vzeos (Mechanical)On the equivalent length for the "T" branch.I can only assume that at best-- Crane values have to relate to no flow thru the run and all three diameters the same.
Crane has some info on standard tees. K thru branch = 60f[sub]T[/sub], where 60=(L/D). For reducing tees, take a look at the note in Example 4-14. You might want to do the same.
vzeos (Mechanical)I don't have the manual handy right now. But does it make sense, that L/D of a branch can be independent of flow thru a run AND vice versa?
If by associating f[sub]T[/sub] with the K values you mean why did they use expressions like K=f[sub]T[/sub] x Constant? The only reason I can think of is to avoid re-doing all their flow tests when they switched to K-factors. The early editions of TP 410 used to give only (L/D) values. The easiest way to convert (L/D) values to K-factors is to multiply by f as indicated by the Darcy equation. The Constants that are used today are legacy values from flow tests probably done in the '30s and '40s. I would guess they chose to use f[sub]T[/sub] to match the flow condition of their tests. My problem with this methodology is that (L/D) is not a constant but K is.
Yes this is an interesting phenomena but it is totally 100%technically wrong to do so. As we've been pointing out throughout this thread, the correct method is given by CRANE (and modified with the 2-K and 3-K methods) to separate the calculation for head losses of fittings and valves from that of pipe as it is not correct to use 'f' for fittings and valves in calculating K, period. This is of course unless you are redfining 'K'? Trying to say it can even be appropriate in some cases introduces confusion into a system that is proven to be the correct way to approach hydraulics calculations and a system that has been accepted by industry. Indeed, I'd almost call it a standard at this point in time.
Thank you for your reply. You asserted above that you “can't excuse graduate engineers from not knowing basic hydraulics.” I agree. Before I retired I used to be pretty good at this stuff and I had a number of young engineers working for me. I would never brush off any of my subordinates saying “…it is totally 100% technically wrong to do so” or “…it is not correct to use 'f' for fittings and valves in calculating K, period” without giving an adequate explanation. Assertions are good in politics but basic hydraulics requires sound theories and proofs. I guess you probably didn’t see the equations in my previous post, so I’ll repeat them here with notes. This is the derivation of your equation 7 from your equation 2.
[tt]dP= 0.00000336{fL[sub]eq[/sub]W[sup]2[/sup]/([ρ]d[sup]5[/sup])}[/tt] This is equation 2 in your article.
[tt] = 0.00000336{f(KD/f)W[sup]2[/sup]/([ρ]d[sup]5[/sup])}[/tt] This is equation 2 in which (KD/f) replaces L[sub]eq[/sub].
[tt] = 0.00000336{(Kd/12)W[sup]2[/sup]/([ρ]d[sup]5[/sup])}[/tt] This is equivalent to the previous equation. Note f canceled f and D was replaced by d/12.
[tt] = 0.00000028{KW[sup]2[/sup]/([ρ]d[sup]4[/sup])}[/tt] In this equation d cancels d and the 12 is incorporated into the constant resulting in equation 7 in your article.
These equations show that your equation 7 is implicitly using the actual, flowing friction factor, f, in the pipe!!! If you were to use L=KD/f[sub]T[/sub] you would not be able to derive equation 7 from equation 2 (the Darcy equation)!!
Yes - Crane's use of the expression
K=f[sub]T[/sub] x Constant
is exactly my objection.
I accept that they had a lot of legacy data that needed to be converted, but calling the conversion factor f[sub]T[/sub] is what has introduced the confusion. Crane noticed that the friction factor in pipe, and the K value for fittings such as bends, varied with the diameter of the pipe at the same rate (assuming turbulent flow). It was convenient to link the K values to the friction factors because they (i.e the friction factors) were well documented. Strictly the changes in friction factor and K values are consequenses of the change in pipe size but Crane have made it appear that the change in the friction factor is the cause and the change in the K value is the consequense of this.
It may seem that I am splitting hairs with this definition, but the confusion amongst experienced engineers in this thread is proof of my claims.
I am not sure what you mean by "My problem with this methodology is that (L/D) is not a constant but K is." Do you mean that K is a constant in Crane's methodology, or that K is a constant in fact? The fact is that for turbulent flow in a given pipe size K is more constant than (L/D).
