Crane 410 fittings
Crane 410 fittings
(OP)
In Crane TP 410, K for a fitting is found by multiplying a number times fT. fT is called the friction factor. Is fT related to the roughness?
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RE: Crane 410 fittings
RE: Crane 410 fittings
RE: Crane 410 fittings
RE: Crane 410 fittings
BigInch
-born in the trenches.
http://virtualpipeline.spaces.msn.com
RE: Crane 410 fittings
1/√fT= 2Log{(3.7D/k)
Crane's equivalent length calculations assume fully developed turbulent flow. See Crane TP 410, Page 26. The fT values provided by Crane imply a k value of about 0.00180".
RE: Crane 410 fittings
You are totally correct. Seems I reversed the question. K is determined by geometry, but the equivalet length is indeed based on 0.0018 roughness.
BigInch
-born in the trenches.
http://virtualpipeline.spaces.msn.com
RE: Crane 410 fittings
The Colebrook-White equation uses the Reyonalds Number, the relative roughness.
RE: Crane 410 fittings
The Crane engineers noted that the K values for fittings generally decreased as the fitting size increased. But it all went wrong when they noticed that this rate of decrease was close to the same as the rate at which the friction factor for fully developed turbulent flow in commercial steel pipe decreased as the pipe size increased. The fatal mistake was to link the two. See Crane Fig 2-14 and associated commentary.
For example, on page A-29 the K value for a 90 degree butt-weld pipe bend with an r/d of 1.5 is given as 14fT. The values of fT are given at the top of page A-26 as a function of pipe size. The values may have been calculated using the function referenced by vzeos, but for the purposes of calculating K values they are constants for each pipe size.
This apparent link between the K value and the friction factor gives the impression that the K value is linked to the pipe roughness, but in fact it is not because fT is defined to be at a particular roughness. Even worse, it is possible to be mislead into believing the Crane K values compensate for changes in Reynolds number because everyone knows that the friction factor is influenced by the Reynolds number. But again, it is not because fT is defined to be in a particular Reynolds regime (fully turbulent).
To use the example of the 90 degree bend I gave above, it would have been better for Crane to give the K value as 14J, where J is simply a fudge-factor and would still be given by the values in the table on Page A-26 but without any reference to the friction factor. (Note that I have selected J as my symbol simply because it has no prior definition in the Crane Nomenclature table.)
The upshot of all of this is that in Crane's treatment, the K value of a fitting is a function only of the pipe size (or geometry to use the terms used by wfn217 and BigInch). This was an improvement over previous work where the K value had been assumed to be constant for all sizes of fittings, and at the time that Crane first published this method it was rightly acclaimed as an important advance but IMHO it was badly worded and newer editions of 410 have unfortunately done nothing to remove the confusion.
I have awarded a star to BigInch for his comment that if you want to convert the Crane K value to an equivalent length, you must use the fT value from Crane's table on page A-26 (which is based on a roughness of 0.0018") and NOT the actual friction factor of the pipe you are using. The Crane description of this on pages 2-8 to 2-11 is extremely confusing, and the example 4-7 is just plain wrong because the K values given in the 410 manual apply only to fully developed turbulent flow and should never be used for laminar flow.
If you are working with laminar flow it is much better to work with equivalent lengths than with fixed or even Crane K values. Resistance values for fittings increase rapidly at low Reynolds numbers, but so does the friction factor. This means that if you use fixed L/D values, which get multiplied by the friction factor in the Darcy-Weisbach equation, the high resistance values are automatically compensated for. Or even better, use the 2-K or 3-K methods proposed by Hooper and Darby.
[Close rant mode - thanks for listening!]
Harvey
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Crane 410 fittings
And I select Harvey as the preferred Ranter of the day and worthy - as well - of recognition for bringing to everyone's attention the importance of really understanding and reading through what is put in front of our eyes. We, as professional engineers, are not being asked to believe or accept 100% of what we are offered or given - regardless of how "sacred" the Cow may seem. Everything in engineering is subject to scrutiny and improvements.
