19 replies to this topic

[ankur2061]

Dear All,

Crane paper 410M gives method for finding equivalent length of pipe fittings for fully turbulent flow based on friction factors for fully turbulent flow as given in Appendix A-26. The Crane method however does not give an idea about how to calculate excess head loss or resistance coefficient K when dealing with laminar flow (extremely low Reynolds number such as N_Re< 100). Examples of such flow could be pumping wet crude in large diameter pipelines with extremely high viscosities of the order of hundreds of centipoise.

The 2-K method proposed by 'Hooper' is supposed to be a panacea for all flow regimes and accurately predicts the 'K' factors for all flow regimes. I have made a spreadsheet using the 2-K method for 'K' factor calculation and the results are startling to say the least at extremely low reynolds number with very high 'K' values at low Reynolds number. Also note that at very high Reynolds number beyond a certain value there is practically no change in the 'K' value with increasing Reynolds number as calculated by the 2-K method.

Two of our luminaries on 'Cheresources', Art Montemayor and Katmar (Harvey) had a very enlightening discussion on the merits of Crane 410 method for evaluating equivalent lengths at the following link:

http://www.eng-tips.....cfm?qid=173164

I would like the readers to go through the attached spreadsheet and give their valuable comments on it. Special request is made to Art Montemayor and Katmar to critically review its content and give suggestions and comments for correction/improvement.

Hoping to get a lot of responses from the esteemed readers of the forum.

Regards,
Ankur.

[ankur2061]

Dear All,

Further to my post below, when calculating the equivalent length for 90 deg elbow (R/D = 1.5) for low and high N_Re based on the 2-K method the following observation was made.

NPS Sch Pipe ID N_Re f K Le
12", 40, 11.938", 100, 0.64, 8.2, 3.9m

12", 40, 11.938", 100,000, 0.013, 0.22, 5.1m


The emphasis here is on the point that equivalent length calculated by the 2-K method indicates that for low N_Re (laminar flow) the calculated equivalent length is lower as compared to that for high N_Re (turbulent flow).

This difference could become a significant factor when calculating pressure drop for an existing piping system having a large proportion of fittings in comparision to its straight length which needs to be modified and available pressure drop is limited.

Hope, I am able to give some insight regarding the importance of estimating the correct equivalent lengths for pipe fittings.

Regards,
Ankur.

[katmar]

Dear Ankur,

This is a very useful table that you have produced here. I think all engineers find it rather a shock when they first see the K values for fittings at low Reynolds Numbers. The predictions of the 2-K method agree well with the small amount of experimental data that I have been able to find. As an example of fairly easily available data see Perry 7th Ed, Table 6-5 on Page 6-18 (Also in earlier Perry editions).

I think that a possible extension to your spreadsheet would be to add columns for the friction factor and the equivalent length, as per the formulas at the top of your sheet. This would show how the friction factor also increases dramatically as the Reynolds Number decreases into the laminar range. The reason I ask you to add the equivalent length column is to show that this is relatively constant. The example in your second post shows that as the Reynolds Number decreases from 100,000 to 100 the friction factor increases by a factor of 50x and the K value increases by a factor of 37x. Compared with these huge changes the variation in the equivalent length by a factor of only 0.75 makes the equivalent length virtually a constant.

Many fluids texts mock the equivalent length method as being outdated and inaccurate, but your example shows that while it may not be as good as the 2-K method it is perfectly good for quick estimates. Also, when the equivalent length is expressed as a number of pipe diameters (i.e. Le/D) it is reduced to a single number which applies over a very wide range of Reynolds Numbers and pipe sizes.

Regards
Katmar

[ankur2061]

Dear Katmar,

Your suggestion was very useful and I have updated the spreadsheet by adding the calculation for the friction factor and equivalent length. Now for a given fitting or valve all you have to do is to provide the input as Reynolds number, pipe nominal size in inches and the pipe schedule. The rest all gets calculated. Of particular interest is the large change in equivalent length of 'globe valve standard' and 'check valve lift' for a Reynold number change from 1 to 500.