Your diligent re-processing of pleckner's example proves the case. Given that we have turbulent flow and a fixed pipe size, we can take K values as virtually constant. However, when we use the (L/D) method we are saying that a fitting is equivalent to a certain length of pipe, and if the characteristics of the pipe (i.e. its friction factor) changes then of course the length of the pipe that would give rise to an equivalent pressure drop must change too.
For example, water flowing at 2 m/s through a standard radius 90 degree 4" bend (K=0.24) will result in a pressure drop of 480 Pascal. This pressure drop will be virtually the same irrespective of the material or roughness of the bend, provided that the bends are geometrically identical. Pleckner also stated this (22 Dec 06, 18:37) - "..we all agree that we do not adjust the K value for the fitting according to the actual pipe friction factor..." vzeos, I noticed that you do not agree with this and I think this is something you need to re-examine. You stated (23 Dec 06, 10:12) "If you are using cast iron pipe or plastic pipe or any other pipe material, you need to use an f[sub]T[/sub] value appropriate to your pipe diameter and your pipe roughness." This is probably our main point of disagreement. Please re-read my post of 22 Dec 06, 15:51 where I described the elements that make up the pressure drop through a bend, or read the original in Crane 410 page 2-12.
If the pipe attached to this bend was commercial steel pipe with a roughness of 0.05 mm then that pipe would have a pressure drop of 366 Pascal/meter. The bend is therefore equivalent in pressure drop to 480/366 = 1.311 meter of this pipe. Since the ID of Sch40 pipe is 0.102 m the L/D ratio for this pipe is 1.311/0.102 = 12.86
However, if the attached pipe was highly polished with a roughness of 0.0015 mm then the pressure drop in the pipe would drop to 307 Pascal/meter. The pressure drop through the bend is now equivalent to 480/307 = 1.564 meter of the polished pipe and the L/D ratio becomes 1.564/0.102 = 15.33
This is exactly what you have done in your re-work of Pleckner's example. You have taken the K values as a given (i.e. constant) and workeded out the length of the actual pipe that is truly equivalent to that K value by applying the friction factor in that pipe, so the calculation has to come back to the same answer.
I'm afraid I have to disagree with Pleckner's analysis of your calculation where he says "This is an interesting phenomenon but it is totally 100% technically wrong ." What you have proven is no phenomenon - it is a bog standard hydraulic calculation and it is 100% totally technically defensible.
Well, it's Christams Eve so we should take time out to celebrate what we do agree on. I wish you all a peaceful time over the holidays.
First off, your implications that I would "bush off" a young engineer with a statement of "just do it" without the reasons behind it is totally unfounded. For this specific topic, I would give, and have given many engineers my paper.
Second, if you read (or reread my paper more carefully) you will see that:
(a)Equation 2 in my article is one of the forms of the Darcy Weisbach equation and is actually taken from CRANE's equation 3-5, Page 3-2. As I us it, it is specifically for pipe only.
b)For valves and fittings, you can't replace Leq with (KD/f). The definition of K as given in CRANE is that K is a function of fT, NOT f so as I explain in my paper you would need to replace Leq with [KD/(fT)]. Therefore, "f" will not cancell "fT" in your analysis of the equations I show.
Third, my equation 7 is one of the forms of CRANE's equation 3-14, Page 3-4. It is indeed used to calculate head loss for valves and fittings and valves and fittings ONLY because of the use of K as shown. Again, this goes back to the definition of K, that being a function of "fT" and NOT "f". To get the total head loss, one would add the results of equation 2 to equation 7.
And I think this is exactly where Harvey has his trouble with CRANE (and I can NOW agree with Harvey on this) because they totally confuse us by implying on page 3-4 that "f" and "fT" are the same. However in my paper I show how CRANE's use of the equality K=(f)L/D cannot be as shown and is really K=(fT)L/D.
So your concluding statement, "These equations show that your equation 7 is implicitly using the actual, flowing friction factor, f, in the pipe!!! If you were to use L=KD/fT you would not be able to derive equation 7 from equation 2 (the Darcy equation)!!" is just wrong (NOTE: I didn't devrive the equations, I extracted them from CRANE and provided the appropriate references to show this in my paper). And, if you don't want to or can't agree with this, then so be it; we'll just have to agree to disagree. And you can tell Hooper and Darby that they too have misinterpreted the use of fT in their 2-K and 3-K methods, respectively.
Again to all, Happy Holidays. What a great discussion. Many more to come from all of us in the coming year!!