I have a lot of respect and gratitude for what has gone into putting together Crane's Tech Paper #410. However, everything Harvey has stated regarding the concept of their K values is not only valid, but 100% positive criticism that should be heard and applied. Major world-class engineering firms agree with what Harvey states - and so do some of the biggest chemical process companies. To quote one: "Until recently, the use of K coefficients for valves and fittings has been considered more accurate than the use of equivalent lengths of pipe, but recent research has disclosed that K coefficients are not constant for all sizes of any one type of valve or fitting; so the use of equivalent lengths, with some exceptions, is now preferred." And this is in addition to the problems of understanding/interpreting what TP 410 is saying. We have a better option, as Harvey states, in the 2-K or 3-K methods.
Great comments and good engineering knowledge, Harvey!
RE: Crane 410 fittings
RE: Crane 410 fittings
?P = ( fL/D + K ) ?V2 / 2
So if you want to express the resistance of a fitting in terms of the equivalent length (i.e. L/D) instead of K then you have to calculate
L/D = K/f
and since Crane express their K's as (Constant) x fT you would get
L/D = (Constant) x fT / f
If f is evaluated at the same conditions as fT (which is what my rant above was all about!) then of course
L/D = (Constant)
which means that for commercial steel pipe in the fully turbulent regime the (Constant) used by Crane will indeed be the L/D value given by Cameron. You just have to remember that because Crane evaluated these (Constants) for commercial steel pipe in the fully turbulent regime, if you want to get back to the L/D values you must use fT and not the friction factor in your particular case.
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Crane 410 fittings
My point was that I don't see why equivalent lengths are now prefered (per Montemayor).
RE: Crane 410 fittings
it has been found experimentally that the resistance factor (i.e. K value) for a fitting depends on both the fitting size and the Reynolds number. In the Darcy-Weisbach equation (in which I managed to get the wrong symbols before)
ΔP = ( fL/D + K ) ρV2 / 2
you can see that if you use a K value the pressure drop is not influenced by the fitting size or the Reynolds number. When you use Crane K values the value is corrected (via the table on page A-26) for fitting size before you insert the value into the D-W equation, but many of the older references gave single K values for all fitting sizes.
On the other hand, you can see that if you use equivalent lengths, then the value is multiplied by the actual friction factor for your application, and because the friction factor does depend on the fitting size and the Reynolds number it automatically corrects the calculation for both these factors. This makes the equivalent length method both easier to use, and more accurate than K values. It is easier to use because you only have to remember a single L/D value for a given type of fitting.
As Montemayor and I said before, the very best way is to use the 2-K or 3-K method but these are computationally much more involved. In my software I use 3-K because once it is programmed it makes no extra work to use it, but if I am doing a hand calc then I use the equivalent length method.
Hope this makes it clear
Harvey
RE: Crane 410 fittings
I have questioned Crane myself, but learnt to accept that its findings were as practical as required.
I think that younger engineers blindly use equations and computer programs - because they are there. They do not understand the applicable circumstances or the limitations. In fact whilst reading the post one of the junior engineers questioned me regarding recommended pipe diameters. They had sized the steam piping for maximum flow and minimum pressure. They were blindly going to use a calculated diameter because it was less than or equal to the recommended velocity without considering the application and whether the worst case conditions could occur at the same time, (they can't and a smaller pipe diameter was my recommendation).
I have printed the post and passed it to my younger engineers.
RE: Crane 410 fittings
I don't agree that using equivalent lengths is the proper way to perform a system hydraulcs calculation (my arguments are in the above mentioned article). You must not mix the friction factor for a fitting with the friction factor of a pipe because they are not the same, whether we are talking about CRANE's friction factor at fully developed turbulent flow or the two-K or three-K methods. The pressure loss of a fitting obtained from these methods is not the same nor nearly the same as the pressure loss of a fitting obtained from multiplying the pipe friction factor x the equivalent length of the fitting.
The most accurate way to perform the calculation is to use one of these methods (three-k perferred) and add the losses to those of the pipe, not to combine them all into an equivalent length of straight pipe and multiply by the pipe friction factor.
The two-K or three-K methods were developed to address the fact that fittings are indded somewhat dependent on Reynolds number, but this is still not the same as a pipe friction factor.