Dear readers, the updated file is uploaded as Rev. 1 and all are free to convey their observations and comments. I will be deleting the old file after a couple of days.

Regards,
Ankur.

Attached Files

•  2K_method_Excess_Head_Loss_in_Pipe_Fittings_Rev1.xls   88.5KB   1596 downloads

[daryon]

Hi Ankur,

I like your spreadsheet it's usefull and in fact has inspired me to develop one which compares the results (K-value and Equivalent length) from the Crane method, 2-K (Hooper) and 3-K (Darby)methods for a few of the most commonly used standard pipe fittings. I have done this as part of a review of a pipe pressure loss in-house calculation. I'm trying to figure out how the different calculation methods effect pipe pressure loss calculation results for typical process plant piping on FPSOs. The flow through the piping is generally in the transition zone with Nre > 4000 but less that zone of complete turbulence. I have posted the spreadsheet if your interested in having a look.

One thing I notice from your spreadsheet is that you calculate the friction factor for laminar flow using 64/Nre but then when Nre>4000 you use the friction factor for fully developed turbulent from Crane pg. A-25. Why do you jump from friction factors for laminar flow straignth to fully developed turbulent flow and miss out the crtical and transition zone friction factors? I guess you are only really interested in laminar flow right?

Kind Regards
Daryon
 K-Value Calculation Comparison Rev00.xls   144.5KB   937 downloads

Edited by Art Montemayor, 16 September 2009 - 06:45 AM.

[ankur2061]

Daryon,

Yes, the original idea of the spreadsheet was to highlight the difference in K-values and thus the equivalent length for laminar flow. But as I mentioned in my post the 2-K method is also applicable for fully turbulent flow. Actually friction factor for fully developed turbulent flow can be calculated using the 'Colebrook' equation or the 'Chen' equation. However, the 'Crane' values are also not off the mark.

However, I am stumped as far as calculation of friction factor for the 'transition' region (2100 < N_Re < 4000) is concerned and hence have considered in my spreadsheet any N_Re value above 2100 as turbulent flow which is not correct. I would greatly appreciate if anybody could provide an explicit equation for the friction factor in the 'transition' region. I could then correct my spreadsheet to calculate the friction factor & in turn the equivalent length for the Reynolds number in the 'transition' region.

Thanks for the spreadsheet you have posted and also for your valuable comments.

Regards,
Ankur.

[daryon]

Hi Ankur,

The Churchill equation is explict for friction factor and valid for all values of Reynolds numbers and all relative roughness. This is the equation I use to calculate friction factor in the spreadsheet I posted. Its not the most accurate equation I think I read somewhere it is good to within 2% of the Colebrook friction factor equation. But its easy to use and valid for all regions of flow including the critical & transition zones. Given the uncertainities in the resitance coefficients for fittings I think to is an accepatble equation to use for these type of caculations.

Ref. Friction-factor equation spans all Fluid-flow regimes, S.W. Churchill, University of Pennsylvannia, Chemical Engineering Magazine, Nov.07, 1977.

[katmar]

The Churchill equation is an excellent tool, but its main advantage is not that it generates accurate friction factors in the transition zone between Reynolds numbers of 2,100 and 4,000, but rather that it generates unique friction factors in this range and allows a smooth continuous way of moving between the laminar and turbulent zones. This is critically important for automated computer solutions.

I do not believe there is such a thing as an accurate friction factor in the range between 2,100 and 4,000 because the flow is not stable and even if you could calculate an instantaneous friction factor you would find that it is constantly varying with time.

From Churchill's paper: "The various sets of experimental data for the transition regime between laminar and turbulent flow are quite scattered."

From Coulson and Richardson Vol 1: "Reproducible values of pressure drop cannot be obtained in this region."

