss it. If this thread is still live when I have the results of the cases I suggest I will try to remember to post them here.

 

[katmar]

One of the major problems in calculating resistance factors and pressure drops for pipe fittings is that fittings from different suppliers are not identical to each other, and even from the same supplier manufacturing tolerances are large enough that you will see significant differences when measuring pressure drops in practice. And of course the smaller the pipe, the larger the influence of dimensional variations. This means that the k-values we get from the various methods are "typical" or "average" and not to be regarded as perfectly accurate for all cases.

If you have access to the Crane TP-410 document, read the section around Fig 2-16 which discusses the variation in k-values for bends. This puts the data in perspective and teaches us not to fuss too much about small differences in predicted k-values.

I agree with your proposed exercise of calculating the pressure drops with a variety of available methods. This sort of sensitivity analysis is the best way to see where the potential sources of error are. Unless you have an unusually high number of fittings it is quite likely that the variations in the k-values will have a small impact on the overall pressure drop.

The e/D ratio does not affect the friction factor in laminar flow.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"