Understanding the Hazen-Williams Formula

3/5/2024

On the MeyerFire University side of things we've been getting into the fundamentals of hydraulic calculations and the basis for how we perform calculations today.

One of the concepts that I had not explored in any kind of detail was the Hazen-Williams formula itself - outside of perhaps a few hand calculations here or there when studying for a NICET or the PE Exam.

It was developed early 20th center by Gardner Williams and Allen Hazen when they studied records of friction loss measurements from a range of experimenters. The formula they derived was empirical. For hydraulic calculations - it's been the staple our industry and the basis behind our systems today.

I'd be particularly interested in diving a little deeper than we typically would to get a job done, and that might come in posts here in the next few weeks.

How do we reduce pressure loss in our systems? What does the actual construction of the formula tell us about flow in our system?

WHAT THE FORMULA SUGGESTS
The exponents here are relevant - because of that 1.85 exponent - if we double our flow, then our pressure loss increases by 260%. If we triple our flow, then the pressure loss is 7.6 times the original!

Exponents affect the C-Factor too. If our C-Factor improves from 100 to 120, our pressure loss drops 29%. What applications could that have for us? Well, if we install nitrogen on a new dry system - our C-Factor goes from 100 to 120. That could be a big deal on the right projects.

What about diameter? With the 4.87 exponent, that has the biggest effect of all. If our diameter doubles, our pressure loss drops 97%! Even going from 2-inch to 2.5-inch drops pressure loss by about 60%!

Of the variables in the Hazen-Williams equation, diameter has the greatest impact on friction loss.

HYDRAULIC PARALYSIS
We know that intuitively as pipe diameter is our first go-to for solving hydraulic issues and is also the one element we have the most control over as a designer.

One concept not to gloss over, though, is the pipe schedule. Even seemingly minor differences in pipe schedule (thickness) can have a major effect on pressure loss considering that the effects of diameter have an exponential effect on pressure loss.

If you're banging your head against a wall trying to round out a hydraulic calculation, make sure that all of your pipe diameters are optimized (of course), but also check that your pipe schedule is accurate. The difference between a Schedule 40 and Schedule 10 calculation over a long enough distance and a sensitive-enough portion of the calculation could have a big effect on pressure loss.

Also - if you're ever stuck - try our tipsheet on ways to get out of a jam (Article #1 and Cheatsheet #2).

In experimenting around with different values, I went ahead and put together a small calculator that does a Hazen Williams calculation with a few helpful lookup tables already included. If you don't see the tool below, click to check it out:

If you're well into your career, this might not present a whole lot of practical need - any sprinkler hydraulic calculation program already has this incorporated of course.

What I wanted to do is simply break out the calculation to explore the effects in a little more detail. Take the sample calculation, and tweak the inputs just a bit - you can do so by clicking on a dropdown, making any selection, then use the up/down arrows on your keyboard to flip through values quickly.

YOUR TAKE
What do you see that people often miss about the Hazen Williams formula?

What, if anything, would you want to see on this tool as a means of learning about the fundamentals?

I think it would be a little interesting to start a dialogue on the limits of Hazen Williams and potential range of accuracy (that is, actually explore it mathematically and possibly disprove some of the frustrating assumptions that tend to pop up regularly).

What do you want to see? Water velocity? Limits? Comparison to Darcy-Weisbach?

Let me know below. Hope to nerd out a little and see what we can come up with together.

David Kendrick

3/6/2024 10:39:34 am

My understanding of Hazel Williams formula is limited to flow rates less than 32 feet per second.
With that I recall underwriters limiting projects to velocities less than 20 feet per second placing another “safety factor” on top of the myriad of safety factors already present.

Kicking off the dialogue.

3/6/2024 01:17:27 pm

David,

I've had the same understanding regarding the velocity limit of 32 ft/s on the Hazen-Williams formula. Though I've been unable to find any concrete evidence for where this limitation is derived (possibly old editions of code/standards, but NFPA 13 specifically states there is no velocity restriction when using HW). It seems to be a "rule of thumb" that's been passed on in the industry through the years. When taken down to the 20 ft/s requirements of some jurisdictions it can be extremely limiting.

These velocity limitations on HW formula would be an interesting rabbit hole to explore, if only to understand why/how these limitations exist.