It would be better to say the friction factor in this range is undefined, and many Moody or Fanning charts do indeed simply leave a gap in this range, but computers don't cope well with gaps. By generating a friction factor in this range Churchill is simply allowing an automated solution.

If you find that your Reynolds number does fall in this range it would be better to adjust your pipe size to ensure that you remain either above or below it, or you risk getting surging and instability.

[ankur2061]

That the transition flow regime is still an enigma even as of today does indicate that there are still areas of science and engineering where human endeavour has remained inconclusive.

Thanks 'Katmar' for giving us an insight about the vagaries involved in the transition flow regime. As you have mentioned rightly, it would be better to manipulate your flow parameters to simply avoid the transition zone.

Regards,
Ankur.

[narendrasony]

Dear Ankur & Drayon,

Thank you very much for such useful tables and your vital observations for Laminar flow.
Drayon : Adapted Crane's method is not fully clear to me. It appears that you are back calculating "K" values for the given value of L_eq (calculated by Crane 410M method i.e. 4.242 for 12" 90 Deg elbow with r=1.5d). But instead I feel that "K" value should be taken as constant (e.g. K=14 * fT = 0.182 for 12" 90 Deg elbow with r=1.5d) and then calculate Eqv. Length based on that fixed "K" value.

Head loss through fittings H_L= K * V²/2g

So, "K" should be fixed for given size (as per Crane's method) instead of L_eq. Please correct me if I'm wrong.

Using Crane's method doesn't give accurate values for Laminar flow. Even at low Reylond's no in turbulent region Crane's method may give inaccurate results e.g. for 12" Sch-40 90 Deg elbow (r/d=1.5) with N_Re=7000 "K" value by 2-K method is 0.33 whereas by Crane's method it is 0.182. Even for N_Re=15000 value of "K" (2-K method) is 0.27. Can we use Crane's method even in such scenarios? It appears to me that Crane's method is useful only for high Reynold numbers.

Regards
Narendra

[ankur2061]

Narendra,

From what has been written in the earlier posts it is pretty clear that the Crane method for equivalent length is good for fully turbulent flow but not so for laminar flow. Is there any particular reason for repeating what has been mentioned in the earlier posts? What is it that you want to convey? Are you still not clear on what is mentioned in the earlier posts? I suggest you start reading the thread right from the start to get a clear understanding of what has been discussed up till now.

The only aspect that was a little unclear was how to treat the transition flow regime between Reynolds number of 2100 to 4000, which Katmar has been kind enough to explain on how to deal with it.

Regards,
Ankur.

[katmar]

While I agree with Ankur that Crane made their intended method for calculating K values very clear in their TP410 manual, I can understand Narendra's confusion as well. Many people are confused by the Crane method because it is wrong for laminar flow. If you need convincing that the situation is confusing (and you are very brave and have an hour or two to waste) try reading through the thread at http://www.eng-tips....d=173164&page=1

Many people, including Hooper and Darby, have shown that the principal influences on the K factor for a particular type of fitting are the pipe size (geometry) and the Reynolds number. Crane linked the K value to the pipe size, but unfortunately they did it via f_T (the friction factor at full turbulence). The K value of a fitting has nothing to do with the friction factor of the pipe that the fitting is connected to, and indeed Crane does not claim that there is any link - but because they used f_T as the link between size and K value it appears at first that Crane is saying this.

These two factors, i.e. the claim that the K also applies to laminar flow, and the use of f_T to take the pipe size into account, are the source of all the confusion.

[daryon]

Hi Narendra,

What I've done with 'adapted Crane method' is simply subsitiuted Ft (from Crane 410 pg A26) for the pipe ftiction factor as calculated by the Churchhill equation. I know this is WRONG and NOT how Cranes says the K factors should be used (you must use Ft for fully turbulent flow like you correctly say), but I just wanted to see what the effect was on K if the pipe friction was used instead of Ft. Sorry for the confusion I probably should have omitted this from the spreadsheet.

