K Factor Fire Sprinkler

[Melanie Wendelberger]

Infire protection engineering, the K-factor formula is used to calculate the volumetric flow rate rate from a nozzle. Spray nozzles can for example be fire sprinklers or water mist nozzles, hose reel nozzles, water monitors and deluge fire system nozzles.

K-Factors have also previously been calculated and published using the United States customary units of pound per square inch (psi) and gallon per minute (gpm). Within the United States, US measurements are still often used instead of metric.[3][4]

Care should be exercised not to intermix K-factors from metric and Imperial/US units, as the resulting factors are not equivalent or interchangeable.[5] In case of mix-ups, results can be catastrophic[broken anchor].

Mixing K-factors is acceptable, however, you will want to either designate areas that certain K-factors are to be used, or be very knowledgeable about fluid dynamics. If you have one K-factor in one area, and another K-factor in another area- both areas should be calculated. This also applies to standard and extended coverage in portions of systems.

I had one instance in which I was designing a deluge system for an industrial chemical complex that was on city water, and I was trying to satisfy and insurance underwriter's safety cushion requirement. I had to use a plurality of screwed pipe sizes and orifices in order to minimize over-flow and over pressure situations, as every head was required to flow.

I should add, after reading DAN W's comment above: the example I gave was a directional nozzle deluge system for a pumping station near an exterior dock; in which non-flammable non-combustible liquids were being pumped- mainly ammonia.

Adding to what others have said.

- Mixing temperature ratings is permissible, and fairly common. For example: NYC apartments and condos, I would use regular temp heads throughout, but switch to medium- or high- temp if the sprinkler is too close to a stove, dryer, fireplace, etc.

- Mixing k-factors is NOT allowed for "balancing" or to try and reduce your hydraulic demand. It is (in general) allowed if you need a different k-factor for a specific reason. However - the requirement to separate different k-factors is "by room" or "by area" not by sprinkler system. It is important to review NFPA definitions for these, as the NFPA definitions may not align with an Architect's "common sense"

- As I understand it, mixing Ordinary Response sprinklers with FR/QR sprinklers is NOT allowed.

Mixing K-factor is not a good idea, unless you have good reasons for it (such as a deluge system where the K factor may different depending on the area for the entire surface coverage, but this is not a sprinkler system...).

Mixing different temperatures can be deemed necessary because of possible change of local room temperature (sprinkler heads next to a heater, below a skylight...).

In the 2019 Edition, the chapter is now 9.4.2 (& 9.4.2.5 for a list of examples), and not 8.3.2 (& 8.3.2.5).

You could mix K-factor in the same room (as well as T rating) if you have a change of occupancy that would require this particular change.

For example, if you have a processing area (let's say OH Gr 1 activity with ordinary rated temperature sprinkler heads), but a dedicated storage area representing a higher fire challenge (a few racks, or a idle pallets storage). In that case, you might need to have larger orifice sprinkler heads and/or higher temperature rated sprinkler heads.

But there are rules, as indicated above, because you will need to extend the most demanding area beyond the area of protection (or provide a draft curtain/fire barrier).

This is part of chapter 20.10 of NFPA 13 (2019 Edition) : Adjacent hazards or design methods.

Overall, this discharge density in most systems and settings governed by NFPA 13 is based on the occupancy hazard. However, various factors like sprinkler response types, system types, and architectural features can alter the exact number. Nevertheless, this graph illustrates the essential requirements:

There is much more to hydraulic design, such as accounting for gravity and friction based on the pipe material, etc. You can read a more detailed review of fire sprinkler hydraulic design in our previous blog.

The SIN is more useful than just knowing the K-factor because, in addition to identifying that number, it also reveals every crucial sprinkler characteristic except activation temperature and finish.

Where replacing residential sprinklers manufactured prior to 2003 that are no longer available from the manufacturer and are installed using a design density less than 0.05 gpm/ft2 (2.04 mm/min[2.0 in NFPA 13]), a residential sprinkler with an equivalent K-factor ( 5 percent) shall be permitted to be used provided the currently listed coverage area for the replacement sprinkler is not exceeded.