I once saw a posting that said that ‘Crane’s TP 410 is the piping engineer’s Bible.’ I guess this means that many people quote it; few people read it and fewer still understand it. My problem with Crane’s methodology was that I didn’t fully understand what I read. I re-read pages 2-8 and 2-9 and jotted the following notes:
Note 1)K=f(L/D), f is the Darcy friction factor.
Note 2)K is constant for all conditions of flow.
Note 3)L/D for any given valve or fitting must vary inversely with the change in friction factor for different flow conditions.
Note 4)K is a constant for all sizes when geometric similarity exists.
Note 5)Because of geometric dissimilarity, K for a given line of valves or fittings tends to vary with size
Note 6)L/D tends toward a constant for the various sizes of a given line of valve or fitting at the same flow conditions.
Note 7)K values are given as the product of the friction factor for the desired size of clean commercial steel pipe with fully turbulent flow, and a constant.
To put this together, take a look at PIPE ENTRANCE, Inward Projecting, for which K=0.78. This K-factor is constant for all sizes (Note 4) and applies to all flow conditions (Note 2). When you write the Darcy equation,
0.78=f(L/D),
f will vary with condition of flow and L/D will vary inversely with the change in f (Note 3) to maintain the numerical constant. So the equivalent length for any flow condition is calculated as
L=0.78D/f
Now, take a look at STANDARD ELBOWS, 90, for which K=30f[sub]T[/sub]. This K-factor is not constant for all sizes (Note 5), (Note 6). Specific K values need to be calculated for specific sizes (Note 7). So, for a 2” pipe, f[sub]T[/sub]=0.019 and K=(30)(0.019)=0.57. This K value is constant for 2” pipe and for any flow condition (Note 2). When you write the Darcy equation,
0.57=f(L/D),
f will vary with condition of flow and L/D will vary inversely with the change in f (Note 3) to maintain the numerical constant. So the equivalent length for any flow condition is
L=0.57D/f
To put it generally for K-factors involving f[sub]T[/sub],
K= f[sub]T[/sub]x(Constant1) = Constant2 = f(L/D)for any flow condition !
I must compliment you on an exceptionally well argued posting. And I chuckled over your Bible analogy, although I suspect it may ruffle a few feathers....
You have summarised 20+ pages of postings into a nice concise set of rules. Can we call these Vzeos' 7 Commandments? In my original gripe session I complained (1) that Crane was confusing and (2) that it did not apply to non-fully-turbulent conditions. Well, your 7 Commandments now remove the confusion problem and we had all pretty much agreed that for full coverage of all flow regimes it is best to use the Hooper or Darby methods.
In an offline discussion with one of the other participants I presented some calculations I had done to check the validity of the Equivalent Length or (L/D) method. I have said before that I like (L/D) but these calcs really brought home the usefulness of this method to me. I back-calculated the (L/D) for a standard radius bend in a Sched 40 pipe from the K value derived from the 3-K method. All the calcs assumed water flowing at 2 m/s. This calc confirmed that under these conditions for pipe sizes from 1" to 24" the Equivalent Length of the bend was (rounded to 2 significant digits) 13. This confirms the Crane value of 14, which was probably set just a little bit conservatively to cover their experimental variations.
I then did the same calculation for molasses flowing with a Reynolds number of 26 in a 12" pipe. Amazingly (to me) this gave an (L/D) value of 13 as well. Add to this mix the calc that I posted (on 24 Dec 06 5:49) where I back calculated the (L/D) for a bend in terms of very smooth 4" pipe and got 15. To me, this confirms that the L/D method is far more universally applicable than Crane's version of K values.
In summary I would say
1) For fully developed turbulent flow it is fine to use the Crane method for all materials, but apply vzeos' 7 Commandments (i.e. use the f[sub]T[/sub] values on page A-26 and not the actual friction factor in the pipe). Umpteen million successful calcs have been done this way by all of us.
2) For preliminary or non-mission-critical calcs it is fine to use the (L/D) method for all materials and for all flow regimes. Errors up to 20% may be expected - which we should be allowing for at the prelim stage anyway. The (L/D) method is MUCH easier to apply because there are no intermediate calcs necessary to get the K value. For example, for a standard 90 degree bend (L/D) is 14. Period. That's it. Just remember one number.
3) For serious calcs write or buy some good software based on Darby's 3-K method. In all honesty, this method is just too complex to use for hand calcs. What you gain in theoretical accuracy you will risk losing through arithmetical errors. Use a spreadsheet at the very least. (Note: I have no software to offer in this regard. This is not a plug.)