I will also argue that for fully developed turbulent flow, there is nothing wrong with CRANE's values. I believe you will find that the K values from all three methods are basically the same at these conditions.
RE: Crane 410 fittings
There is a lot more that we agree on than on which we differ. It was never my intention to suggest that there is anything wrong with applying Crane's K values to fully developed turbulent flow. I have recommended MANY times here that people should get their hands on a copy of Crane 410. Probably 95% or more of our flow calcs are for fully developed turbulent flow, and Crane is ideal for this.
My main objection was to the confusion caused by Crane's wording and their linking of the K value to the turbulent friction factor. I believe the posts in this thread confirm that this confusion is widespread, and I have often seen engineers struggle to come to terms with it. Despite the shortcomings of Crane 410, my copy "lives" in the very front of the top drawer of the filing cabinet right next to my desk.
We all agree that the multi-K methods are better than the L/D method. However, I disagree with Crane's statement (which is echoed in your article) that "K is a constant under all flow conditions, including laminar flow". In your example you give the K value for a long radius bend as 0.36. Applying the 3-K method at a Reynolds number of 100 in the same sized pipe gives a K value of 8.3. This means that a pressure drop calculation using the Crane value will be 90% understated, if we take 3-K as the benchmark. I accept that a similar calculation at Re=100 using the L/D method will over-estimate the pressure drop but for most calculations this would be the conservative option.
I have one objection to the example in your article. 92% of the pressure drop is due to the reducer, but nobody would ever try to calculate the pressure drop through a reducer with the L/D method. Including the reducer exagerates the negative aspects of the L/D method.
Neglecting the reducer, the calculated pressure drops using the various methods are
L/D method - 0.97 psi
Crane K - 0.75 psi
Darby 3-K - 0.87 psi
Who would put his neck on the block over which of these numbers is correct? The L/D and Crane answers are within 15% of the 3-K answer, and all three answers are probably adequate for practical purposes.
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Crane 410 fittings
BigInch
-born in the trenches.
http://virtualpipeline.spaces.msn.com
RE: Crane 410 fittings
I put the reducers into the L/D equation only as a means for comparison. I agree with you (Katmar) on that. But then again, I don't use the equivalent length method, ever.
Katmar, I'm one up on you, I keep CRANE on my desk, I'm too lazy to go into my file cabinet.
RE: Crane 410 fittings
RE: Crane 410 fittings
Great article. I appreciate your logical presentation. I am curious, however, about your representation that in 1979 Crane "...discussed and used the two-friction factor method for calculating the total pressure drop in a piping system...(f for straight pipe and ft for valves and fittings)." It is my understanding from reading the TP 410 Foreword (4th paragraph, quoted below) that Cranes's intent was to have the pipe friction factor, f, apply to the K factor calculation and that the K factor was intended to apply to the full range of flow regimes from laminar to full turbulence. Can you comment on this?
RE: Crane 410 fittings
The example in pleckner's article shows how the "old" (i.e. pre-1976) L/D method over-estimates the pressure drop in fittings for low Reynolds numbers. All my calcs agree with and confirm pleckner's result. Crane were quite correct to make this claim in the 1976 foreword.
It is true that using the "new" K values avoids the overstatement of the pressure drop in the laminar regime, but my example (See 5 Dec 5:15) shows how the Crane K values now understate the pressure drop by 90% at a Reynolds number of 100. If you were designing a new pipeline would you rather estimate the pressure drop as 40% too high or 90% too low?
Your query, and the latest post by wfn217, are typical examples of the confusion that is caused by the Crane method, and which lead to my rant near the start of this thread.
I have probably stretched everyone's patience to the limit by going on and on about this problem so I will leave it at this now.
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Crane 410 fittings
Thanks.
To me that statement in the Foreword just means that they made a change on how they relate the new K value to pipe friction factor. The statment obviously doesn't give any specifics as to how to apply the two, that is left to the rest of the document. Indeed, everywhere K for a valve or fitting is calculated within TP410 they are very careful to note the friction factor as fT and NOT f.
