The “two-thirds” Rule; Some Bottom Lines

In the three posts preceding this one, we have been  exploring the “2/3 rule” for locating the sensors controlling pump and fan speed in variable flow systems.  While we have been exploring this topic in the context of a simple variable flow chilled  water distribution loop, the concepts also apply to variable flow air handling systems.

The bottom line is that the further down the distribution network (towards the load) that we move the sensor controlling a variable speed pump in a variable flow application, the better the optimization of the system will be. If there was only one load in the system, then the ideal location would be at the point where the load connected to the mains. Unfortunately, most of our systems are much, much more complicated than this and contain tens or even hundreds of loads.

Figuring out which load represented the worst case pressure drop requirement could be quite time consuming and would probably vary with the operating conditions. So, being practical sorts and being a bit math phobic, we application engineers came up with a rule of thumb that serves us well; locate the sensor 2/3rd of the way from the pump to the load. Why exactly someone picked 2/3 instead of 3/4 or 7/8 or 5/8? I don’t really know; any of those ratios would probably have worked out.

Like all good rules of thumb, the 2/3 rule has enough slop in it to keep us out of trouble most of the time.  For instance, no matter what you interpret 2/3 to mean, be it physical distance, hydraulic distance, radial distance from the pump location, etc. a sensor located based  on any of those interpretations will most likely deliver a working system that uses less energy than one with the sensor at the pump discharge.

But, like all good rules of thumb, the 2/3 rule is not the optimized answer for each and every situation.  For a one load system, having the sensor at the load is the best answer.  For a modestly complex system, the perfect answer and the 2/3 rule could be with in fractions of a decimal place of each other.  For a complex systems with complex hydraulics, a bit of analysis may reveal that multiple sensors at multiple locations can be justified.

How do you know which way to go?  Engineering judgment, which to some extent is what they are  paying us for when they hire us.  How to do you obtain engineering judgment?  By reading things like this blog and other resources and by taking the time to occasionally analyze something back to the fundamentals until you own it at that level.  Once you own something at that level, you will find that your intuition will lead you in the right direction.

And, there is always something to be learned in this business by taking the time to do a little math and think things through, even though we don’t have the luxury of doing that on every project.

So, in parting, I would encourage you to take the time to do the math to answer your own questions on occasion, or at least see  if somebody else has answered them.  If you have a burning curiosity to understand why something works use that fire to understand it  or explain it to someone.

That’s all I did to create this string of posts, and guess what, I learned something in the process.

David Sellers
Senior Engineer – Facility Dynamics Engineering

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5 Responses to The “two-thirds” Rule; Some Bottom Lines

  1. Nice job David. And to think I went to all the trouble of
    concocting that homework problem for my HVAC class when you had
    done it already! I ran them through one more step in a hypothetical
    3 load circuit: what’s our pumping savings when we optimize the dp
    setpoint so that the critical load just has its valve at 100%
    open…. I appreciate the light shed on the “1.9” rule as well.
    Keep up the good work. Jason Burbank, P.E.

  2. Marcus Hay says:

    One thing is not clear to me. In a system where you have multiple loads coming off of the pipe network, is the transducer to be placed 2/3 of the way between the pump and the first load or 2/3 of the way between the pump and the final load.

    I came to this blog posting as I received a design that had the DPT placed at the very end of the line so that it was measuring the pressure differential across the last AHU in the system only. That didn’t look right to me but I have limtied experience in this and decided to seek some information.

    Your blog is very informative and I will bookmark it and read more of your postings. Thanks,

    • Hi Marcus,

      Glad to hear that the blog is helpful to you.

      The answer to your question is probably “it depends” which as Jay Santos would point out (one of FDEs founding principles), is the answer to most HVAC questions.

      In a perfect world, if you had a system with multiple loads and placed the sensor at the most remote load in terms of system hydraulics, then you would only need one sensor and it would be at that location.

      But in a real system, there are a couple of things to consider.

      One is that the physically most remote load may not be the hydraulically most remote load. Meaning that a load that is close to the pumps physically but which is constricted in terms of pressure drop due to undersized piping or a lot of fittings may require more pressure at the piping mains than the load that is physically further away but served by an oversized straight run of pipe with very few fittings.

