The “two-thirds” Rule for Locating Sensors to Control Variable Flow Systems

Recently, I was out in the field scoping out an existing facility for retrocommissioning opportunities.  One of the operating engineers pointed out that the differential pressure
sensor controlling the chilled water distribution pumps was located so that it sensed the pressure across the mains leaving the plant.  He had heard that you could save energy by locating the sensor two thirds of the way between the pumps and the most remote load, so he thought that relocating the sensor might represent an opportunity. But, he wasn’t exactly sure why.

For one thing, what did “two thirds of the way to the most remote load” really mean; physical distance or feet of pipe or something else?  He also was wondering why “two thirds” instead of “three  quarters” or “seven eights” or “fifteen sixteenths”?   Finally, he was curious about exactly how the point where  the sensor measured pressure impacted the energy consumption of the system.

He knew that both the pressure and flow a pump produced impacted the power it required, all as stated by the equation for pump power.

But he wasn’t sure how the relationships applied in a working system.  Finally, he wondered if there were other things to consider.  For instance, if the sensor was located at remote point in the system, what would happen if someone isolated that portion of the system for service?  And from a practical standpoint, it seemed like it would be a lot harder to remember the location of a sensor at some remote point in a 500,000 square foot facility versus a location that was in the immediate vicinity of the pumps it served.

These are all good questions and come up a lot in the field when I start talking about using a remote pressure sensor to optimize the energy consumption of a variable flow system, be it an air system or a water system like we are discussing here.  So, I thought the subject might make good fodder for a few blog posts.

As a starting point, lets consider a simple system like the one illustrated in the system diagram below.

Our discussion will focus on the distribution piping network served by Pump P1; i.e. the flow path from A through B, C, D, E, F, and back to A.  For the purposes of our discussion, I’ve made a few simplifying assumptions.

  • The reference pressure is the pressure established by the expansion tank at the suction of pump P1 and is assumed to be 15 psi (6.5 ft.w.c.).
  • The loads served by the system are identical; specifically at full load, both AHU1 and AHU2 require 400 gpm and a differential pressure of 20 ft.w.c. at the point where they connect.
  • The pumps, piping network, and air handling units are all at about the same elevation;  thus the effects of elevation on the pressure readings can be ignored.
  • Piping lengths will be discussed in terms of equivalent feet.  In other words, when I say that the distance from point A to point B is 200 equivalent feet of pipe, I’m saying that if I were to convert the resistance due to flow of all of the fittings between point A and B to an equivalent length of straight pipe, and add it to the actual length of straight pipe, it would be the same as 200 feet of straight pipe with no fittings in it.  If there were no fittings, then the distance would literally be 200 feet, but as the number of fittings increased, the physical distance associated with 200 equivalent feet of straight pipe would be reduced.

One of the key concepts that you need to understand with regard to this topic is that the pressure required to move water through a system is a function of the flow in the system.  This means that if the control valves on AHU1 and 2 are both closed, the pressure reading at the discharge of pump P1 would be identical to the reading at the tee where the supply piping splits to serve the two AHUs, even though the tee is three hundred equivalent feet away from the pump.  (Remember, we have assumed that both points are at the same elevation, so the impact of elevation on pressure can be ignored).

If the control valves in  the air handling units start to open, the pressure at the tee will start to drop relative to the pressure at the pump.  The magnitude of the drop will be a function of the flow rate.  Common wisdom is that this relationship is a “square law”.

In other words, if you reduce the flow by 50%, the pressure drop associated with the flow drops to 25% of what it was (50% of 50%),  assuming nothing changed in the system (no valves changed position, the piping was not modified, etc.).  Research has shown that for most real piping systems the exponent is more like 1.89 versus 2, but out in the field, we probably couldn’t measure the difference as illustrated by the following graph.

X Squared vs. X to the 1.89 Power

So for our purposes, we can still think of it as the “square law” instead of the “one point eight nine law”.

Now, lets look at the pressures required by our system in two different operating modes.  In the first operating mode, the system is at full load.  Both AHUs are using 400 gpm and the pump needs to deliver 20 ft.w.c. at the tee serving the AHUs while moving 800 gpm through the mains to and from the air handling units.  The total length of the piping circuit is 600 equivalent feet;  300 equivalent feet from the pump discharge to the tee that serve the units and 300 equivalent feet back to the pump suction.

