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# DIVERSITY FACTOR - HEAD PUMP - CHILLED WATER SYSTEM

## DIVERSITY FACTOR - HEAD PUMP - CHILLED WATER SYSTEM

(OP)
Hello everyone,

I am new to forums, I hope you can help me solve a question that I have had for a long time, which is not directly found in books or websites.

I have a variable primary chilled water system as you can see in the attached image, it's just a small sketch. Don't pay too much attention to details like valves, just focus on the chiller, pump and cooling coils. You can see that for each coil, its total cooling capacity and its design water flow were determined. The peak load of each coil occurs at different times. With this, if we add the peak loads of each coil, it would give 95 Tons, however, for reasons of diversity, which is 85% (here also ignore if this value is very high or low), the block capacity would be 80.75 Tons. Therefore, the capacity of the chiller would be 80.75 Ton considering the diversity of the system. I hope so far I have made myself understood.

With the block load of 80.75 Ton, it would determine the maximum flow that the pump would handle, which gives 193.8 gpm (considering a DT=10°F). Now, the question is: if I want to determine the head pump, how much water flow do I consider that passes through each coil? Is the diversity in the water flows of each coil considered to determine the head pump?

1. Multiply the diversity factor by the design flows for each coil. For example, for COIL 1 its design flow is 48 gpm, this multiplied by 0.85 gives a flow of 40.8 gpm. For COIL 2 72gpm*0.85= 61.2 gpm and for COIL 3 108gpm*0.85=91.8 gpm. I don't consider this option very viable because the diversity factor of 0.85 is applied to the entire system (for the three coils), it cannot be applied to a given coil, because if the diversity factor of only two coils is analyzed in this case , would give another factor of diversity, affecting the flow of each coil.

2. Do not take into account the diversity factor and work with the design flows at peak conditions, and work with those flows to determine the head pump. This option, perhaps in a practical way, can be viable since this can be solved with a VFD. However, analytically during the mechanical design I don't see it feasible.

3. Work with the water flows required by each coil in block time. That is, the block load in this example is 80.75 Tons and occurs on Jan 15:00, for this time the water flow required by each coil would be determined. This means determining the water flow required by COIL 1 at Jan 15:00, the water flow of COIL 2 at Jan 15:00, and the water flow of COIL 3 at Jan 15:00. This information is not given by default by the software, but it is possible to obtain the water flows at various times with software such as HAP and CHVAC from Elite. This option seems to me the most reliable, since we are working with the block load and the water flow during the block load, and the water flow of each coil during the same block load. That is to say, everything is working for a certain moment, which is the one of maximum demand, and we are not mixing peak times.

### RE: DIVERSITY FACTOR - HEAD PUMP - CHILLED WATER SYSTEM

All good questions.
I assume some load software determined the load and diversity. So that will be as accurate as your assumptions were and typically we add some safety factor. How much safety factor depends on how sure yo are. For a new building you likely know the window data well, but not for an existing building. Same for infiltration. Some diversity may be based on operating schedules, which may change. There also are different calculation methods that more or less account for thermal mass. Bonus points if you calculated correct R-values for stud walls (many use wrong values!).

You also need some capacity for heat up or cool down due to heat capacity of the system and building. A chiller also doesn't have a 80.75 ton capacity. And that capacity also changes with ambient temperature. And you also have some capacity losses due to heat gain of the system. So in your case you may end up with a 100 ton nominal capacity chiller.

A dT of 10° seems pretty outdated. More dT reduces the flow, but consider the chiller minimum requirements.

Once you have a good idea for the actual block load and flowrate, i would determine the pressure drop of the system assuming peak flow. Because lower flow is accomplished by throttling valves (increase pressure drop). So use the block flowrate, but the peak pressure. Again, safety factor and a pump comes in nominal sizes and always will be a bit larger than needed. Also use the manufacturer sizing software to account for the water temperature. chilled water is harder to pump. Same for hydronic sizing, make sure you use chilled water and not standard water.

A peak in January sounds like you are in the southern hemisphere?

I think I provided more questions than answers....... but I hope it gave you some ideas.

### RE: DIVERSITY FACTOR - HEAD PUMP - CHILLED WATER SYSTEM

(OP)

Yes, I'm indeed in the southern hemisphere. The value of DT 10 and other values (water flows, diversity, capacities, etc.) are from a fictitious example. The idea was to understand how the head pump would be calculated and the use of the water flows.