Kind Regards
Daryon

Edited by Art Montemayor, 21 September 2009 - 01:53 AM.

[narendrasony]

Dear Ankur,

My concern was : " Is Crane's method good even for turbulent flow with low Reynold's numbers (e.g. 7000-15,000)? " I'm sorry if I could not convey it in right manner.
And from Katmar's elaborate description on the suggested thread I've got some reply for that. In one such example by Katmar (originally taken up by Pleckner), dP calculated for N_Re =13,000 is within 15% of 3-K answer and adequate for practical purpose.

Also, I'd doubt regarding Daryon's approach to 'Adapted Cranes's method' which was similar to Equivalent length method where a constant L_eq is used for all flow conditions. Daryon has already replied for that.


I've another doubt now regarding Crane's method and Equivalent length method .
As per Cranes's method "K" is a function of fitting type and size only and it was demonstrated experimentally also. But if you calculate "K" or dP by Equivalent length method (i.e. K = f * L_eq/D, where f is pipe friction factor) then "K" becomes a function of N_Re. Is it not contradicting Crane's experiments or possibly Crane's experiments were done near total turbulent flow conditions only ? (Prior to the time of multi-K methods).

Katmar, Thanks for removing one long cherished myth about "K" and "f_T". I've kept a not in my diary : There is good correlation between "K" and "f_T" but no relation exists between them.

Regards
Narendra

Edited by narendrasony, 22 September 2009 - 05:34 AM.

[katmar]

But if you calculate "K" or dP by Equivalent length method (i.e. K = f * L_eq/D, where f is pipe friction factor) then "K" becomes a function of N_Re. Is it not contradicting Crane's experiments or possibly Crane's experiments were done near total turbulent flow conditions only ? (Prior to the time of multi-K methods).

Although Crane have given their formula 2-4 in exactly the format you have expressed it,
i.e. K = f * L_eq/D
it seems that their intention was actually to allow an L_eq/D to be calculated from a known K and a calculated f. At the bottom of page 2-8 Crane states "K is therefore considered as being independent of friction factor or Reynolds number." This seems reasonable to me if we restrict ourselves to the turbulent zone (although Crane go on to say "including laminar flow"). If we accept that geometrically identical fittings (say 90 degree bends) have exactly the same K value, and therefore the same presure drop for a given flow, even if one is made of ultra-smooth plastic and the other is commercial steel then the length of smooth plastic pipe that would give the same pressure drop as the bend would be longer than the length of commercial steel pipe required to give an identical pressure drop. So the pressure drop relationship when expressed as an equivalent length would be different for plastic and steel pipe, i.e. a longer equivalent length of smooth pipe. But this is probably a case of splitting hairs.

I tried to find a statement in Crane of the range of Reynolds numbers that they tested, but could not find anything explicit. The best I could find was the two figures (2-4 and 2-5) on page 2-4. From these the lowest Reynolds number would occur with a water velocity of 0.6 m/s in a 10 mm pipe, and this turns out to be a value of 6,000. I wonder if Crane ever actually did any laminar flow tests? If anyone has any specific information it would be very intersting to know.

[narendrasony]

Dear Katmar,
Thankyou very much for your patience and nice explainations so far. I am sorry to reply very late.

I've still some doubts while going through the thread you had referred.
Please refer to the post by "VZEOS" with seven commandments on 26th Dec'06 09:42 AM.
In the last line he writes: "...Therefore, the commonly held belief that Crane’s equivalent lengths apply only to fully developed turbulent flow is a myth". This again brings forth us to the same point. I hope you will also disagree with his statement.

Again please refer his Note 4) "K is a constant for all sizes when geometric similarity exists". and Note 5) "Because of geometric dissimilarity, K for a given line of valves or fittings tends to vary with size".
Subsequently he had shown that "K" factor is constant for all sizes for PIPE ENTRANCE but not for 90⁰ elbows.
Are 90⁰ elbows with a given r/d ratio not a case of Geometric similarity? What kind of geometric dissimilarity exists in this particular case ? And is really "K" a constant for all sizes for geometrically similar fittings?