CRANE notes that the friction factors (f and fT) will essentially be the same in the zone of complete turbulence.
But you are correct in that it appears CRANE was intent on having K applied throughout all flow zones and that is where they got it wrong as we've been pointing out in these Postings.
RE: Crane 410 fittings
Thanks for your comments and their effects on this discussion.
BigInch,
You have pointed toward one of my pet peeves, the dreadful misunderstandings brought about by the ability of computers and calculators to thrash around 10 digit numbers. If the accuracy to which most parameters are known is only 1%, 5%, 10%, and sometimes even worse, most of those many digits presented by the mighty computer or calculator are really just so much drivel. Unfortunately, there is never a shortage of people who want to believe that all of those digits are significant (and are willing to make expensive/dangerous judgements and decisions as though they were valid).
RE: Crane 410 fittings
Somewhere in Tips, I recall seeing a comment I liked questioning how many digits were actually needed before the answer became believable, or something to that effect. Guess we should have stayed with 8 bit computers. Even if all variables were known to 1%, it seems to me that most systems would spend an excessive amount of time operating outside the range where those accuracies were valid.
Lastly, risking repeating myself, sooner or later any given system reaches capacity at one extreme end of operational range or another, so over the long term is using Eq.Len at max turbulence really a bad thing?
BigInch
-born in the trenches.
http://virtualpipeline.spaces.msn.com
RE: Crane 410 fittings
Thanks for directing my attention to your “rant”. I agree that the ft factor depends on geometry. Your j-factor theory, however, leads to the unlikely result that two different pipe I.D.s, say, 4” sch 40 (I.D. = 4.0260”) and 4” sch 160 (I.D. = 3.4380”) could have the same K-factor. How do you reconcile this situation? Also, how would you get the K-factor for a 36" XS L.R. Ell.?
Thanks.
RE: Crane 410 fittings
Regards
RE: Crane 410 fittings
http
and click on <next> for the following page
BigInch
-born in the trenches.
http://virtualpipeline.spaces.msn.com
RE: Crane 410 fittings
Great site, thanks! But I didn't see any info on K-factors or ft.
RE: Crane 410 fittings
Let us also not forget that we can obtain various fT values from the graph on Page A-23. This graph allows us to choose the fT for the type of pipe being used (and this translates into a constant absolute roughness for that type of pipe) and the diameter of that pipe. So I don't agree that CRANE TP410 necessarily publishes conservative values of roughness. It all depends on how you want to manipulate the piping material you are using, e.g. For pharmaceutical grade highly polished SS pipe I might choose to use the roughness for Drawn Tubing (an absolute roughness of 0.000005 feet) rather than clean commercial steel pipe (0.00015 feet). Note that with this table, I can also try to interpolate and obtain fT for various pipe diameters!
Let us also not forget that the published fT values given in the table at the top of Page A-26 are strictly for CLEAN COMMERCIAL STEEL PIPE and for the schedule of pipe listed on Page 2-10. If one desires the the K value for another fitting of a different schedule pipe, they should adjust it using Equation 2-5 on that same page or go to the Graph on Page A-23.
One last thing for now, one can still use published equivalent lenghts as per the reference given by BigInch but just remember to calculate the pressure loss through that fitting using fT for that fitting rather than the pipe friction factor as I've shown in my paper and my post above.
RE: Crane 410 fittings
http://
BigInch
-born in the trenches.
http://virtualpipeline.spaces.msn.com
RE: Crane 410 fittings
Yes, indeed (assuming we are still talking LR bends) the Sch40 and Sch160 fittings would have the same K value using my J factor, or using the Crane method. The table at the top of page A-26 has a note "K is based on use of schedule pipe as listed on page 2-10". And page 2-10 seems to say that the K values apply to Schedules 40 to 160, but that the velocity that is used to calculate the velocity head must be based on the actual ID of the fitting. Makes sense to me. If you take a look at Figure 2-16 on page 2-13 of Crane 410 you will doubt every calculation you have ever made. This figure shows the variability in the experimental data on which the K values we use are based. A great deal of license has been used in getting to the "averages" we accept as gospel.