Let me see if I understand... You told me to use the peak water flow in each coil to determine the head pump, that is, I use 48 gpm, 72 gpm and 108 gpm for COIL 1, COIL 2 and COIL 3 respectively. And to select the pump, I use the block water flow and the head (this is determined with the peak flows). Actually, this makes a lot of sense.

If I have misunderstood, please correct me. Again, thanks for your input.

### RE: DIVERSITY FACTOR - HEAD PUMP - CHILLED WATER SYSTEM

How is the cooling controlled?

By varying the water flow or some other means?

Also what happens when you turn the system on? I would presume all units will initially flow at max flow to cool the rooms down and only then start to throttle back?

So you need to cater for the occasional full flow but maybe optimise the pump efficiency for the "normal" flow.

you do also need to work out the min flow with some units off or very low flow to see if you can do this with one pump or you need two.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: DIVERSITY FACTOR - HEAD PUMP - CHILLED WATER SYSTEM

No, the opposite. Use block for flowrate, and peak (all coils peak flow) for pressure.
Typically the coil is sized to be approximately your desire. They may give you a 10.4° dT coil with a 30.2 gpm flow since coils also are made in increments and your AHU size may be given. so the coil will be larger than needed.

but you really have to judge safety factors here and there since you know how certain all your assumptions are. For example, for an old building i may assume more infiltration since quality of construction is unknown an usually bad. For a new tightly controlled building, I may assume less infiltration. No one on the internet can tell you what to sue for your design.

You also don't want to oversize and safety factor on top of safety factors. there will be some rounding up here and there and upsizing to the next unit size. Just don't overdo it so you don't end up with a 200 ton chiller

### RE: DIVERSITY FACTOR - HEAD PUMP - CHILLED WATER SYSTEM

(OP)
Thank you EnergyProfessional and LittleInch

### RE: DIVERSITY FACTOR - HEAD PUMP - CHILLED WATER SYSTEM

@EnergyProfessional, can you clarify again,
The pump head calculation to be done without any diversity factor, the ordering for a pump-based block flow with head at full flow rate? In this example, the pump sizing for 193.8 GPM @peak head. is it correct? Thank you

The problem with the world is that intelligent people are full of doubts, while stupid ones are full of confidence.
-Charles Bukowski-

### RE: DIVERSITY FACTOR - HEAD PUMP - CHILLED WATER SYSTEM

Just calculate the pressure as if all branches are in design flow. this will over-estimate the pressure loss in the main pipe a bit, but that isn't large to begin with. It will be correct for the branches. What software are you suing for hydraulics? I use Revit and there isn't a great way to reduce flow below peak design anyway. Make sure you include all the control valves. then you have the head and use your blockflow to size that pump.

But be really sure your diversity is correct! Will there be times when all AHU start up the same time and require full flow at once. If so, judge if that is acceptable to not perform 100% for each zone. Like if the building gets an hour "cool-down" phase before occupancy, it may not matter. and if you start up the system at 7am, you have no high solar and people loads, so it may be fine. There is a LOT of judgment.

FWIW, every building I ever saw with heating or cooling system was based on zone devices too small, the plant and main distribution usually is fine and bored while people sweat or freeze.

I also usually size pumps assuming I run both in parallel at design load. that still gives me redundancy (2/3 of flow) but allows smaller pumps and VFD. that way it is easier to just oversize a bit. You really have to look what the manufacturer has and what nominal sizes they offer. More modern pumps seem to rely on higher rpm and better controls and can modulate much better. Remember, your peak is only for one hour.

A lot of it will depend on your load accuracy and where you applied appropriate safety factors. If you have much safety in the load, you needless in the pumps.

### RE: DIVERSITY FACTOR - HEAD PUMP - CHILLED WATER SYSTEM

Here’s an example of a simple approach that is slightly conservative and doesn’t take much any extra effort. Let’s say you have 4 coils that each need 60 GPM, but your max load is 200 GPM.

Identify your critical run, and do the pressure loss calc of the most remote branch at 60 GPM, when it gets back to the main and joins with another coil add in the next 60, then when it’s joins the next coil add in the next 60, but then when joining with the last coil just call it 200 (not 240) from that point back to the pumps and heat exchangers.

This lets you get the branch DP correct since you are losing a coil peak flow, and then you may overestimate a little in the mains when you peak all the other adjacent remote coils, but in the end you at least don’t size the plant equipment for a flow that doesn’t ever happen.

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