Hello Yassin, and welcome to the forum.
Generally the NFPA 13 "K factor" for sprinklers is K=5.6. Generally sprinklers are 1/2" (~DN15) connection size.
The K factor is determined experimentally, but NFPA 13 currently mandates the use of a nominal K factor (e.g. 5.6) rather than the actual K factor. Makes things less confusing I think.
It is used in the following formula:
Q = K * (P)^0.5
Q=gpm through the sprinkler
P=pressure across the sprinkler
Note: If you are already familiar with K factors, the NFPA 13 "K factor" is not to be confused with K factors used as loss coefficients in Darcy Weisbach based hydraulic calculations (fL/D). This one is wholly unique to sprinkler design.
You can use sprinklers with K factors smaller than 5.6 but only in certain restricted instances (see NFPA 13). You can use K factors larger than 5.6 also, for example K=8.0 sprinklers are often used when a water supply is poor.
I act as both the owner's agent and the AHJ, and often have sprinklers contractors say "please issue a change order for a pump" when I already accepted the engineering design with a documented flow test, and they must think I am an idiot or a pushover one to let them get a fat change order. I simply tell them to increase their pipe size and/or use K=8.0 heads. Problem solved.
As for larger K factors, use them as necessary for the hazard involved, and install them within the limitations of their listing. K factors larger than 8.0 are only for specialized use like extended coverage (EC), CMSA, storage, and similar uses.
Real world knowledge doesn't fall out of the sky on a parachute, but rather is gained in small increments during moments of panic or curiosity.