Again, the best option is to replace a sprinkler with the exact same model and install new ones with the precise specs (including K-factor) called for by the system design. And the easy way to do that is by selecting the appropriate SIN with the preferred finish and necessary activation temperature.

In this article, we are looking at the flow of water through an orifice, and we will define the orifice as an opening (with a closed perimeter) in an element of a flow system. This orifice will be a fire sprinkler head or water mist nozzle in a fire protection system. We can use the k-factor formula for almost any rounded orifice.

In 1644 an Italian physicist Torricelli (a pupil of Galileo and also invented the barometer), discovered that the flow through an orifice varied to the root of the pressure and later determined the following basic relationship:

The formula above is theoretical, and once we take into account the effects of friction, turbulence, and the contraction of the water stream, the formula can be simplified to what we know as the k-factor formula for fire protection systems by reducing its complexity to a single constant "k".

When we start any hydraulic calculation for water-based fire protection systems such as fire sprinklers and water mist systems, the k-factor formula is the first one we will need to use. As it is so fundamental, all fire protection engineers must understand how it works. The formula calculates the discharge flow from the nozzle (fire sprinkler, water mist or deluge nozzle) in its most common form. If we are given the head pressure and k-factor, we can also calculate the k-factor or the pressure required with this formula.

The units which we use are essential and much not be mixed. You much also be very cautious with the k factor and ensure that you get the correct value for a metric or imperial calculation. The units for both are given below:

We can also use K-factors for many other applications in fire hydraulics, such as flow from a fire hydrant, wet riser outlet, hose reel or foam monitor. The list is almost endless, so being familiar with the above formulas is essential.

Often K-factors are given as an imperial value in gpm/psi. This value cannot be entered into FHC without first converting to its metric equivalent L/min/bar. To convert gpm/psi to L/min/bar we need to multiply by 14.275 to ascertain an approximate value.

For many standard types of sprinklers, the design standards such as EN 12845 & NFPA 13 specify the standard k-factors and minimum pressure, which should be used for different Hazard classifications and design densities. For all other types of sprinkler heads, the manufactures data sheet should be referred to for the k-factor and minimum head pressure.

The graph below shows the relationship between the k-factor, pressure and flow. You can clearly see from this that the flow from the head or nozzle increases for the same pressure with a high k-factor nozzle. We can sometimes use this to our advantage by selecting the correct sprinkler head k-factor to provide the design density required with the minimum energy requirement (water pressure).

As an example, if we have the pressure of 1.50 Bar and a k-factor of 50 the flow rate would be 61.20 L/min for a k-factor of 100 it would be 122.50 L/min and with a k-factor of 150, the flow rate would be 183.70 L/min. You can see that the flow has insecure by about 61 L/min each time we changed the k-factor by 50, this is because the pressure has remained the same at 1.50 Bar and if you look at the k-factor formula above the pressure is squared which will give us 1.225, this is then multiplied by the head k-factor in this case 50, 100 and 150 in our example. As the k-factor has increased by 50 each time the increase in flow has also increased by the same amount.

To select the appropriate temperature rating for the sprinkler, one must be careful to match the temperature rating of the sprinkler to the maximum expected ceiling temperature to avoid inadvertent discharges. See table below from NFPA 13 (2016 Ed) Table 6.2.5.1 Temperature Ratings, Classifications, and Color Codings.

Additionally, FM Global Data Sheet (FMDS) 3-26, Fire Protection Water Demand for Nonstorage Sprinklered Properties, requires the use of high temperature sprinklers for all dry pipe systems in Section 2.1.1.1.

K-factor is a mathematical constant established by the sprinkler manufacturer that relates the flow of water that is discharged from the sprinkler at a given pressure. When water is discharged through the sprinkler orifice, the orifice diameter and the hydraulic characteristics of the orifice determine the flow achieved through the sprinkler at a given pressure. An increase in the K-factor of a sprinkler corresponds to a higher flow (gpm) at a given pressure, and a decrease in the K-factor corresponds to a lower flow at a given pressure.

K-factors may be chosen based on water supply characteristics. For a supply with higher available water volume at a lower pressure, higher K-factor sprinklers can be used. For water supplies with lower water volume available at a higher pressure, smaller K-factor sprinklers can be used.

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