Thanks to all for a very interesting discussion - I must admit I now have a much better feel for the whole problem.
Thanks for your kind words. If you need to codify my notes you may want to call them Crane’s Stipulations or Crane’s Postulates.
I would expand on your first summary point: (i.e. use the f[sub]T[/sub] values on page A-26 and not the actual friction factor in the pipe to determine the K-factor. For diameters not covered in A-26 you may use the von Karman equation with your actual diameter to determine f[sub]T[/sub] but you must use the roughness of clean commercial steel pipe (about 0.0018) regardless of the your pipe material. The roughness of your pipe is used in determining, f, the Darcy friction factor. This is how the K-factor is translated to materials other than clean commercial steel.).
We should be grateful to Pleckner for bring to light the dP Paradox: the impossible situation in which two calculation methods leads to two entirely different dP values even though both methods are based on the Darcy equation and the empirical data is the same for both methods. Of course, Pleckner’s Paradox is the result of plausible reasoning leading to an incorrect result. Perhaps we can get Pleckner to revise and amend his article to include Crane’s Stipulations and a third calculation method outlining the correct way to calculate equivalent lengths. This would be a great service to the industry.
Referencing your December 27 post (how can I not respond after taking that shot?):
It is apparent that since this thread has grown to such an enormous length, the meaning of my paper and all of previous responses have been lost, forgotten or just ignored.
The whole meaning of my paper was simply, do not combine equivalent lengths of valves and fittings with straight line length and use the Darcy equation with the actual pipe flow friction loss to calculate total head loss. Head loss for valves and fittings (whether you want to use K or equivalent lengths) should be calculated using the Darcy equation and the Darcy friction factor at complete turbulence and this should be added to the head loss of the pipe using the Darcy equation and the Darcy friction factor at actual flow. That’s all my paper was saying.
In trying to summarize something as comprehensive as CRANE TP410 into several simple rules, it is not surprising that some things could be lifted out of context and / or some details can be omitted. I would like to address some of vzeos’ seven notes that have been dubbed “Crane’s Stipulations” by Harvey (katmar).
Note 1 states, “K=f (L/D), f is the Darcy friction factor”
When dealing with valves and fittings, the Darcy friction factor to be applied is the friction factor at fully turbulent flow. It is not the actual fluid flow friction factor in the pipe. Most of us have agreed with this before, see above posts, again.
Note 2 states, “K is constant for all conditions of flow.”
The reasoning for this conclusion is left out in this short statement but should be understood by everyone. CRANE, Page 2-8 says:
============================================================
“Pressure losses in a piping system result from a number of system characteristics, which may be categorized as follows:
1. Pipe friction, which is a function of the surface roughness of the interior pipe wall, the inside diameter of the pipe, and the fluid velocity, density and viscosity…
2. Changes in direction of flow path
3. Obstructions in the flow path
4. Sudden or gradual changes in the cross-section and shape of the flow path
In most valves or fittings, the losses due to friction (Category 1 above) resulting from actual length of flow path are minor compared to those due to one or more of the other three categories listed. The resistance coefficient K is therefore considered as being independent of friction factor or Reynolds number, and may be treated as a constant for any given obstruction (i.e. valve or fitting) in a piping system under all conditions of flow, including laminar flow.”
===========================================================
CRANE engineers recognized that there is a frictional loss component but are declaring this small in comparison, so for practical purposes they suggest it is to be ignored. Obviously, Hooper and Darby don’t agree and neither do we…see above posts, again.
Note 6 states, “L/D tends toward a constant for the various sizes of a given line of valve or fitting at the same flow conditions.”
I ask, which flow conditions? The flow conditions of complete turbulence. The complete paragraph reads:
“Based on the evidence presented in Figure 2-14, it can be said that the resistance coefficient K, for a given line of valves or fittings, tend to vary with size as does the friction factor, f, for straight clean commercial steel pipe at flow conditions resulting in a constant friction factor and that the equivalent length L/D tends toward a constant for the various sizes of a given line of valve or fitting at the same flow conditions.”
I interpret this as saying that as the fitting sizes were changed, the flow was maintained so as to produce a constant friction factor. The only flow condition that I know of where friction factor would be a constant almost all the time (for a given size) would be at fully turbulent flow.
