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Friction factor question 8
- Thread starter PD2
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It's not so easy to avoid transitional flow with viscous liquids.
A linear interpolation is often made between f1 at typically at Nre=2000 and f2 typically at Nre=4000, or at whatever values of Reynold's number defines onset of transition and turbulence in your specific case. Its not always 2000 and 4000.
--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
A linear interpolation is often made between f1 at typically at Nre=2000 and f2 typically at Nre=4000, or at whatever values of Reynold's number defines onset of transition and turbulence in your specific case. Its not always 2000 and 4000.
--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
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- #4
The starting point in answering this has to be to define what is meant by "transitional flow". Unfortunately the fluid hydraulics literature has not been consistent in its use of this term.
In his 1944 article presenting one of the first friction factor charts, Moody used the term "critical zone" to refer to the range of Reynolds Numbers from 2100 to 4000. He used the term "transition zone" in referring to flow conditions between the smooth flow (Blasius) line and the zone of complete turbulence where the friction factor is no longer a function of the Reynolds Number.
This terminology is still used by Crane TP410, which probably has the most valid claim on being the hydraulics standard in the English language (and probably in other languages too).
However, there have been many other sources which used the term "transition zone" in referring to the Reynolds Number range from 2100 to 4000. See the quote from Churchill below.
I prefer the Moody/Crane terminology, but there have surely been times where I have added to the confusion.
If you are using "transitional flow" in the Moody or Crane sense then the friction factor can be obtained using the charts in either of these documents, or if you want to use an equation then the Colebrook-White or Churchill equations are probably a good place to start. If you click on the FAQs button at the top of this thread you will see a document "Friction Factor Expressions - Implicit and Explicit" by member Quark that presents an excellent summary of the other equations available.
If you are actually referring to the "critical zone" between Reynolds Numbers of 2100 and 4000 then you should be aware that there are no accurate friction factors that can be calculated for this zone because the flow is unstable and the friction factor will vary from moment to moment. It is better to either increase the diameter of the pipe to ensure laminar flow or decrease the diameter to ensure turbulent flow - depending on the pressure drop you have available.
Here are some quotes regarding the friction factor in the critical zone from an earlier post of mine:
From Churchill's 1977 paper - "The various sets of experimental data for the transition regime between laminar and turbulent flow are quite scattered." Here you will see that Churchill himself is guilty of introducing some of the confusion on the definition of the zones.
From Coulson and Richardson Vol 1 - "Reproducible values of pressure drop cannot be obtained in this region."
From Rennels and Hudson - "For pipe Reynolds numbers between 2100 and 3000 to 4000, the friction factor can have large uncertainties and is highly indeterminate."
Katmar Software - AioFlo Pipe Hydraulics
"An undefined problem has an infinite number of solutions"
In his 1944 article presenting one of the first friction factor charts, Moody used the term "critical zone" to refer to the range of Reynolds Numbers from 2100 to 4000. He used the term "transition zone" in referring to flow conditions between the smooth flow (Blasius) line and the zone of complete turbulence where the friction factor is no longer a function of the Reynolds Number.
This terminology is still used by Crane TP410, which probably has the most valid claim on being the hydraulics standard in the English language (and probably in other languages too).
However, there have been many other sources which used the term "transition zone" in referring to the Reynolds Number range from 2100 to 4000. See the quote from Churchill below.
I prefer the Moody/Crane terminology, but there have surely been times where I have added to the confusion.
If you are using "transitional flow" in the Moody or Crane sense then the friction factor can be obtained using the charts in either of these documents, or if you want to use an equation then the Colebrook-White or Churchill equations are probably a good place to start. If you click on the FAQs button at the top of this thread you will see a document "Friction Factor Expressions - Implicit and Explicit" by member Quark that presents an excellent summary of the other equations available.
If you are actually referring to the "critical zone" between Reynolds Numbers of 2100 and 4000 then you should be aware that there are no accurate friction factors that can be calculated for this zone because the flow is unstable and the friction factor will vary from moment to moment. It is better to either increase the diameter of the pipe to ensure laminar flow or decrease the diameter to ensure turbulent flow - depending on the pressure drop you have available.
Here are some quotes regarding the friction factor in the critical zone from an earlier post of mine:
From Churchill's 1977 paper - "The various sets of experimental data for the transition regime between laminar and turbulent flow are quite scattered." Here you will see that Churchill himself is guilty of introducing some of the confusion on the definition of the zones.
From Coulson and Richardson Vol 1 - "Reproducible values of pressure drop cannot be obtained in this region."
From Rennels and Hudson - "For pipe Reynolds numbers between 2100 and 3000 to 4000, the friction factor can have large uncertainties and is highly indeterminate."
Katmar Software - AioFlo Pipe Hydraulics
"An undefined problem has an infinite number of solutions"
LittleInch
Petroleum
Excellent post by Katmar.