Jack G

3/6/2024 05:28:24 pm

My understanding also , according to my grandfather and father, is the equations are accurate with velocities up to 32 fps.
When I was much younger and installed systems I was “ pitot crazy “ — I’d pitot end heads, compared it to hydraulic calcs— hand calcs.
Systems with pumps, hazes Williams wasn’t accurate at all. Opinion.

Mark Harris

3/6/2024 09:07:24 pm

Long time ago when IRI was still around I think their rules were max 32 fps and fm Global was 20 fps (or maybe 25). Current Tyco watermist documents allow Hazen WIlliams for up to 25 fps and Darcy-Weisbach formula. for above 25 fps.

Had somebody tell me the C factors were for 20 year old pipe to add more safety factor but have never seen that anyplace in writing.

Fritz Descovich

3/14/2024 06:16:28 am

Hi Joe. Thanks for bringing up such a relative topic once more. May I offer the following suggestions. I am coming up on my 49th anniversary in the fire sprinkler industry on the contractor side of
things starting back in 1975 at dad's sprinkler company in CA.

He taught me hand calculations and loaned me his original copy of Clyde M. Wood's manual "Automatic" Sprinkler Hydraulic Data. If you can get your hands on a copy, it is the preeminent guide to sprinkler system (Hazen Williams / Darcy-Weisbach hydraulic calculations.

I might suggest when talking by "pipe schedules" to please use the term "pipe wall schedules". Many of us old dogs are use to the term "pipe schedules" as meaning the NFPA 13 pipe schedule tables used years ago for pipe sizes based upon the quantity of sprinkler served by the piping versus hydraulic calculations.

Regarding the piping C value (friction loss coefficient) in the HW formula and the values in NFPA 13. Please see the NFPA 13-22 Handbook Appendix Section B.2 and B.2.1.3. New unlined steel pipe has a HW C coefficient close to 140, but the inner surface of the pipe deteriorates rather quickly to C of 130 and eventually to a C of 120.

Some AHJs in the past have even ruled that very old systems must be calculated using a C of 100, similar to that for piping in dry pipe systems. This was mostly meant for very old systems that were not maintained (inspected, flushed, etc.) per more modern periodic ITM servicing per NFPA 25 (ITM).

To Mark's point, FM Global's limit on hydraulic calculation velocity we 20 fps. They later removed that restriction on the concept that high water flow velocity was self regulating in the amount of high pressure loss due to friction that would develop within the piping system calculations.

I was around when IRI and Kemper insurance companies had hydraulic calculation rules but I can't recall off hand if the velocity limit was 32 fps. Mark is most likely correct regarding IRI.

From my classes teaching the concepts of sprinkler system hydraulic calculations, I have found it very helpful to look at the entire relationship between the most remote sprinkler, individual sprinkler flows, and the maximum velocity developed in calculations. Significant sprinkler flow "over-discharge" compared to the minimum require sprinkler flow, indicates significant "system imbalance"

Some designers chase the concept of getting the total system pressure demand below the available water supply pressure at the system demand flow (a safety margin). However, they may overlook the significant over discharge developing at sprinklers flowing in the area of application. If possible, the concept of "system balancing" should not be overlooked. A high velocity value in a sprinkler main can indicate two things. First, a pipe diameter that is too small, and second, significant "system imbalance".

In other words, system balancing is a true road test of the Hazen-Williams formula. Although flowing water velocity is not part of the HW formula or required in the hydraulic calculations, you can use this value to check the system imbalance of individual sprinkler overdischarge compared to the system pipe sizing, friction loss values and the total required system pressure at the water supply.

A good explanation of this concept falls into computer hydraulic calculations that in theory shift the area of application one sprinkler at a time to find the most demand area of application. Please see the NFPA 13-22 Handbook Appendix Section B.2 and B.2.1.3.

You may have noticed a good teaching tool is to hydraulically calculate sprinklers in the same area of application design, but trying four (4) cross main location scenarios using central-fed, side-fed, a main loop and a gridded system design.

Sorry for the War and Peach commentary, Joe. You just happened once again to hit upon a very interesting and important topic. Especially regarding the younger designers in our sprinkler industry.

Comments are closed.

Understanding the Hazen-Williams Formula

ALL-ACCESS

SUBSCRIBE

AUTHOR

FILTERS

ARCHIVES