In the second operating mode, one AHU has shut down but the other is still operating at full load. This means that the pump still needs to deliver 20 ft.w.c. at the tee serving the unit, but only needs to move 400 gpm through the piping network. The two operating modes are compared in the following table.

Note that the friction rate for the second mode is significantly different from that associated with the first mode.  In the next post, we will look at the results in more detail.

David Sellers
Senior Engineer – Facility Dynamics Engineering

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8 Responses to The “two-thirds” Rule for Locating Sensors to Control Variable Flow Systems

  1. nadim chabab says:

    Further your above valuable notes, please note that in our application 2 way constant flow pressure independent control valves are installed. I beleive the theory of two-third still applicable. but I would like to conifrm what do we mean by two third. If for example the pump pressure head is 3Bar, then the two third is 2 Bar, So the sensor should be installed in a location in the longet run where the Differentail pressure is 2 Bar when the system is operating at full load???

    • Hi Nadim,

      I would agree with you that even though you have pressure independent control valves installed, the two-thirds rule concept will likley be worthy application.

      To be clear, the “two-thirds” in the two-thirds rule is a general reference to distance, not pressure. What it really is trying to say is that you should put the sensor as far out in the system as possible. In a perfect world, we would figure out which run has the highest pressure drop and then put the sensor at the end of it, as close to the load as possible.

      And in a simple system like the one in my example, you would likely do just that. Meaning you would install the sensor to pick up the pressures at C and D in the diagram. But few systems are that simple, and all systems are dynamic. So, its not out of the question that in a complex system, under some load conditions the critical branch (the one with the most pressure drop) might move around some due to the dynamics of the system. Or, someone might make a change to the system (add a load, change the setting on balancing device, etc.) that would impact which branch was the critical branch.

      So, to provide some measure of protection from problems like that, the two thirds rule is in effect, saying “don’t put the sensor all the way at the end of the critical branch; rather locate two thirds of the way there so you have a safety margin if something changes”. Two-thirds is an arbitrary number; a while back, I was talking with Chuck Dorgan about it (sort of the grandfather of the commissioning industry in a way) and he said that ASHRAE had done some research and nobody really knew where it came from, but it probalby came from a control vendor engineering bulletin.

      So bottom line, the rule could have been the “one-half” or the “five-eights” or the “three-quarters” or the “fifteen-sixteenths” rule, dependiung on how much safety margin you wanted. The idea is to put the sensor as far out the pipe as possible so that the pressure you control at reflects the square law pressure drop due to flow that occurs and minimizes the pumping energy you need use to deliver flow to your loads.

      In a working system, frequently the best way to find this point is via some field testing. Specifically measure pressures around the system at points where you can gain access (vents and drains are good opportunities for this). Do this under a number of different operationg conditions and compare what you measure to what you think you need at that point to deliver design flow. Most of the time, a pattern will emerge that will lead you to both the appropriate location for your sensor and also the ideal set point to maintain.

      Hopefully this clarifies things and answers your question, but if not, don’t be afraid to ask additional questions.



  2. Rajulukose says:

    Respected sir,3 floor bldg pump room roof 3rd floor bldg length 80mtr 50mtr width with 4nos riser how to calculate diffrencial sencr for chilled water system.Raju.hvac supervisor .Bahrain

    • Hi Raju,

      Its been a busy week so not much time to devote to the blog lately. If I am understanding you correctly, you are trying to figure out the correct set point and location for a differential pressure sensor in an existing chilled water system. If that is the case, then the fast answer is that instead of doing a calculation, you can do a few tests and take a few readings and let the building tell you the answer.

      Specifically, you would start the process by going around and taking differential pressure measurements at the various loads on a day when the system has a pretty good load on it (i.e. control valves are allowing a lot of flow). Even if there are not gauge ports in the piping, usually, at least in the States, you can find a point to connect a gauge, often in the form of a vent or drain connection. When you take the reading, it would be good to note the position of the control valve if you can and also the pressure being produce back at the pumps if possible. The latter can often be handled automatically by running a trend or using a data logger.

      Once you have done that, when you compare the readings, you will probably see a pattern that points to the critical load or loads. One of those loads is the probably the location for the sensor. If it is a complex system, them maybe you put 2-3 sensors in at various points and let the control system pick the worst case.

