Friction loss 3

[friend81]

Dear Friends,

I would like to get a clarification in calculating friction loss in a PVC pipe of 100m length.Using the formula

hfs = 4f L/D x V*2/2 X g,

Q = 30cub.m/h
L = 100m
D = 51.4mm (ID of UPVC pipe)
Kin.Viscosity of Water @ 30deg.C = 0.801 cSt

Results i got are as follows

V = 4.018119 m/sec
Re = 258164.17
f = 0.003509

And finally the head loss per 100m pipe is 22.50m.

But friction loss chart provided by the pipe manufacturer shows 19.88m for same diameter & flow.

So i applied Hazen Williams equ. but the result was 28m.

I would like to know was there anything wrong in my calculation ?

Please throw me some light.

 

[rconner]

There may be nothing necessarily wrong with any of your "calculations", though I suspect the "manufacturer may have assumed that the pipe will be hydraulically smoother in your application (than you did by the various approaches). A fact that is not intuitively obvious to many folks in general is that very small pipes result in quite high and perhaps non-obvious head losses.

 

[Montemayor]

Friend:

I believe you’ve got the Fanning equation written wrong. It should be:

h[sub]L[/sub] = (4f) (L) (v[sup]2[/sup] / (D) (2g)

Where,
h[sub]L[/sub] = loss of static pressure head due to fluid flow, in feet of fluid
4f = 4 times the Fanning Friction Factor = the Darcy Friction Factor (dimensionless)
D = internal diameter of pipe, in feet
L = length of pipe, in feet
v = mean velocity of flow, feet per second
g = acceleration of gravity = 32.2 ft/sec[sup]2[/sup]

My next comment is a question. What is your Friction Factor and how did you come up with it? It is not a result unless you generate it with a relationship like Churchill’s, Chen, Serghides, etc. If you generated it with one of these equations, what absolute roughness did you employ for your PVC? The big difference in your “results” could be the absolute roughness assumed.

I would not rely on the Hazen-Williams relationship as giving you an acceptable level of accuracy as compared to the Fanning (or Darcy) equation(s).

I don’t know what roughness you used, but if you resort to the US Hydraulic Institute tables for water pressure drop, and look up under 132 gpm (30 cm/hr) and 2.067 inches ID (instead of 51.4mm = 2.023 in.), I get 28.8 ft/100 ft (28.8 m/100 m). This is with a relative roughness of 0.00087 – which is probably much higher than one would expect for PVC. Therefore, I would say your calcs are OK.

I haven’t done a detailed Darcy calculation since I just want to check if you’re in the “neighborhood” of the expected answer. And I think that’s really all you want. The real answer is to be found in the real, accurate roughness value that your PVC has.

I hope this helps you out.

 

[25362]

It is not uncommon to find deviations of [±]20% for [Δ]P[sub]f[/sub] estimations among designers using different formulas. Therefore, it is futile to use so many significant figures.

For example, it has been established that the Darcy-Weisbach equation is an empirical one, valid for water at 15.6[sup]o[/sup]C (60[sup]o[/sup]F) and average flow velocities below 3 m/s.

Besides, the smaller the pipe the larger the rugosity ratio.
For a commercial polyethylene pipe (I don't have for PVC) the surface roughness [ε] ~ 0.1 mm with a ratio [ε]/D ~ 0.002, what would it be for a drawn PVC tube ?

As for myself, I'd take the [Δ]P[sub]f[/sub] results with a pinch of salt, in particular if there is dissolved air that may be released along the way.

 

[katmar]

As Mr. Montemayor has pointed out, your friction factor is wrong, but only slightly. For rigid PVC pipe I use an absolute roughness of 0.005 mm, which would give you a Fanning friction factor of 0.00394 and a friction pressure drop of 25.2 metre water. My software uses a slightly modified Churchill relationship to calculate the friction factor, but I have checked it against the plot in Perry and get the same number.

For practical purposes, there is not much difference between your answer and mine.