PD2 - Can you enlarge on your issue and why you are trying to find this?
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
PD2 - Can you enlarge on your issue and why you are trying to find this?
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
As the object is usually to eventually get out of the transition range, changing diameter of a pipe that should have already been optimized for a particular target normal turbulent flow rate doesn't appear to be a practical solution and one is still left with the question of what to use for friction factor while in the transitional flow regime.
A very heavy or waxy oil transported at elevated temperature may be in the transitional flow regime for days at a time, as the pipe and soil heat up to a stable operational temperature typically somewhere in the turbulent regime. So the practicality of finding a friction factor to use during extended time in the transitional flow regime becomes necessary. The interpolation algorithm is the only way I know to do that and is the method used by the pipeline simulation programs used for that type of analysis. It would be good to know of any other methods, but as far as I know, there are none.
--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
A very heavy or waxy oil transported at elevated temperature may be in the transitional flow regime for days at a time, as the pipe and soil heat up to a stable operational temperature typically somewhere in the turbulent regime. So the practicality of finding a friction factor to use during extended time in the transitional flow regime becomes necessary. The interpolation algorithm is the only way I know to do that and is the method used by the pipeline simulation programs used for that type of analysis. It would be good to know of any other methods, but as far as I know, there are none.
--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
In the light of 1503-44's comment I must accept that my advice to "use a larger diameter and force the flow into the laminar regime" is rather glib. I was of course interpreting the question in the light of my own experience, which is very different from that of 1503-44.
It is a very different matter to use a larger diameter for 200 ft of molasses piping than it is for a pipeline with a length of hundreds of miles, And using a larger diameter for a winter design case may result in the flow becoming critical in summer when the viscosity decreases.
The only alternative I know of to using interpolation between laminar and turbulent friction factors is the correlation of SW Churchill (1977). I use this correlation in my own software - mainly because it gives unique and continuous values of the friction factor for all values of Re. This is crucial for a computerized trial and error solution to be able to converge. However, I have always recommended my customers to stay out of the critical regime.
From what I have seen of the mathematics of the transition from laminar to turbulent flow all that I can say is that it is way above my mathematical ability. Hopefully in a long enough pipe the instabilities will be localized and over the length of the line they will average out and not make the flow rate too unstable.
I guess that for short lengths of pipe it is a reasonable strategy to use a larger diameter pipe, but for long pipelines you really do need to be able to design the mechanical aspects of the line to withstand a bit of instability.
Katmar Software - AioFlo Pipe Hydraulics
"An undefined problem has an infinite number of solutions"
It is a very different matter to use a larger diameter for 200 ft of molasses piping than it is for a pipeline with a length of hundreds of miles, And using a larger diameter for a winter design case may result in the flow becoming critical in summer when the viscosity decreases.
The only alternative I know of to using interpolation between laminar and turbulent friction factors is the correlation of SW Churchill (1977). I use this correlation in my own software - mainly because it gives unique and continuous values of the friction factor for all values of Re. This is crucial for a computerized trial and error solution to be able to converge. However, I have always recommended my customers to stay out of the critical regime.
From what I have seen of the mathematics of the transition from laminar to turbulent flow all that I can say is that it is way above my mathematical ability. Hopefully in a long enough pipe the instabilities will be localized and over the length of the line they will average out and not make the flow rate too unstable.
I guess that for short lengths of pipe it is a reasonable strategy to use a larger diameter pipe, but for long pipelines you really do need to be able to design the mechanical aspects of the line to withstand a bit of instability.
Katmar Software - AioFlo Pipe Hydraulics
"An undefined problem has an infinite number of solutions"
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- #8
I found this paper:
EPANET uses Dunlop's cubic interpolation: (see pages 189-190).
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"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill
EPANET uses Dunlop's cubic interpolation: (see pages 189-190).
============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill
That's nice to know. Unfortunately I can't change the linear interpolation in this software.
OK, I can agree with that one Katmar. It can be practical to change diameter with short pipe lengths, but I like your Churchill method even better. I don't know why Colebrook et al aren't simply deprecated these days. I'm rewriting all my stuff to use Churchill. No need to waste time and complexity with iterations any more, but then again it's been a long time since wood stave pipe has been around. We'll get there some day.
I did the hydraulic design of a Venezuelan very heavy oil pipeline, now quite a few years ago, but that lesson stuck. We did not use heat tracing, so from cold startup it took 30 days to get up to speed. Start the pumps in series at full power and no flow and in 30 days we got to parallel pumping at 80% power and turning down the control valves. Interestingly enough, sometimes we had simultaneously annular flow with no flow, laminar flow, transitional flow and turbulent flow, all at the same cross section. I've since found out it was much like what vulcanologists see when the lava changes from surface flow to flow within a lava tube. Fortunately at much reduced temperatures. I doubt linear interpolation gave a correct solution, but practically, it worked well enough.
