First - last week I put together a draft PDF cheatsheet for fire alarm design in elevators. Lots of great response to that tool. One major flub on my part - I didn't actually link to it. Here's an actual working hyperlink (fingers crossed).
K-Factor & Pressure Versus Area & Density
One of the hand calculations I do frequently when laying out sprinkler systems is comparing the k-factor, minimum pressures, and resulting flow for the sprinkler. It comes up all the time with residential-style, extended coverage, special application, and storage sprinklers.
Many hydraulic calculation programs do this comparison automatically. That being said, it is important to understand and compare the minimum flow from sprinklers for a hydraulic calculation.
Reducing unnecessary flow from a sprinkler reduces the total calculated flow from a system, which has major impacts on pipe sizing for some branch lines, cross mains, feed mains, and even the underground service size.
Driver #1: K-Factor and Minimum Pressure
There are two drivers for the actual minimum flow that must come from a fire sprinkler.
The first driver is the K-Factor and Minimum Pressure. This equation is
Q = k√P
Q = Flow (gpm)
k = Sprinkler k-Factor
P = Pressure (psi)
With a 5.6 k-factor and a minimum pressure of 7.0 psi (as is required by NFPA 13), we get a flow of 5.6 x √7 = 14.8 gpm
There's a wide array of k-factors available on the market, and a wide variety of minimum sprinkler pressures too. Extended coverage, residential, attic, storage, and ESFR all vary in required minimum pressures.
Driver #2: Area and Density (When Using the Density/Area Design Approach)
When reviewing cutsheets for sprinklers it's easy to take a k-factor and minimum pressure and assume that you then know the minimum requirements for a sprinkler and you're done. If you're using design criteria that only uses that approach, then you may actually be done.
However, if you're using the density/area approach of NFPA 13 then you also have to ensure the sprinkler is actually delivering the minimum density for the area its protecting.
It's easy to skip over this step. If you've ever laid out residential-style sprinklers, then you probably already know this.
Residential-style sprinklers can have small k-factors and relatively low minimum pressures to cover a reasonable floor area. However, these sprinklers can be used in NFPA 13, 13R, or NFPA 13D systems. 13R and 13D specifically can allow densities less than 0.10 gpm/sqft. The cutsheets often offer the minimum pressure for a given k-factor and floor area coverage, but the cutsheet may be assuming a 0.05 gpm/sqft density.
When we have higher densities (such as residential-style sprinklers in an NFPA 13 design), we have to consider this second driver for sprinkler flow.
The equation for density/area coverage is also straightforward:
Q = D x A
Q = Flow (gpm)
D = Minimum Density (gpm/sqft)
A = Area Covered by Sprinkler (sqft)
A sprinkler spaced at 15 ft x 15 ft with a minimum design density of 0.10 gpm/sqft requires a flow of 22.5 gpm.
With this, a k-5.6 sprinkler at 7 psi, spaced 15 x 15 feet with a 0.10 gpm/sqft density will actually need to flow 22.5 gpm.
Here's how this scenario looks when graphed:
The red line above represents the hydraulic pressure/flow relationship that a k-5.6 sprinkler offers. As the minimum pressure increases, the flow will increase. Similarly, as the flow needed through the sprinkler increases, the minimum pressure required to deliver that flow also increases.
For this scenario, the actual flow through the sprinkler must be the higher of the two amounts, or 22.5 gpm which will occur at 16.1 psi (see the blue lines above).
This means for a light-hazard, typical sprinkler we're demanding that the pressure at the sprinkler is over double what the code minimum is!
Will this difference break your calculation? No, it won't.
But let's look at another example where these decisions become a little more critical.
Take a Viking VK460 residential sidewall sprinkler. It's a 5.8 k-factor and has varying coverage areas with varying pressure and flow requirements.
Based on a 12 ft x 12 ft spacing, the minimum pressure required under the product data is 7.6 psi.
The Sprinkler-Driven minimum flow becomes Q = k√P = 5.8 x √7.6 = 16.0 gpm.
Assuming an NFPA 13 design, the Density-Area minimum flow becomes Q = 0.10 gpm/sqft x (12 ft x 12 ft) = 14.4 gpm.
In this scenario, the flow is Sprinkler-Driven. The actual flow through the sprinkler is driven by the k-factor and minimum pressure, and not the density/area point.
This same sprinkler, however, at a 16x20 spacing, looks a little different.
Based on a 16 ft x 20 ft spacing, the minimum pressure required under the product data is 20.1 psi.
The Sprinkler-Driven minimum flow becomes Q = k√P = 5.8 x √20.1 = 26.0 gpm.
Assuming an NFPA 13 design, the Density-Area minimum flow becomes Q = 0.10 gpm/sqft x (16 ft x 20 ft) = 32.0 gpm.
The demand through this sprinkler now becomes density-driven, and notice the actual pressure required to achieve this density is now 30.4 psi. If you have a poor water supply then these decisions can begin to really impact your hydraulic calculations.
Do you need to assess whether your sprinklers are driven by the k-factor and pressure or density/area? No - many hydraulic calculation programs cover this already.
These differences to become critical though with sprinkler selection, reducing the system demand, reducing the system pressure, and refining a design to end up with the most efficient system possible as an end result.
This Tool Available Now
If you're a Toolkit user, you can give this new tool a try today. Click here for online access to it.
This tool comparison tool allows different k-factor inputs, minimum pressures, density and areas with immediate graphed comparisons.
This tool will also be available for download with the latest Toolkit release here in a few weeks. More on that to come.
Thank you for reading and have a great, safe week!
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Joseph Meyer, PE, is a Fire Protection Engineer in St. Louis, Missouri. See bio on About page.