This question again highlights the reason I disagree with the Crane fT method. People want to start fiddling with the fT for their particular pipe, whereas Crane's intention was that if you have a 4" fitting you use an fT of 0.017 irrespective of the schedule or actual roughness of that pipe. That is why I suggested that we call it "J" and eliminate the false link to the friction factor that is confusing everybody. All the experimental work shows that the K value has almost no dependency on the roughness, and if you look at Fig 2-16 again you will see that there is no room for hair splitting here.
Using the Darby 3-K method to calculate K values for the Sch40 and Sch160 bends gives values on 0.28 and 0.29 respectively (at Re = 300,000). If I was doing a calculation that involved these fittings I would use these two different values for the two different schedules, but only for the sake of computational consistency and to allow anyone to later check my calcs using the same methods. In my heart I would know that in fact they are for all intents and purposes the same. Of course for the same flowrate the pressure drop is higher through the Sch160 bend because of the higher velocity, but not because of any real change in K value. To try to calculate the actual K value from the Crane method by interpolating fT between Sch40 and Sch160 is IMO like measuring the length of a football pitch with a micrometer.
For the 36" bend I would use 3-K and get a K value of about 0.18. The rate of decrease with size gets less as the sizes get bigger. You could use Crane fT of 0.0105 (interpolating from the figure on page A-24) because there is a substantial increment to 36" from the data on page A-26, but the fact that Crane neglected to give values on page A-26 for 36" pipe does not detract from my argument that their procedure is confusing.
@Sailoday28,
Crane have neglected to give K values for welded or flanged Tee's. I have no idea why. As always I would use 3-K. A good reference for this type of data is the classic article by Larry Simpson and Martin Weirick (Chemical Engineering, April 3, 1978).
@pleckner,
I am confused over what you are saying Phil. If we apply your example of polished SS with a roughness of 0.000005 inch to our 4" LR bend we would have to have a Reynolds number of over 100 million to get to full turbulence (See Crane A-24). Under these conditions you would get an fT of about 0.007. This compares with an fT of 0.017 for a 4" fitting given on page A-26. Using the value of 0.007 would make a 4" highly polished LR bend have a K value of 17x0.007 = 0.119 and not the 0.28 that I would calculate from Darby's 3-K. Is this what you are saying, or have I got the wrong end of the stick?
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Crane 410 fittings
I got confused between inches and feet for your roughness in my working of your example with the polished SS. The fT is more like 0.010, making the K value 0.17. The numbers are different from my earlier calc but the principle is the same. My question is, are you proposing that we use the calculated fT value of about 0.010 rather than Crane's 0.017 to calculate the K value of a highly polished LR bend?
Sorry for the calculation error - its nearly midnight here!
Harvey
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Crane 410 fittings
RE: Crane 410 fittings
@katmar: My example is to show how one can manipulate, or try to manipulate absolute roughness to suite the type of piping material they have rather than just blindly following the table on A-26 that most people do. And yes, for this instance, I don't see anything wrong with using a lower K value for polished stainless steel pipe (actually tubing for bio-pharm use) over clean commercial steel pipe. The frictional losses will be significantly less for pharma pipe/tubing than for the standard chemical/petrochemical industry steel pipe.
BTW, I am doing a project for vegatable oil tank farm expansion and we are using a smaller diameter 304 SS pipe than I would normally choose for our flow rates (asked for by the client) because in their experience, there is essentially very little effective friction at all, the stuff just glides right down the pipe!
An please don't get me wrong, I am a big advocate of using the 2-K or 3-K method over CRANE for the same reasons you have been pointing out.
RE: Crane 410 fittings
Equation 2-1, hL = v2/2g, this is the velocity head of a flowing fluid.
Equation 2-2, hL = K v2/2g, this defines the K-factor as the number of velocity heads lost due to a valve or fitting.
Equation 2-3, hL = (f L/D) v2/2g, this is the Darcy equation.
Equation 2-4, K = (f L/D), this is the familiar K-factor equation.