Note 7 states, “K values are given as the product of the friction factor for the desired size of clean commercial steel pipe with fully turbulent flow, and a constant.”
The complete sentences are: “These coefficients are given as the product of the friction factor for the desired size of clean commercial steel pipe with fully turbulent flow, and a constant, which represents the equivalent length (L/D) for the valve or fitting in pipe diameters for the same flow conditions, on the basis of test data. This equivalent length, or constant, is valid for all sizes of the valve or fitting type with which it is identified.”
Note in CRANE, Page 2-10 continues with the relationship between K of fittings and valves and flow in the zone of complete turbulence.
Then in vzeos’ post an example is presented that attempts to relate K=fT (L/D) with f (L/D), followed by the statement, “Therefore, the commonly held belief that Crane’s equivalent lengths apply only to fully developed turbulent flow is a myth .”
I’m sorry vzeos that you can’t see the concept that Crane’s equivalent lengths for valves and fittings only apply to fully developed turbulent flow.
I will admit, again, as I did in a previous post that CRANE in their discussions makes it confusing. But when reading the whole manual without taking anything out of context as has been the case throughout these posts and observing how CRANE uses the various friction factors in their example calculations, it is clear which Darcy friction factor is to be applied in which situation. It is clear, at least to most of us who have participated in this thread, that the head loss for valves and fittings is to be based on the friction factor at fully turbulent flow; use K, use equivalent lenghts, I don't really care, just use fT.
An finally, to respond to vzeos’ statement,
“We should be grateful to Pleckner for bring to light the dP Paradox: the impossible situation in which two calculation methods leads to two entirely different dP values even though both methods are based on the Darcy equation and the empirical data is the same for both methods. Of course, Pleckner’s Paradox is the result of plausible reasoning leading to an incorrect result. Perhaps we can get Pleckner to revise and amend his article to include Crane’s Stipulations and a third calculation method outlining the correct way to calculate equivalent lengths. This would be a great service to the industry.”
I don’t see any dP Paradox, only your lack of understanding as to how to apply CRANE’s results. And in order to execute this “great service to the industry” I invite any specific comments on where I need to amend or revise anything that is contained in any of the papers I've written. I’m not afraid to admit where I am wrong, I’ve actually already had to make a correction in my example calculation thanks to a reader pointing out an oops. And since my paper is really only an explanation of how one should apply CRANE’s procedure in calculating a piping system, perhaps you should also write to CRANE asking them to make some revisions and amendments to TP410 before those of us in industry continue to recommend that young engineers purchase this document?
Believe me, I’m not taking this huge amount of time in responding to your comments because of hurt feelings or trying to justify what is written in my paper. We’re all big boys and been around for some time. I’m more concerned that a young engineer will read this post and get the wrong idea on what to do.
pleckner, the reason there appears to be so much disagreement amongst us is that we have all been guilty of making statements and not defining the world in which we believe those statements to be true. In the realm of pressure drop calculations there is the World according to Crane 410 and then there is the World as it truly is.
As an illustration of this, let us take the example you used in your paper. In your discussion after the table giving the results of the example you say yourself
"One can argue that if the fluid is water or a hydrocarbon, the pipeline friction factor would be closer to the friction factor at full turbulence and the error would not be so great, if at all significant; and they would be correct."
In the World according to Crane 410 it is clear that using the traditional (L/D) method results in an overstatement of the pressure drop. However, in the World as it truly is the K values you have calculated using Crane are not correct because the actual Reynolds number in your example is far away from the zone of complete turbulence. If you calculate the K values using Darby's 3-K method you will find that in the World as it truly is the (L/D) method is the more accurate of the two results that you presented.
Similarly, you took vzeos to task for saying "Therefore, the commonly held belief that Crane’s equivalent lengths apply only to fully developed turbulent flow is a myth." In the World according to Crane 410 vzeos may be wrong, but I have proven to my own satisfaction that in the World as it truly is vzeos is 100% right. We have to see the context in which the statement is made to be able to say whether it is true or not.
If your motivation really is to avoid giving young engineers wrong ideas, then I question your summing up of the results of your article where you said (27 Dec 06, 19:08)
"The whole meaning of my paper was simply, do not combine equivalent lengths of valves and fittings with straight line length and use the Darcy equation with the actual pipe flow friction loss to calculate total head loss. Head loss for valves and fittings (whether you want to use K or equivalent lengths) should be calculated using the Darcy equation and the Darcy friction factor at complete turbulence and this should be added to the head loss of the pipe using the Darcy equation and the Darcy friction factor at actual flow. That’s all my paper was saying."
