2-k Method For Excess Head Loss In Pipe Fi.
ankur2061 17 Aug 2009
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 NRe < 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:
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.
ankur2061 18 Aug 2009
Further to my post below, when calculating the equivalent length for 90 deg elbow (R/D = 1.5) for low and high NRe based on the 2-K method the following observation was made.
NPS Sch Pipe ID NRe 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 NRe (laminar flow) the calculated equivalent length is lower as compared to that for high NRe (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.
katmar 18 Aug 2009
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.
ankur2061 19 Aug 2009
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.Source: www.cheresources.com