It should be completely evident that the link between the friction factor and the K-factor is established by virtue of the Darcy equation and that f is the Darcy friction factor. The purpose for inventing a K-factor and doing this algebraic manipulation is to develop a dimensionless group to be used for model scaling and to generalize experimental findings based on a limited number of experimental results. It should be further noted that the friction factor, f, applies only to straight pipe; there is no friction factor associated with any valve or fitting.
The Darcy friction factor can be obtained using your favorite charts or equations. For the special case of fully developed turbulent flow, fT, which represents the maximum possible friction factor, the von Karman Rough Pipe Law should be used, namely 1/√fT = 2Log (3.7D/k) or fT = 1/[2Log (3.7D/k)] 2, where k is the pipe roughness. There is no special significance given to the fT values provided on page A-26. Indeed, the first paragraph on page 2-10 states that these fT values are provided for “convenience.”
K-factor values for valves and fittings are determined experimentally by measuring the head lost due to the valve or fitting during a flow test. Once the K-factor value is determined for a valve or fitting it can be equated to a hypothetical pipeline (having particular values for the parameters f, L and, D) by using equation 2-4. The values for the parameters of the hypothetical pipe are not set in stone.
For example:
A flow test for a 2” valve produced a pressure loss equal to 3 velocity heads under fully developed turbulent flow. What is the length of 2.067” ID hypothetical pipe that would cause a 3 velocity head loss if the hypothetical pipe roughness were 0.0015”?
Using the rough pipe law, fT = 1/[2Log (3.7*2.067/0.0015)] 2 = 0.01819
Using Equation 2-4, LT = (3* 2.067)/0.01819 = 340.9” or 28.4 feet
LT is the equivalent length of the valve under fully developed turbulent flow.
RE: Crane 410 fittings
RE: Crane 410 fittings
We engineers learn best by example, so let me also give an example to illustrate the point. Equation 2-16 on page 2-12 gives the head loss through a bend as
ht = hp + hc + hl
where
ht = total loss through bend
hp = excess loss
hc = loss due to curvature
hl = loss due to length
For a standard radius bend the average flow length through the bend would be 1.5 times the diameter, and it could be argued that hl is therefore influenced by the actual friction factor in the fitting. Page A-29 shows that the equivalent length of a standard radius bend is 14 diameters. We can therefore say that 1.5/14, or approximately 11% of the head loss through the bend is influenced by the friction factor. In an extreme case the actual friction factor may vary by 50% from the given value of fT. In this extreme case the overall pressure loss would change by 50% of 11%, or 5.5%. This is well within the confidence limits of the values for K, and it is therefore meaningless to adjust the K value according to the friction factor. In most real life cases the actual variation would be much less than this 5.5%
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Crane 410 fittings
I must disagree with vzeos’ statement, “There is no special significance given to the fT values provided on page A-26. Indeed, the first paragraph on page 2-10 states that these fT values are provided for “convenience.”” First, I read the referenced paragraph differently and believe the word “convenience” as used in the above quote is being taken out of context. I believe the authors are saying they present this table as a convenience so you don’t have to go looking things up in the graph they present on page A-23, not that they have no real significance. Second, the significance of fT is that the experiments were carried out very specifically with flow in the zone of full turbulence; or perhaps I’m misinterpreting the meaning of vzeos’ statement? To me the CRANE engineers are trying to distinguish between this friction factor and the friction factor in the pipe, this is the significance of fT.
Before the next salvo, I want to wish all happy holidays and a happy and healthy (and profitable) New Year.
RE: Crane 410 fittings
I agree that you are misinterpreting the meaning of my statement. I said “no special significance”; you restated it as “no real significance.” The reason that I said no special significance is that there is a notion out there that if you use the Crane K-factor formulas you must use the fT values from table on page A-26. This is not true. The fT values on page A-26 apply to clean commercial steel pipe and are assembled there for the users convenience. If you are using cast iron pipe or plastic pipe or any other pipe material, you need to use an fT value appropriate to your pipe diameter and your pipe roughness.
On a more interesting subject. I read your article and I’ve been working with your example. I found that if you calculate the equivalent lengths using f instead of fT, the calculated dP using the Equivalent Length method is the same as the dP you get using the K-factor method. I have posted the numbers I calculated below. Please check my math.