You fail to point out that this is true in the World according to Crane 410, but false in the World as it truly is. Any young engineer trying to do calculations at low or intermediate Reynolds numbers needs to know this.
Anyone reading the above may conclude that I have a very negative opinion of your paper, and I would like to point out here that your article was one of the most useful resources to me when I was trying to resolve the confusion in the Crane method for myself. You did a great job in highlighting the hidden traps in Crane, long before I saw them myself, but maybe vzeos is right and you need to update the paper and particularly explain that it is now known that K values are not constant for all flow conditions (and especially not in laminar flow).
Fortunately for us, the overwhelming majority of hydraulics questions that we face have the same answers in the World according to Crane 410 and in the World as it truly is because we normally work with fully developed turbulent flow in steel pipe. And this was even more true in 1976 when Crane put forward their method. These days there is an increasing use of plastic and smooth alloy pipe where the low relative roughnesses mean that we are often not as close to full turbulence as we would have been with steel pipe. Also, we are expected to work to ever tightening tolerances so any advance we can make in getting to more accurate and reliable pressure drop estimates should be embraced. We need to understand the shortcomings of any methods that we use and to use them only where they are applicable. Your paper also makes this point (i.e. that we should continually strive for improvement).
There is one statement that you made in your latest post that I would appreciate you expanding on. While discussing the elements that make up the pressure drop through a fitting you stated
"CRANE engineers recognized that there is a frictional loss component but are declaring this small in comparison, so for practical purposes they suggest it is to be ignored. Obviously, Hooper and Darby don’t agree and neither do we."
Please can you give the references to where Hooper and Darby state that the frictional component is not small. My reading of both of these authors is that they see the K values increasing at low Reynolds numbers, but I cannot find the link to this being due to friction becoming more important at these low Reynolds numbers. Indeed, my observation that the (L/D) of a fitting remains virtually unchanged as we move into laminar flow makes me believe that the proportion of the pressure drop due to friction remains largely unchanged in the World as it truly is. But I would be happy to defer to these authors if they believe otherwise.
You got a great way with words and I basically agree with your comments in your last post and I thank you for them. I need to again clarify some things.
I don't think I fail to point out where I'm coming from in my paper. My whole article is indeed based on the World of CRANE 410 and I say this almost right up front.
In the second section of the paper, RELATIONSHIP BETWEEN K, EQUIVALENT LENGTH and FRICTION FACTOR, I start the process of discussing why I think equivalent lengths are beng applied incorrectly with this sentence:
"The following discussion is based on concepts found in reference 1, the CRANE Technical Paper No. 410."
So when you say, "You fail to point out that this is true in the World according to Crane 410, but false in the World as it truly is.", I think my sentence covers the former quite sufficiently. I agree that I don't specifically say it is not based on the "World As It Truly Is" because it isn't and I don't lead anyone to believe it is! Most engineers' hydraulic calculations are still typically based on CRANE.
However, to address the latter fact, I indeed do introduce the "World as it truly is" at the end of my paper. I include a section called, "Final Thoughts - K Values" where I discuss Hooper and Darby and how they are the more correct way in performing the calculations. However I also point out that:
"The use of the 2-K method has been around since 1981 and does not appear to have “caught” on as of yet. Some newer commercial computer programs allow for the use of the 2-K method, but most engineers inclined to use the K method instead of the Equivalent Length method still use the procedures given in CRANE. The latest 3-K method comes from data reported in the recent CCPS Guidlines4 and appears to be destined to become the new standard; we shall see."
So this is why, when I wrote my paper, there was not a more comprehensive comparison in calculational methods. I don't think this is a disservice because when I wrote the paper (a couple of years ago) these other methods were not and still aren't, in my opinion, considered widely accepted practice. But thanks to this thread, perhaps it is time to take my example and expand on it in an update...a goal for 2007!
To address your final point, perhaps I did mis-speak as I made it sound like this was a given and it was never specifically stated. This is only my interpretation of what the authors may have been gettng at by realting K to Reynolds number. Darby gives an example and an explaination which to me implies there is a flow element to the overall K value.