Thanks again for your elaborate explanations.

Regards
Narendra

Edited by narendrasony, 03 October 2009 - 03:49 AM.

[katmar]

The spreadsheet developed by Ankur (see above) confirms that the equivalent length does not vary much between fully developed turbulent flow and laminar flow. Certainly the L/D ratio is much more constant than the K value. So I would say, as a first approximation, that it is true that Crane's L/D ratios can be used for more than just fully developed turbulent flow (but their K values cannot).

I share your suspicion that there is more to the change in K value with fitting size than can be explained by lack of geometric similarity. As you say, all bends with r/D of 1.5 should be geometrically similar. There will be slight differences because wall thicknesses change, and in the catalogues "long radius bends" do not all have exactly the same r/D. I don't believe geometry is the full story, but I don't know the true answer.

According to Hooper, pipe entrance and exit losses do not change with pipe size when expressed as K-values.

[narendrasony]

In the attached file, I've used Ankur's original spread sheet to tabulate the range (min-max) of Le/d (=K/f) and K/f_T for nominal pipe sizes 1"-36" (Sch 40, roughness "e" = 0.0018") and for Reynolds number as follows (Pl. refer the "Summary" sheet):
(1) N_Re >= 1 (Only Le/d as K/fT range is too wide)
(2) N_Re >= 4100
(3) N_Re >= 35000

"K" values were calculated by Hooper's 2-K method, fT by Karmann's law of rough pipes and line friction factor by Colebrook's equation for turbulent flow (macros to be enabled).

For a given type of fitting, these back calculated Le/d and K/fT values should be nearly constant for Equivalent length method and Crane's method respectively for all pipe sizes and Reynold numbers. So, narrower the range, better the method.

I could make following observations (for "e"=0.0018) :
(1) For entire range of Reynold numbers (N_Re >=1), as expected Le/d values are quite flatter (min/max ratios in the range of 0.35-0.40) except for some cases of globe & check valves. Crane's method is not good for Laminar flow.
(2) For N_Re >=4100, both methods are comparable with ratios of 0.4-0.45
(3) For N_Re >=35000 Crane's method is better with K/fT min/max ratios of 0.7-0.75, Eqvlnt Length method is comparable with Le/d min/max ratios of 0.40-0.45.

Crane's constants (K/fT) has the advantage that they are independent of pipe roughness "e". One can change "e" in the attached file to see its effect on Le/d ratios.
While 2-K and 3-K methods are available today, but Crane's and Equivalent method are still popular. Crane's method appears to be more appropriate for turbulent flow and with good accuracy when NRe > 35000. For Laminar flow we have the only option of Equivalent length method but with slight less accuracies (Le/d min/max ratios ~0.35-0.40).

I request Katmar and other esteemed forum members to review the attached file.

Regards
Narendra

Attached Files

•  Crane vs Eqvlnt Length method for fittings.xls   1.09MB   801 downloads

Edited by narendrasony, 09 October 2009 - 12:52 PM.

[katmar]

Wow Narendra, you have certainly done a very thorough job of testing what I have been saying. I'm pleased that your findings confirm so well what I had said. And you have made a good summing up of the situation as well. The Crane method has been popular because the zone where it is most accurate (Re > 35,000) probably covers 95% of industrial applications. It's a pity they claimed their method is accurate for laminar flow when it is not. There is apparently a new version of Crane 410 coming out at the end of the year and it will be interesting to see if they have finally addressed this short coming.

[bernath]

Hi All,

I'd like to purchase the latest edition of Crane410. Is there any revision on above mentioned issue? If there's no significant revision, I certainly be content with the scanned version of 1991 edition.

thank you.