If you assume a perfectly smooth pipe you get a friction head of 23.8 metre water, so I would say that your supplier is being overly optimistic. I have experienced similar "propaganda" from plastic piping suppliers here in South Africa, and claims are made that you will save energy (or even get away with a smaller pipe) if you use plastic instead of steel. As Mr. Montemayor has calculated, with a roughness value applicable to commercial steel pipe your pressure drop would be 28.8 m H2O, which is hardly any more than the 25.2 I calculated for PVC pipe. And with larger pipes the relative differences between plastic and steel would be even smaller.





Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[rconner]

I think the experts who followed my admittedly quite simplistic post gave you some very good advice. One other thing you might check is in general installing pvc pipe to service with a flow velocity of 4 m/sec (13+ ft/sec)?? -- I believe many authorities, perhaps at least outside your "manufacturer"?, might also judge this some risky business.

 

[25362]

To Mr Montemayor, I think I found a sch[ö]nhait's failure in your message, cubic meter shouldn't be written cm (used for centimeter) but cubm, or meter[sup]3[/sup] or better m[sup]3[/sup]. Agree ?

 

[katmar]

25362 makes a good point regarding the expected accuracy for pressure drop calcs. I would hope to be within 20% for friction in straight pipe, but it must be recognised that there is no single "right" answer. The situation gets worse when you introduce fittings and valves and aging pipe. If it weren't for these problems we engineers would not have jobs - the accountants would do the calcs themselves and "right-size" us.

It is true that the Darcy-Weisbach equation is an empirical one, but (as I have posted here before) it reflects work of true genius and is one of the outstanding achievements of engineering. The restrictions 25362 mentions (water at 15.6oC and average flow velocities below 3 m/s) do not apply to D-W. The equation takes changes in density, viscosity and velocity into account. I think you are confusing this equation with that of Hazen Williams, which does have severe restrictions. D-W also takes into account any changes in roughness (or rugosity ratio).




Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[BigInch]

Slow down the velocity if at all possible, otherwise be sure to do a surge analysis.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[Montemayor]

25362:

Your impeccable scrutiny detected my metida de pata resulting from my haste to finish the post by simply using ad hoc abbreviations. I certainly agree that you can’t equate volumetric flow rate units with velocity units. My only excuse is that I’ve been divorced from the metric system for quite some time now and never really got involved with SI units at all. Does this mean I’m prohibited from entering Metric Heaven?

On a more serious note, I thoroughly agree with you and Harvey on the accuracy to be expected from such fluid flow calculations. We can only prediict with accuracy with what we guess to be the internal surface conditions of a pipe that is differentially getting worse in roughness. A margin of 15% inaccuracy is not a surprise to me with this type of application - it all depends what the local conditions, the timining, and the application are.

Saludos

 

[25362]

My impression is that there are at least two factors afecting results in determining [Δ]P[sub]f[/sub] by the various equations, beside inaccuracies in pipe dimensions and fluid physical properties:

1. The value of the friction factor "f", as clarified by the experts. "f" is frequently estimated using the Colebrook equation which is said to be within 10-15% of experimental.

2. The exponent of the flow rate in [Δ]P[sub]f[/sub] = K.Q[sup]n[/sup] has been found to vary in the range 1.9-2.1 or wider.

I wonder whether point (2) could be the reason of the discrepancy between the results offered by the pipe manufacturer and those estimated by friend81 ?

 

[friend81]

Montemayor

thanks for ur comments.

but the equation i applied was Darcy Weisbach & not fannings equations ,hence i derived f value by using the formula

f = (0.0791/Reynolds No)power 0.25.

Any comments

 

[BigInch]

I don't recall seeing that one. What's the name of that formula?

Since Hl = f * L/D * V^2/2/g,

I think you got lucky approximating the accepted results and that the formula only "works" when,

(0.0791/Re)^(1/4) = Hl * D/L * 2 * g /V^2,

Which I believe would be for cases where Re is equal to 1E+6. At lower turbulent flows, your friction factor could be up to about 50% too high, at higher velocities, its 20% too low and getting lower. For laminar flow, forget it.

Using a conventional formula when possible would make it easier for you and other engineers to check your work.


BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[25362]

To friend81

Your formula for "f" is similar to the Blasius (1913) equation for turbulent flow in hydraulically smooth pipes. That equation for the Darcy friction factor is:

f = 0.3164/Re[sup]0.25[/sup]​

But its validity is up to about Re~10[sup]5[/sup].

