Spray Discharge Fire Sprinklers
The definition of K value for fire sprinklers is:
where Q and ΔP can be in the units of your choice. The preference in the USA is gal/min for flowrate and psid for pressure. In Europe it is frequently liter/min for flow rate and bars for pressure. Note that Ksprinkler is not dimensionless, but has units associated with it. Also, note that sprinkler vendor values for Ksprinkler implicitly assume that water is the fluid, so there is a built-in density of 62.3 lbm/ft3 or 1,000 kg/m3. If this sprinkler is used for something other than water, the Ksprinkler value will need to be adjusted.
Also note that if the spray is into the atmosphere, as is typical, the ΔP is the same thing as the gage pressure. That is why the previous equation is stated by some vendors as just P in the denominator, rather than ΔP. When stated as just P, the pressure is gage.
Finally, note that the Exit Pressure, as defined by AFT Fathom, is different than the concept of Discharge Pressure, an often used parameter in the Fire Protection industry. AFT software defines exit pressure as the pressure of the ambient surroundings, which in an unpressurised location at sea-level, is 1 atm.
Note: The fire sprinkler K is not the same as the dimensionless K value as given by Equation 1
in the Loss Model Summary topic and used extensively throughout AFT Fathom.
The Ksprinkler is related to the discharge coefficient. It can be shown that the relationship is given by