      In terms of the proper set point to maintain at those locations, the exact number will depend a bit on what is in the pipe between the two points where you measured pressure. Say for instance you picked up the high pressure at an air vent ahead of the control valve serving the coil and the low pressure at the drain on the leaving side of the coil. That would mean that the pressure drop was generally composed of the control valve, the pipe in the circuit between those two points, and the coil pressure drop.

      Typically, the pressure drop in the piping is fairly insignificant in the context of the coil and the control valve. So, you could get in the ball-park for the right number by looking up the coil and control valve performance data in the submittal drawings and then adding a little bit more to that value to come up with your set point.

      So in terms of the example above, you might look up the coil submittal or call the coil manufacturer and discover that at design flow the coil pressure drop was 12 ft.w.c. (about 35 kPa I think; not sure what your units system is). And, if you looked up the valve, you might discover that it had a flow coefficient that resulted in a wide open pressure drop of 10 ft.w.c. (about 30 kPa if my little unit conversion program is doing its thing correctly). (If you need to know how to use a valve flow coefficient to calculate the valve pressure drop from the flow, the MCC Powers valve sizing bulletin I link to from the resources on the blog or the Honeywell Gray Manual I link to in one of the posts has that information in it).

      So, based on your research, you now know that you need at least 12 plus 10 or 22 ft.w.c. (66 kPa) of differential pressure at the points where you measured it to deliver design flow to that particular load. If you add 1-2 feet to that to cover the pipe and fittings in the circuit between your two measurement points, you probably have a pretty good set point to start with.

      Once you have the necessary sensors and control logic in place, you can use trend data to help you fine tune the set point. Say for instance on a hot day, you discover that you are not quite holding the required supply temperature from the coil, even though the valve is wide open and that back at the central plant, you still had reserve pumping capacity available (meaning the pumps had not been driven to full speed). In that case, I might increase the set point by 1-2 ft.w.c. (3-6 kPa) and keep watching what happened until I found something that worked on that design day.

      In contrast, if you noticed that the control valve to the load was always throttling a little bit, even on a heavy load, then you might conclude that you could drop the set point 1-2 ft.w.c.. The point is you can use the building operational data to fine tune the system.

      So far, I have discussed this as if you were trying to figure it out for an existing system. But the reality is you can use a similar technique for new system and then fine tune it via the commissioning process once it comes on line. The only part of the technique that is different for new construction is that you either have to make an educated guess regarding where the critical load(s) are or do the hydraulic calculations. Typically, unless a load has a very high pressure drop relative to the others, the critical loads will be the ones with the longest piping runs. So, you often can decide where to locate the sensor with a bit of engineering judgment, especially if you provide a couple of them at different locations.

      I need to head off and do something else at this point, but hopefully this gives you enough to go on.

      Thanks for visiting and supporting the blog and for asking a good question.


  3. sureshbob says:

    HI This is Suresh,

    I have one AHU which is having the two branches duct in different length. Now where I have to install the pressure sensor to drive the VFD.
    Note : In all Duct have the VAV’s and 1st Branch length is 30 meters 2nd Branch is having 15 meters.

    • Hi Suresh,

      Sorry for the slow reply; I have been pretty overwhelmed with stuff the past few months and have not even had a chance to post anything.

      As you probably suspect, the concept regarding where you would locate the sensor for an air handling system are identical to the ones I discuss for a pumping system in the post you are replying too. To find the exact, right location, you would have to do a lot of math of course. But generally speaking:

      1. I would pick a point in the longer duct because that is more likely to be the duct run that set the fan system static. So you might select 2/3 of the physical distance down that duct. Once the sensor is installed, you could fine tune the set point there as necessary to ensure that you had adequate pressure everywhere else. Ideally, there would be one terminal unit that was nearly wide open someplace in the system.

      2. You might consider installing a sensor in both duct branches about 2/3 of the physical distance down the duct and then using the software to select the sensor that required the highest fan speed to meet set point.