To anyone reading this very long thread, and please don't take this the wrong way, before I get any more comments on what my paper says and does not say, I only ask that you read the whole thing first. As I've demonstrated, I am more than happy to address any issues and am more than willing to revise, amend, correct, whatever, that which is necessary, if it is necessary.
I’m sorry if I hurt your feelings in my last posting. It was not intended as a shot. By referring to your dP Paradox, I was trying to dignify what could otherwise be considered a foolish error. I was trying to give you a graceful way out.
Katmar has a good point. Crane is a self contained frame work from which one can draw to solve a certain class of fluid flow problems. Your presentation of Crane’s method deviates (probably unintentionally) from Crane’s frame work. I’d like to show you where I believe this happens.
Below there is a paragraph taken from your article in which you develop your f[sub]T[/sub] expression. I have numbered each sentence for ease of reference.
[tt] (1)Pipe friction in the inlet and outlet straight portions of the valve or fitting is very small when compared to the other three. (2)Since friction factor and Reynolds Number are mainly related to pipe friction, K can be considered to be independent of both friction factor and Reynolds Number. (3)Therefore, K is treated as a constant for any given valve or fitting under all flow conditions, including laminar flow. (4)Indeed, experiments showed that for a given valve or fitting type, the tendency is for K to vary only with valve or fitting size. (5) Note that this is also true for the friction factor in straight clean commercial steel pipe as long as flow conditions are in the fully developed turbulent zone. (6)It was also found that the ratio L/D tends towards a constant for all sizes of a given valve or fitting type at the same flow conditions. (7)The ratio L/D is defined as the equivalent length of the valve or fitting in pipe diameters and L is the equivalent length itself.[/tt]
(1) This sentence is ok. (2) Technically incorrect but I know what you mean. (3) This sentence is ok. (4) You failed to say that K is constant for any pipe size for all flow conditions. (5) This is a true statement but here it is a false association with sentence (4), it is a red herring. Crane does not make this association between K factor and friction factor in this train of thought. But, by including this statement here, you are falsely implying that this association exists. You can draw any number of false conclusions using false associations. Take for example the syllogism: All dogs are mammals; all men are mammals, therefore, all men are dogs.
You are using similar reasoning to characterize equivalent lengths. Your syllogism would say: The tendency is for K to vary only with valve or fitting size; this is also true for the friction factor in straight clean commercial steel pipe as long as flow conditions are in the fully developed turbulent zone. Therefore, to associate K for a valve or fitting with the equivalent length of pipe, the flow must be in the fully developed turbulent zone. This is not true. One does not follow the other. Especially if you consider that K is constant for all flow conditions, for any one pipe size, which you say in sentence (3).
(6) This sentence is ok. (7) This sentence is ok. But you would have been better off sticking to the definition of equivalent length in TP 410. The definition of equivalent length according to Crane page 2-8 (just below Equation 2-4):
“The ratio L/D is the equivalent length, in pipe diameters of straight pipe, that will cause the same pressure drop as the obstruction under the same flow conditions.”
It bears repeating: “…the same pressure drop as the obstruction under the same flow conditions.”
@plecner, Great reply - I think we have wrapped this topic up as tightly as it ever will be. I will accept a share of your challenge for 2007 and instead of my usual knee-jerk reaction of simply advising posters here to "get a copy of Crane 410" I will qualify that with a mention of Hooper and Darby.
@vzeos, I really like your analogy in your comment on sentence (5). This is the point that I have been trying to make all along, but I was never able to state it as clearly. It is unfair to accuse pleckner of introducing this red herring. Crane 410 made the original association between f[sub]T[/sub] and the K value, and pleckner has simply explained what they did.
If you compare the complexity of the K value expressions in Crane and Darby it is understandable why Crane chose the simple route and based their expression on f[sub]T[/sub]. However, I still maintain that they have caused enormous confusion by doing this.
To any young engineer who has persevered through all 50+ posts here, please take this one bit of information away with you - K values are not constant for all flow rates, despite Crane's claims.
A happy and prosperous New Year to all Eng-Tippers.
vzeos: I accept your right to interpret the elements in that particular paragraph as you did but I don't necessarily agree with all of your conclusions, especially since I was trying to paraphrase and not repeat verbatum what is in TP410. Perhaps that was a mistake considering how confusing the document can be. Harvey said it best so no need to rehash this point.
Harvey, vzeos, thank you for an informative, comprehensive discussion/debate on this issue. Perhaps we should strive to make the 3-K method the more acceptable standard practice within industry?