For a wider range up to and including Re~10[sup]7[/sup] there are modified formulas, for example:

f = (0.3164/Re[sup]0.25[/sup]) (1+2.32[×]10[sup]-6[/sup] Re)[sup]0.125[/sup]​

 

[Montemayor]

Friend81:

The form I cited:

h[sub]L[/sub] = (4f)(L)(v[sup]2[/sup]/(D)(2g)

is, in reality the Famous Darcy formula – but with “f” being the Fanning Friction Factor. As you probably know, there is a BIG difference between the Darcy (a.k.a., “Moody”) Friction Factor and the Fanning Friction Factor. The Darcy Friction Factor is equal to 4 times the Fanning Friction Factor.

From page 1, Chapter 1, of the Crane Technical Paper #410 we read, “The Darcy formula is also known as the Weisbach formula or the Darcy-Weisbach formula; also, as the Fanning formula, sometimes modified so that the friction factor is one-fourth the Darcy friction factor.” The reason for the factor of 4 is that Fanning used a hydraulic radius instead of a straight radius in that version. In my well-worn and beaten-up copy of TP #410 I find a note I wrote many years ago: “The Fanning Friction Factor does not apply to formulas here unless multiplied by 4.” That was a Lesson Learned many years ago.

As Katmar has stated so many times in the past, the Darcy version is an ingenious tool worthy of engineering respect. The Darcy formula can be derived rationally by means of dimensional analysis; however, one variable in the formula (the Friction Factor) must be determined empirically. This has led, as 25362 points out, to a variety of favorite equations for “f”. I prefer to revert to a physical value – the absolute roughness measurement – as a means to derive the Friction Factor by applying the Colebrook relationship or one of its explicit variants (Churchill, Chen, Serghides, etc. ) since the Colebrook equation is an implicit one that seems to have been derived by an aspirin manufacturer.

All calculations (and assumptions) of the Friction Factor are based on experimental or empirical values and, as such, represent the variances and “inaccuracies” detected by actual field measurement. However, although I know in my heart that there will be an inaccuracy in my resulting calculations, nothing can predict the actual, real, instantaneous field conditions at any one time in a given application – and much less after operations have taken place over a period of time. Only at the initial startup can we ever have any hopes of “nailing” the values of “f”. And after that happens the values starts generally to degenerate to a worse state due to corrosion, contamination, fouling, etc.

So all we can hope to have is a general, average value subject to fluid properties, cleanliness, and maintenance.

 

[BigInch]

But then its no problem, as you can usually measure the head loss and flow then backcalculate to get a very good f to design for new heads and flow capacities. Many times I have found (esp.) gas systems where the pipe had better roughness than the recommended new steel pipe roughness value of 0.0018 used to design the system. I have had to use a values of 0.0007 to 0.0009 to get close to the measured flows in some systems.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[25362]

Great advice. A star is the proper reward.

 

[Montemayor]

BigInch:

You've provided an excellent and salient comment to an interesting and excellent subject. Your comment provides what I failed to insert in my attempt to explain where the friction factor "resides" and the need to fully understand and deal with it on a practical basis.

There's a lot more to fluid mechanics than just "cranking away" with equations and generating numbers.

Thanks.

 

[BigInch]

I didn't realize it was such a profound statement, but glad you're all happy with it. Knowing the host of inaccuracies surrounding hydraulics, of which roughness is probably the least in comparison to stepping up the flowrate over design, bringing on 2 additional wells, or simply outright fouling with wax, etc., I just prefer to work with conservative data, or with actual data, if it is available.

And clarifying somewhat... make that "design of a new pipeline using 0.0018", a figure which is actually supposed to approximate the roughness of a steel pipe after 5 years of operation.

(Actually I think we had so much sand in those gas lines, we were continuously blasting them clean ;-)

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[25362]

BigInch, somewhere I've read that "practice" teaches that in conventional carbon-steel pipes the friction factor doubles in ~25 years for light HC gases, ~15 years for medium distillates, and 10 years for residual streams. Any comment ?