Calculating K Factor (odd oriface size)

[Glorified Plumber 84]

I've got a weird design I'm working on, and it's not for a fire sprinkler system. The head has a 2.5mm or 0.0984252 inch orifice........how can I convert that to a k factor? The head itself has a recommended operating range of 1.5gpm at 45 psi. Applying fire sprinkler math, the k factor would .2238 or something........but any advice would be appreciated!

 

[cdafd]

Is it just one sprinkler protecting an oxygen tank or chlorine or other????

Or what is it for?

 

[Danefre]

My understanding is that a K-factor is just the nominal factor that relates flow and pressure, based on the famous formula. It's derived as shown:

(from the Viking Technical Article)

Q = av

Q= flow in cubic feet per second
a= the cross sectional area in square feet
v= velocity in feet per second

The formula for area in square feet is:
a= πD² ÷ 4

Converting the formula to find the area in square inches the formula is modified to:

A= πd² ÷576

Velocity can be expressed as: v= √2gh where:

v= velocity

g= acceleration due to gravity (32.2 ft/sec)

h= the head in feet ( 2.31P)

The theoretical flow from an orifice formula can be written as : Q = πd² ÷576 √2gh

Understanding that we will have to convert Q to gallons per minute the formula needs to be modified further to insert 7.48 gallon per cubic foot and 60 seconds in one minute:

Q = 60 x 7.48 x πd² ÷ 576 √2gh

When simplified, and the discharge coefficient (c) is added for the orifice, the formula is written as:

Q = 29.84cd²√P

This formula should be familiar to anyone who has evaluated a water supply by measuring velocity pressure from a fire hydrant. The formula can be reduced further to a single constant “K” for a given sprinkler: Q = K√P

During testing, the flow and pressure are measured and the K-factor is calculated. For example, if the resulting factor is within the K5.6 range (5.3 - 5.8) then it's labeled as a K5.6. That's all it is, just a factor that represents the relationship between flow and pressure in the context of fire sprinklers.

A 0.09in orifice would be about 3/32".. that just seems way too small. K2.8 is a ~ 3/8" orifice.

 

[MGXFP]

One can use the formulas above to model any flowing orifice having water as the agent. K-factors can model fire sprinklers, pipe branch lines, or entire fire sprinkler systems. Your K-factor would be 0.22 in this instance. You could also use Hazen Williams to determine friction loss since it is also used in small orifice systems like lawn irrigation systems.

 

[Glorified Plumber 84]

Thanks all, this is for an outdoor perimeter home protection system. The manufacturer's calculation method is "Add all the sprinklers x 1.5gpm and bam you've got your flow needed!" This doesn't account for overage/friction loss, so I wanted to provide some more in depth calcs but to do this in our program we need a k factor to assign to the sprinkler head.

 

[cdafd]

Glorified

In my opinion will not work

Look at other ways to make a house safer

 

[TravisMack]

Glorified

In my opinion will not work

Look at other ways to make a house safer

I can't agree with this more. We look at water supply durations of 1-3 hours when looking at reliable and tested interior sprinkler systems. These deliver anywhere from 10-200 gpm / sprinkler depending on application. These outside perimeter systems are just feel good systems that likely won't do anything. Something may be better than nothing, but don't rely on this to save a building. And 1.5 gpm per sprinkler is not going to do anything.

 

[MGXFP]

I believe these types of systems are only intended to prevent ember ignition, not prevent a wildfire from consuming a structure. In that case, they may be effective. To prevent a wildfire from consuming a structure, firebreaks, clearing, and other strategies should be used.