      Another issue is that for variable flow systems, the dynamics of the system can make the load that is hydraulically most remote shift around. That is because much of the pressure required to deliver flow to the load is a result of the pressure drop due to flow in the piping network serving the load. And the pressure required varies with the square of the flow, so the relationship is non-linear.

      For instance, if the load is turned off and using no flow, then there is absolutely no pressure drop in the piping to it, even if the pipe run is thousands of feet long. So the pressure you would see at the end of the run would basically be the pressure where they connected to the mains (assuming no elevation change).

      So for complex systems, selecting a single point to sense pressure can be tricky, thus the general recommendation to place the sensor “two thirds” of the way out the system. But whom ever came up with that could also have set “thirteen sixteenths” or “five eighths” or “twentyfive thirty seconds” instead of “two thirds”.

      What the rule is really trying to say is that choosing the sensor location is a balancing act between putting the sensor at the hydraulically extreme end of the system (which in theory delivers the most savings) or at some point that is significantly out the system, but also not at the end, thereby providing a safety factor in terms of the changes that occure due to system dynamics.

      For complex systems, I typically put in several sensors at locations I select based on my pressure loss calculations. Or, if I have a robust enough system to handle the necessary network traffic, I might use some for of a “trim and respond” strategy where I keep dropping the pump pressure until one or more of the loads have control valves that are nearly fully open (meaning they are on the verge of not being able to provide the required flow at the current load condition with out more pressure from the pump).

      You may also want to consult the free Cool Tools resource that is available from Energy Design Resources on their web site at

      The resource consists of a chiller plant design guide ( that I believe woudl provide additonal guidance regarding your question.

      In addition, the resource includes a pipe size optimization tool and a chiller life cycle cost bidding tool (

      Hope that helps but let me know if you have questions.

      Hope you have a nice weekend,


  3. irshad ahmad says:

    Dear Mr. David,
    I am a Hvac Mechanical engineer. I am facing one problem that chilled water always run on 56 Hz. It not responding as per the pressure transducer which installed at 2/3rd of most remote line. Our set point 2 bar. Also most of the 2 way valve closed. But it running on almost full load .
    Can u advise me what are main reason of not responding the vfd as per set poinr.

    Irshad ahmad

    • Hi Irshad,

      There probably are a number of things that could be causing the problem you are challenged with. But the thing that struck me as I read through your message is that the set point for the control process seems really high to me, assuming I am doing the unit conversion properly. Many of the systems I have worked with have a design requirement that, I think, would be 25-50% of the value you indicate you are controlling for.

      The pressure difference across the mains typically needs to be high enough to provide the pressure required to deliver the design flow through the branch piping, control valve, and heat exchanger for the load with the highest design pressure drop. In my experience, the heat exchanger and control valve would dominate this and a design rule of thumb is to select the control valve so that it has a wide open pressure drop approximately equal to the load it is serving.

      So, you might start by checking what the design pressure drops are for your typical loads and what the wide open pressure drops are for the control valves serving them. The set point needs to be at least equal to the sum of the two highest values plus maybe 5-10% more for the branch piping unless the branch piping runs to the loads from the mains are extremely long.

      You could simply try doing an experiment and see what the building has to say about the issue. Specifically, you might try gradually lowering the set point a bit at a time and watch how the system reacts. You may discover that you can satisfy the loads on a design day with a lower set point.

      Other things that I have seen cause a problem similar to what you are seeing include wiring or programming problems where the sensor you think is controlling the drive is actually not wired to the appropriate input or the control process is not programmed to use the correct input. For instance, if the control programmer mistakenly picked the system fill pressure input as the reference for the control loop, the drive would probably ramp up to full speed and just stay there because the speed of the pump would have very little impact (in theory, no impact) on the system fill pressure.

      There could also be issues with how the drive parameters are set up; most drives these days have a lot of programming settings and its not out of the question that one of the drive parameters was not properly set up.

      Its also possible that something has the drive speed locked to a fixed value. Frequently, there are a number of places this can happen, including an operator over-ride that is not obvious, a manual override switch that is in the “hand” position instead of the “auto” position on the circuit boards where the control system output wires are connected, or a manual over ride in the drive itself.

      Hope this helps,

      Best for the New Year,

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