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Hazen-Williams formula
The Hazen-Williams formula is an empirical equation and has long been used for calculating the friction loss in pipework for water based fire protection systems. This equation uses the coefficient C (C-factor) to specify the pipes roughness, which is not based on a function of the Reynolds number, as in other pressure loss equations. This however has the disadvantage that the equation can only be used when water is flowing and is within the ‘turbulent’ flow range. If the system is outside the normal pressure and flow range or the system is to use additives, or will be subject to unusual temperature conditions then the Darcy-Weisbach equation may be more appropriate.
when:
p = pressure loss in bar per meter
Q = flow through the pipe in L/min
C = friction loss coefficient
d = internal diameter of the pipe in mm
Value of C for use in the Hazen-Williams formula
Listed in the table bellow are typical values for the coefficient C, which can be used in the Hazen-Williams formula for different design standards. The value of C represents the pipes roughness with higher values of C giving lower friction losses. The values given in the design standards allow for degradation of the pipe, for instance new cast iron pipe has a C coefficient of 130 and EN 12845 gives the value of 100, this is equivalent to a pipe, which is about 20 years old
K-Factor formula
The discharge from a sprinkler head can be calculated from the formula bellow.
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:
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.
Velocity in pipe
Some design authorities limit the velocity through pipes and valves in 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:
When: v = Velocity m/s
Q = flow of water in L/min
d = internal diameter of pipe in mm
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