--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
OK, I can agree with that one Katmar. It can be practical to change diameter with short pipe lengths, but I like your Churchill method even better. I don't know why Colebrook et al aren't simply deprecated these days. I'm rewriting all my stuff to use Churchill. No need to waste time and complexity with iterations any more, but then again it's been a long time since wood stave pipe has been around. We'll get there some day.
I did the hydraulic design of a Venezuelan very heavy oil pipeline, now quite a few years ago, but that lesson stuck. We did not use heat tracing, so from cold startup it took 30 days to get up to speed. Start the pumps in series at full power and no flow and in 30 days we got to parallel pumping at 80% power and turning down the control valves. Interestingly enough, sometimes we had simultaneously annular flow with no flow, laminar flow, transitional flow and turbulent flow, all at the same cross section. I've since found out it was much like what vulcanologists see when the lava changes from surface flow to flow within a lava tube. Fortunately at much reduced temperatures. I doubt linear interpolation gave a correct solution, but practically, it worked well enough.
--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
georgeverghese
Chemical
If you find the flow for a case of interest to be in the transition zone, use the higher of the f values obtained for laminar (at Nre = 2000) or for turbulent flow (at Nre=4000). This approach is also stated in Perry Chem Engg Handbook.
Inspection of the Moody Chart shows that the friction factor at Re=4000 will always be higher than at Re=2000, even with the smoothest pipe. Selecting the higher of the two is the same as just using the value at Re=4000. This might sound like it is being unnecessarily conservative, but there are cases where this is not the most conservative option.
Also from the Moody Chart, we see that as the Re No decreases (from very high values) down to 4000 the friction factor increases. The first reference given by fel3 shows that there are instances where the friction factor continues to increase as Re decreases below 4000, before dropping down rapidly to the laminar value. This occurs particularly with very smooth pipe. Interestingly, the Churchill equation exhibits exactly this behavior.
I compared a range of friction factors in the critical zone derived from Churchill with the values obtained using 1503-44's simple interpolation technique. The agreement was rather good - mostly within 5% of each other with some going out to 10%.
With all the other uncertainties that we have in piping design, I feel comfortable continuing to rely on the 1977 Churchill correlation for the friction factor. But it would be nice to see some case studies of real-world experience in the critical zone.
Katmar Software - AioFlo Pipe Hydraulics
"An undefined problem has an infinite number of solutions"
Also from the Moody Chart, we see that as the Re No decreases (from very high values) down to 4000 the friction factor increases. The first reference given by fel3 shows that there are instances where the friction factor continues to increase as Re decreases below 4000, before dropping down rapidly to the laminar value. This occurs particularly with very smooth pipe. Interestingly, the Churchill equation exhibits exactly this behavior.
I compared a range of friction factors in the critical zone derived from Churchill with the values obtained using 1503-44's simple interpolation technique. The agreement was rather good - mostly within 5% of each other with some going out to 10%.
With all the other uncertainties that we have in piping design, I feel comfortable continuing to rely on the 1977 Churchill correlation for the friction factor. But it would be nice to see some case studies of real-world experience in the critical zone.
Katmar Software - AioFlo Pipe Hydraulics
"An undefined problem has an infinite number of solutions"
Churchill all the way!
The transition region was always a temporary condition, so we didn't purposely stay there any longer than we needed to to verify we were getting through on time. It was always pretty close to schedule as it moved down the pipeline. After that, it was really strange to see flow always increasing even though we changed from series to parallel pumping while contining to reduce pressure, eventually reaching target flow rates after a month.
--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
The transition region was always a temporary condition, so we didn't purposely stay there any longer than we needed to to verify we were getting through on time. It was always pretty close to schedule as it moved down the pipeline. After that, it was really strange to see flow always increasing even though we changed from series to parallel pumping while contining to reduce pressure, eventually reaching target flow rates after a month.
--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
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- #13
![[banghead]](/data/assets/smilies/banghead.gif "[banghead] [banghead]")
pierreick…
I published a similar analysis on the PTC Mathcad forums about ten years ago: I had seen an earlier paper on the subject by Brkic, but not this newer one. Thanks for posting it.
Fred
============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill
I published a similar analysis on the PTC Mathcad forums about ten years ago: I had seen an earlier paper on the subject by Brkic, but not this newer one. Thanks for posting it.
Fred
============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill
Hi,
Thanks Fred,
a more recent one from Wikipedia:
Pierre
Thanks Fred,
a more recent one from Wikipedia:
Pierre
pierreick…
Thanks. I already had Genic's paper and I had saved an earlier version of the Wikipedia article. There are several new entries in the Wikipedia article.
Fred
============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill
Thanks. I already had Genic's paper and I had saved an earlier version of the Wikipedia article. There are several new entries in the Wikipedia article.
Fred
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"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill
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