      3. Either way, in an air handling system, unless it is a small system or a system, I actually prefer to control for the pressure at the discharge of the fan and then reset that set point based on what is going on at the remote location. The reason I do that is that if you try to simply control the system based on the remote sensor, you may find that there is a significant lag between when the fan speed changes and when the at the remote location sees the change and reacts to it. That is because to pressurize the duct, the fan has to move enough air through it and the holes in it (which we call diffusers) to set up a new pressure gradient and that can take some time. In some ways, the fan is trying to inflate a really leaky balloon, so the volume of air it has to add to change the pressure is related to much more than just the volume of the duct. I discovered this the hard way by blowing up a duct and then realizing what David St. Clair meant when he said in his book about loop tuning that “it is all about the lags”. (Here is a link to a blog post that hooks you up with the book if you want So, a loop running based on a signal picked up right at the fan discharge is fairly immune to the transportation delay issue (along with a couple of other things). And using the remote sensor to optimize its set point kind of lets you have the best of both worlds.

      Hope this is helpful and again, sorry for taking so long to respond.


  4. eyad says:

    dear Sir,

    what do you mean by two-third distance ? should i calculate the whole distance from pump discharge to the furthest point of networks then to put sensor on 2/3 of it ? or to calculate load as tonnage then to take 2/3 of it ?

    please could you clarify by example

    thank you for patience .

    • Hi Eyad,

      Sorry for the delayed response; things have been busy for me and I am behind on responding to comments.

      The short answer to your question is that the two thirds rule is a distance based rule vs. a tonnage based rule. So that means you would want to locate the sensor at the point that was two thirds of the way to the hydraulically most remote load.

      But, like most engineering decisions in something as dynamics as a building, that is not as easy to figure out as it sounds. The further out the system that you go, the more energy you will save.

      But, if it turned out that you had not picked the hydraulically most remote load after all, or it moved due to system dynamics or changes in the use profile of the facility then if you were way out at the end of the system, the set point you maintained there may not be the one you needed. So, the two thirds rule is a sort of compromise targeted at maximizing the saving you achieve while minimizing the risk you are taking in terms of the location and set point you pick and the system dynamics that can cause that to not always be the right place or number.

      If you really were going for the most optimized sensor location, then you would identify the load on the system that required the most pressure from the pump serving the system to deliver its design flow rate; i.e. the load that was used to establish the design pump head. This load if often termed the most “hydraulically remote” load.

      Usually, but not always, the hydraulically most remote load will be the load with the most feet of pipe between it and the pump and we frequently assume this is the case when we do our pump head calculations.

      But for large, complex variable flow systems, figuring out exactly which load is the hydraulically most remote load can be a complex undertaking. In addition, as a result of system dynamics, the hydraulically most remote load can move around.

      For instance, if the load that is determined to be the hydraulically most remote load on the design day at the design hour with all loads in operation is off line and there is not flow to it, then it is no longer the hydraulically most remote load. The critical load will shift to a different load that is in operation and requires the most pump head to deliver its required flow rate to it at the current operating condition.

      In a general sense, what the two-thirds rule is saying is that the further out the system you put the sensor controlling the speed of the distribution pump, the more energy you will save. That is because when the sensor is at the end of the system it “sees” the pressure drop due to flow that is required by the current operating condition and automatically drives the pump to deliver that much pressure in addition to the pressure it is trying to maintain at its installed location.

      Since pressure drop due to flow varies as the square of the flow, you can capture the bulk of the benefit associated with using a remote sensor. You can see this in the table that is provided at the end of the third post in the series. Notice how locating the sensor at the two thirds point captures 77% of the possible savings compared to a base case, which is a pump selected for best efficiency operating at the reduced flow condition associated with the system at 50% load.

      So, as I indicate in the last post in the series, the two thirds rule could have been the three quarters rule or the fifteen sixteenths rule or the twenty-seven thirty-seconds rule; it’s simply a rule of thumb that tries to simplify a complex engineering decision in a way to captures most of the potential savings by also protects you from putting a sensor at a load that turns out not to be the hydraulically most remote load after all and having to deal with the consequences of that.

      As an aside, I should mention that Chuck Dorgan actually did a little research project for ASHRAE to try to figure out exactly where the two thirds number came from. It turns out that, to the best he could tell, it came out of a technical application bulletin one of the major control vendors had developed to guide their field technicians and provide a easily remembered number that would save energy but keep things “safe” in terms of ensuring the performance of the system.

      Hope that helps; thanks for visiting the blog.


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