Hazen-Williams Equation Accuracy? 8

A gentleman named A.M. Friend, then an ASCE Fellow, undertook a study and presented a paper in a 1968 ASCE national meeting in San Diego, California entitled, "Flow of Water in Pipelines". I know that in that paper he presented some comparison curves for 12" and 24" piping head loss at 0-10 ft/sec water flow velocity reportedly by different Hazen-Williams, Manning, Scobey, and Darcy formulae approaches (these were among those discussed in his paper at the time). If I remember correctly these curves all converged quite closely together in e.g. the 2-6 ft/sec flow velocity range. [Frankly, I'm not sure there was any huge magnitude divergence in Friend's curves at the extremes of near zero or 10 ft/sec.]
This of course does not say at what flow velocity the results of any of the formulae was most "accurate", just that it didn't make a huge amount of difference in the calculation result (at least with the Friend'sinput parameters) depending on what approach was used. I suspect the "accuracy" of any head loss determination can also be affected by the "accuracy" of parameters input in the specific approach.
I think you will find many more discussions and opinions concerning these matters with an archive search on this and other lists.

the original research used by Hazen and Williams when they published their book of hydraulic tables indicates that the researchers tested pipes in the range of about 0.26 to 10.4 feet/sec for iron pipe and calculated C coefficients ranging up to 148.5 (this being for new cast iron pipe, coated and well laid as reported by Williams, Hubbel and Fenkell).

The C coefficient needs to be evaluated carefully and understanding made between the appropriate value for new versus old pipe, well laid versus not so good, good condition vs tuberculated, conservative design value versus actual/existing value. I believe this may be where you might find some discrepancy.

Why Hazen-Williams? That is probably the worst equation to use for pipe flow. Not only is it terribly inconvenient to use for any product other than water, as it does not consider viscosity, but it also fails to differentiate between laminar and turbulent flow conditions. In its unmodified form, it should only be used in the transition zone and slightly thereabove, for large diameter pipelines with cool water.

ASCE has a paper on the use of this equation, from which I

The Hazen–Williams formula is frequently used for the design of large-diameter pipes, without regard for its limited range of applicability. This practice can have very detrimental effects on pipe design, and could potentially lead to litigation.

Finally, it is important to point out that the indiscriminate application of the Hazen–Williams formula either in the design or verification of water-supply systems is far from a simple academic problem. It may lead to serious practical and conceptual implications in otherwise straightforward computations.

Click to expand...

The full text of the 8 page paper can be found here,

Why not download some spreadsheets that use, Darcy-Weisbach, Colebrook, or the [I recommend] Churchill equation, decide which one to use as your standard and make sure everyone gets on the same page.


BigInch-born in the trenches.

The larger the pipe the worse the correlation.

Why not use a modern method such as Darcy Weisbach to determine the friction factor?

Geoffrey D Stone FIMechE C.Eng;FIEAust CP Eng

BigInch, the article you referenced is excellent. I really appreciate you sharing your amazingly wide knowledge and experience here. I always thought that H-W was just a bit less accurate than Dary Weisbach and I did not realize that there are fundamental flaws in its formulation and in its area of applicability.

Another very interesting factor in that reference is that even if the original engineers in the case study had used Darcy Weisbach they would still have made significant errors, although the errors would have been less than those actually made by using H-W. We tend to get wrapped up in our design equations and forget that if the input data is wrong, so is the result irrespective of the accuracy of the formula. In this case study the pipe roughness was almost 10x the expected value. It seemed that at the time of writing that article there was a court case pending on whose mistake caused the under capacity of the system. It would be interesting to know who was found culpable - the engineer who used the H-W formulation or the supplier of the bad piping.

Katmar Software
Engineering & Risk Analysis Software

It is a great article.

The use of the D-W equation, while generally quite accurate, is just another proof of the I.T. adage, "Garbage in = garbage out". No equation or computer program will help if somebody simply happens to miss adding an 800 m length in the suction piping of a 40ºC gasoline line, as I found a previous client's engineers had done.

I wonder if those court records are to be found in some online data vendor's files?

And, thanks, but its not my amazing knowledge. Although I was aware of the limitations of the H-W equation from my (too many) years of pipeline hydraulics, where a very small error in [Δ]H makes for a big error in [Δ]$$$, I can't be blamed for much of what I say here as most as 99.99% of it comes from the 22 GB of data I've stored on the portable hard drive. The truely amazing thing about this subject is that a 250 year old equation has continued to be used although its shortcomings are well documented. But then again I suppose, most of you guys are still using V1 + V2 instead of (V1 + V2)/(1 + V1 * V2) for calculating relative velocity.

As for pipeline hydraulics, a [Δ]P error of as little as +7 psi (=> 1 mil pipe wall thickness) can mean a cost of up to $ 3E+6 on an avg cross country pipeline (not counting future operating expense), so it pays to use the hydraulic equation most applicable to your specific scenario. Which, B/W, I think Churchill usually fills the bill (and requires no iteration for friction factor).

BigInch-born in the trenches.

Well... trying to guess the particular munincipality involved in the apparent lawsuit has so far been fruitless. Googling this subject brings an immense number of munincipalities that have inadequate water supplies and an equal number of official agencies that are still requiring that the Hazen Williams formula be used in water supply works calculations. Sounds worthy for a Blog topic.

BigInch-born in the trenches.

