When we start any hydraulic calculation for a water based fire protection systems such as fire sprinklers, water mist, hose reel and deluge systems the k-factor formula is one formula which all fire protection engineers must know and understand. It allows us to calculate the discharge flow from any type of nozzle (fire sprinkler, water mist or a deluge nozzle) for which we have a k-factor. We can also calculate the k-factor for any nozzle if we have not been given one, however you must check with the manufacture that this is acceptable.
The k-factor formula is the start of all hydraulic calculation for fire protection systems for both manual and computerized calculations and is also required for the checking of both types.
The discharge from a sprinkler head or nozzle can be calculated from the formula bellow:
q = kp0.5
when q = flow in L/min
k = nozzle discharge coefficient or k-factor for head in Lpm/bar0.5
p = pressure in bar
This formula can be rewritten to give us:
k = q / p0.5 and p = ( q / k )2
Our Hcalc Hydraulic Calculator will allow you to explore the K Factor formula in more detail and will allow you to calculate the flow, pressure or find the k factor for a nozzle or fire sprinkler. You can freely download and use our Hcalc software.
For standard type sprinkler heads the many design standards specify standard k-factors and minimum pressure, which can 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.
We 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. In fact the list is almost endless and this is why it is important to be familiar with the above formulas.
Often K-factors are given as an imperial value in gpm/psi½ this value cannot be entered into FHC without first converting to its metric equivalent Lpm/bar½. To convert gpm/psi½ to Lpm/bar½ we need to multiply by 14.4 (Approximate)
Example: A sprinkler head has a discharge coefficient of 4.2 gpm/psi½ what is its metric equivalent valve. 4.2 x 14.4 = 60.48 Lpm/bar½.
We only need to use K-factors to one decimal place so 60.48 becomes 60.5 Lpm/bar½.
Some fire sprinkler design authorities such as EN 12845 limit the velocity through pipes and valves in fire sprinkler systems; this is the case with EN 12845 however NFPA and FM do not have any restriction. The case for limiting velocity is that the Hazen-Williams formula is less accurate outside its normal range and equivalent pipe lengths for fittings, which are generally used, start to lose their validity. Some authorities believe that velocity is self-limiting as pressure losses increase exponentially as velocities increase, so pipe sizes must be increased to make use of available water supply pressure.
EN 12845 limits velocity to 6 m/s through valves and flow switches and 10 m/s at any other point in the system.
Velocity in pipe can be calculated using the following formula:-
The following table lists the maximum flows in litres per minute which can be obtained through steel pipework to EN 10255 specifications for both 6 m/s and 10 m/s.
Maximum flows through pipes for EN 12845 fire sprinkler systems