Equivalent Lengths Using f
3" pipe 31.5
(2) 90deg Long Radius Elbow 6.167
(1) Branch Tee 9.250
(1) Swing Check Valve 7.709
(1) Plug Valve 2.775
(1) 3” x 1” Reducer4 496.088
TOTAL 553.489
dP=0.00000336{(0.02985)(553.489)(63,143)2/(( 112.47)( 3.068)5)} = 7.2398
Also, if you use f instead of fT to calculate equivalent lengths, Leq= KD/f, then the equivalent length dP formula can be algebraically transformed into the K-factor dP formula. This implies that it would be correct to use the flowing friction factor, f, in the K-factor formulas instead of fT when appropriate. Please check my math below.
dP= 0.00000336{fLeqW2/(ρd5)}
= 0.00000336{f(KD/f)W2/(ρd5)}
= 0.00000336{(Kd/12)W2/(ρd5)}
= 0.00000028{KW2/(ρd4)}
Happy holidays!
RE: Crane 410 fittings
Regards
RE: Crane 410 fittings
Crane has some info on standard tees. K thru branch = 60fT, where 60=(L/D). For reducing tees, take a look at the note in Example 4-14. You might want to do the same.
RE: Crane 410 fittings
RE: Crane 410 fittings
Yes. The analysis is steady state and K only represents resistance.
RE: Crane 410 fittings
If by associating fT with the K values you mean why did they use expressions like K=fT 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 fT to match the flow condition of their tests. My problem with this methodology is that (L/D) is not a constant but K is.
RE: Crane 410 fittings
Your clarification on the paragraph in CRANE now puts us in agreement on that topic.
I ran the equivalent length numbers using only the pipe friction factor and this is what I get:
3" pipe L=31.5
(2) 90deg Long Radius Elbow K=0.418 each; Leq total=7.167 (elbows r/d = 1.5)
(1) Branch Tee K=1.791; Leq=15.34
(1) Swing Check Valve K=1.493; Leq=12.78
(1) Plug Valve K=0.537; Leq=4.6
(1) 3” x 1” Reducer4 K=57.92; Leq(pseudo)=496.09
TOTAL 567.47
I get dP = 7.42 (close enough).
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.
That's my take on this.
RE: Crane 410 fittings
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.
dP= 0.00000336{fLeqW2/(ρd5)} This is equation 2 in your article.
= 0.00000336{f(KD/f)W2/(ρd5)} This is equation 2 in which (KD/f) replaces Leq.
= 0.00000336{(Kd/12)W2/(ρd5)} This is equivalent to the previous equation. Note f canceled f and D was replaced by d/12.
= 0.00000028{KW2/(ρd4)} 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/fT you would not be able to derive equation 7 from equation 2 (the Darcy equation)!!
Happy holidays!
RE: Crane 410 fittings
Yes - Crane's use of the expression
K=fT 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 fT 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 fT 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.
regards
Harvey
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Crane 410 fittings
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!!
RE: Crane 410 fittings
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=30fT. 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, fT=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 fT,
K= fTx(Constant1) = Constant2 = f(L/D) for any flow condition !
fT Fully turbulent friction factor.
Constant1= Legacy (L/D).
Constant2= Numerical K-factor
f=Darcy friction factor.
L=Equivalent length.
D=Pipe diameter.
Therefore, the commonly held belief that Crane’s equivalent lengths apply only to fully developed turbulent flow is a myth .
…the Good News according to Crane.
RE: Crane 410 fittings
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 fT 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.
Harvey
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Crane 410 fittings
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 fT 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 fT 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.
RE: Crane 410 fittings
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.
Happy New Year to all, and to all a good night.
RE: Crane 410 fittings
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.
Harvey
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Crane 410 fittings
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.
RE: Crane 410 fittings
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 fT expression. I have numbered each sentence for ease of reference.
(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.
(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.”
RE: Crane 410 fittings
@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 fT 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 fT. 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.
Harvey
Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com
RE: Crane 410 fittings
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?
Again, a Happy and healthy New Year to all!!