The HW equation is used because it is an equation that has a single term. It was developed exclusively for water in distributions systems using THAT distribution system to calibrate the equation. It continues to be put to use because it works, and complicated networks can be analyzed through this single equation. It is not good for laminar flow but the cases of laminar flow in municipality water systems are extremely rare, and typically the when there is laminar flow it is not a case when the system is interesting (3am) and even then the error is in the conservative direction.
Good technique in using the HW equation includes field monitoring and selected flow tests to see what the current performance of the pipe is. The different qualities of water will change the flow characteristics of the pipe over time. It is difficult to look at a 50 year old pipe and measure the [ε]/d roughness for the d-w equations without taking the pipe out of service.
HW equation is for water and nothing else. It uses a valid simplification because it uses is bounded by the use in the application. That simplification allows the engineer to evaulate extremly complex networks with excelent results.

Hydrae

No doubt, but anyone doing any complex network analysis would obviously have a computer powerful enough to use a better equation. Today, it is really not important that HW has only one term. We can use an equation that has 100 terms with little penalty, so that argument dosn't hold water in 2006. You can't deny there are many far better equations other than HW, neither can you say that there is a reason not to use better engineering tools with todays CPU costs. Especially when you consider that you may be found liable for not using state of the art methods. It is possible to do a complex steady state network analysis using a 1 page xls spreadsheet for any product with almost any equation you like, so why limit your capabilities to water for a HW "calibrated" system? Frankly I don't see any reason not to toss it, except it might be good to keep it around so we can see exacty how bad the decision to use it was when litigation comes up.

BigInch-born in the trenches.

The argument put for continuing to use the HW equation is similar to that for riding a horse because its not as complex as a BMW, is designed for rough tracks and may even show affection to the rider.

Geoffrey D Stone FIMechE C.Eng;FIEAust CP Eng

The Hazen-Williams formula gives good results for liquids which have kinematic viscosities around 1.2EE-5FT2/sec (which corresponds to 60 Deg F water).

At extremely high and low temperatures, the H-W formula can be as much as 20% in error for water.

The H-W formula should only be for water in turbulent flow.
Use of the H-W also requires a knowledge of the coefficient C.

But, but, but... Why [COLOR=red bold]should[/color] it be used at all?

BigInch-born in the trenches.

BigInch,

Some people like horses, blacksmiths, farriers, slide rules, log tables, paper blueprints and cave dwelling. Nostalgia is fine but please not in engineering.

I may be old but I quite willing to adopt modern engineering techniques and practices. Those who dont, give us old guys a bad name and make employers less likely to hire us.

I find that civil engineers are taught to use HW and mechanical engineers Darcy Weisbach and more strangely chemical engineers use Fanning.

Mechanical engineers build weapons, civil engineers build targets!

Rest assured BigInch the civil boys will never become competition in any industry outside of water.

Geoffrey D Stone FIMechE C.Eng;FIEAust CP Eng

Good point, but maybe that's how they get the water system design contracts... they put bigger flowrates on their proposals.



BigInch-born in the trenches.

Geoffrey, I have to jump to the defense of the chemical engineers here! There is absolutely no difference between the Fanning form and the Darcy-Weisbach form of the pressure drop equation.

The only difference is that the Fanning friction factor is numerically 1/4 of the value of the Darcy-Weisbach friction factor (also called the Moody friction factor sometimes). So whereas a mechanical engineer would calculate the number of velocity heads lost to friction as f[sub]M[/sub]L/D we chemical engineers would use 4f[sub]F[/sub]L/D. I am a bit more peculiar than most chemical engineers in that I have always used the Stanton form (=f[sub]F[/sub]/2) of the friction factor because my original college text book (Coulson & Richardson) used it. But we would all get the same answer if we remembered to use the correct multiplier.

A separate question is how to calculate the friction factor for the applicable Reynolds Number range. Quark put together a very nice FAQ on this - "Friction Factor Expressions - Implicit and Explicit" faq378-1236

Harvey


Katmar Software
Engineering & Risk Analysis Software

I gave you that one, all things being equal, but it is somewhat strange that there is some kind of "genetic" favoritism that somehow persists amongst disciplines. I thought DW was used primarily in the US and Fanning was more common in Europe+.

BigInch-born in the trenches.

Ok - let's play nice. FYI - I've worked with several other Civil Engineers in the natural gas industry while in college and to the best of my memory they did not regularly mess up pipelines, compressor stations, etc.

That said, I have had to do some limited natural gas line design to power an emergency generator at a water treatment plant and yes, not only does the engine have adequate fuel supply, but the generator is also putting out enough current to run the entire plant.

Now back to the original topic - From what I've gathered, the HW is highly favored in the Civil community. I've seen this in practice and also in reference books. Pipe manufacturer's HW C factors are readily available, but good luck finding roughness factors for DW.

After this discussion started, I tried to analyze the two problematic hydraulic systems that caused me to question the HW equation to begin with. I used WaterCAD modeling software and did both HW & DW equations. The difference in the results was negligible. Re was in the order of E-5 for both systems.

The part of this thread I agree with 100%, regardless of equation or software: garbage in = garbage out. I'm wondering if some of the minor loss co-efficients I'm using for fittings, valves (by the manufacturer), etc. could be off.

Mike

They wern't using HW for gas, probably Weymouth or something.

OK, I'm not worried. I don't have a HW option on the software I use.

If it was fitting errors, wouldn't you also have the same fitting errors for any equation and get the same net results?



BigInch-born in the trenches.

I believe part of the reason HW is used so much in civil design is that we have to conform to existing standards set by utility companies and development codes. In my area, these entities mandate HW calculations and C factors. In my very limited experience, it is extremely difficult to get reviewing agencies to accept things which are out of their comfort zone. In the fast-paced world of land development, it better to be a little conservative, use the mandated process, and get the project built on time. All of these equations are approximations. For smaller projects, the HW seems to be just as accurate, as sjohns4 says.