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The long way - by hand
In this article, will demonstrate some of the basics for carrying out re sprinkler
calculations by the long hand method with just the aid of a scienti c calculator or our
own hydraulic calculator - Hcal2 (/products/hcalc.html) which you can freely
download from our website
We will for this example use simple three sprinklers and three pipes which would of
course be part of a much larger re sprinkler system These basic procedures can
also be used for calculating many other types of systems such as re hydrant, hose
reel or the discharge from a water cannon or monitor we can also use the same
principal for almost all other water-based re protection systems if we have a
k-factor for the output device ( re sprinkler, water mist nozzle and so on)
In this example, will we use a very simple system with just three sprinklers and three
pipes this is often called a range pipe or branch pipe, which is part of a larger 'tree
system' A tree system is 'end feed', that is water is only fed from one direction as
opposed to a grid or loop system when water may arrive at the sprinkler head from
more than one direction.
Below is a diagram of the three sprinklers and three pipes which we will calculate.
We have dimensioned the pipe lengths and given each junction point a unique node
reference number which we use throughout the calculations.
For each pipe, we need to know the pipe length, internal diameter (ID) of the pipe and
the pipe material so we can determine the pipes c-factor, the table below
(/)
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We will also we will need some additional information such as the type sprinkler
head, the area each head is covering, the design density for each sprinkler head in
the system
For this example, we will use the following design parameters:
design density: 7.50 mm/min
sprinkler head: K-factor of 70 with a minimum pressure 0.5 bar
head area: 10.20 m
In this example, we have kept it very simple and used the same sprinkler head for all
three sprinklers but this may not always be the case so again it may be useful to
summarises the information in a table such as this:
Node Ref Design Density
(mm/min)
Sprinkler k-factor Sprinkler minimum
pressure (Bar)
Head area (m )
The rst step is to calculate the minimum ow which will be required at the most
remote sprinkler which in this case is at node [130], this is a two-step process as will
need to calculate the minimum ow required to satisfy the 7.50 mm/min design
density and then nd the ow rate from the sprinkler given the sprinklers minimum
pressure requirement, whichever is the greater ow will become our initial ow from
the rst sprinkler at node [130]
We will rst calculate the ow given the design density of 7.50 mm/min and the area
the head is covering, we do this by multiplying the design density
(/support-topmenu/support-basichydraulics/54-design-density.html) by the head area:
2
2
Trang 3Equation 1:
q = (design density) x (area per sprinkler)
In this example, this gives:
q = 7.50 mm/min x 10.20 m2 = 76.50 L/min
The second step is to calculate the minimum ow from the sprinkler given the
K-Factor and the minimum head pressure by using the standard K-K-Factor formula
(/support-topmenu/support-basichydraulics/27-k-factor-formula.html):
Equation 2:
q = kp
Where
p = the required pressure
q = the required ow from the rst sprinkler
k = the discharge coe cient of the sprinkler (k-factor)
In this example, this gives:
q = 70 x 0.5 = 49.50 L/min
By comparing the two calculations above we can see that the minimum ow required
from the sprinkler head will be 76.50 L/min as this is the highest ow rate from the
two calculations and is required to meet the 7.50 mm/min design density. We can
also see that the minimum sprinkler pressure of 0.5 bar is not su cient to produce
the required ow rate so the next step will be to determine what pressure will be
required to produce the required ow of 76.50 L/min at the rst sprinkler head at
node [130] we can do this by using equation 3
Equation 3
p = (q/k)
In the example, this gives:
p = (76.50 / 70) = 1.194 bar
We have now determined the minimum pressure and ow for the rst sprinkler at
node [130] which will be 76.50 L/min @ 1.19 bar the next step is to calculate the
pressure drop in the pipe between node [130] and [120] and for this we will use the
1
1
0.5
0.5
2
0.5
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Hazen-Williams pressure loss formula
(/support-topmenu/support-basichydraulics/26-the-hazen-williams-formula-for-use-in-
re-sprinkler-systems.html)
Equation 4
Where
p = pressure loss in bar per meter
Q = ow through the pipe in L/min
C = friction loss coe cient
d = internal diameter of the pipe in mm
We know that the ow rate from the sprinkler at node [130] is 76.50 L/min and this
will be the ow rate in the rst pipe between nodes [130]-[120] As the pipe has an
internal diameter of 27.30 mm and has a C value of 120 this will give us:
The pressure loss in the rst pipe is 0.027 Bar/m and the total pressure loss in the
pipe is 0.086 bar.
We now need to add the pressure loss in the pipe to the start pressure at the
sprinkler head at node [130] which was 1.19 bar to nd to pressure at node [120] and at
the seconded sprinkler head at node [120] this gives us 1.194 + 0.086 = 1.28 bar.
The next step is to nd the ow from the seconded sprinkler head at node [120] to do
this we will use the K-Factor formula
Equation 5
Trang 5
This gives 70 x 1.280 = 79.20 L/min from the sprinkler head at node [120] which we
now add to the ow in the rst pipe node [130]-[120] to nd the total ow in the
second pipe [120]-[110] to nd the total ow in the seconded pipe which is 155.70
L/min
Having found the total ow in the seconded pipe [120]-[110] we can now nd the
pressure loss in, to do this we will use the Hazen-Williams pressure loss, formula 4
which we used above this gives us:
We now add the pressure loss 0.317 bar to the pressure at node [120] to nd the
pressure at node [110] this give us: 0.317 + 1.280 = 1.597 bar
We now need to nd the ow from the sprinkler at node [110] we do this by using the
k-factor given in equation 5 as we now know the pressure at node [110] is 1.597 bar,
add this ow to the ow in the seconded pipe [120]-[110] to nd the total ow in the
third pipe [110]-[100] which will give us the ow of 244.20 L/min.
0.5
0.5
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The last step is to nd the pressure loss in the third pipe [110]-[100] and again we will
use the Hazen-Williams pressure loss formula given is formula 4 above However, the
last pipe has an internal diameter of 36.0 mm so this gives us:
We now add the pressure loss in this pipe to the pressure at node [110] to nd the
pressure at node [100] this will be 0.189 + 1.597 = 1.786 bar. We have now completed
the calculation for all three sprinkler heads and have found the source pressure and
ow required for this system is:
244.20 L/min @ 1.786 Bar
This pressure and ow is often referred to as the source requirement for the system
and is the minimum pressure and ow required for the system for it to be able to
provide the required design density (in this example 7.50 mm/min) at the most
remote head [MRH] at node [130].
You should also be able to see that only the Most Remote Head has the minimum
requirement of 7.50 mm/min design density and all the other sprinklers will have a
higher pressure as they are hydraulically closer to the water source so they will have
a higher pressure and will discharge more water through the sprinkler this can be
seen in the table below:
Node
Ref
min Design Density (mm/min)
Pressure (Bar)
Flow from sprinkler (L/min)
Head Area (m )
Actual Design Density 130
[MRH]
2
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(/HYDRAULIC-CALCULATION-FOR-FIRE-PROTECTION-ENGINEERS/REYNOLDS-NUMBER.HTML)
Sprinkler calculation step by step
1 Calculate minimum ow from the MRH with the sprinkler minimum pressure
and k-factor
2 Calculate the minimum ow given the system design density and sprinkler head
area
3 If the calculation in step 2 is the highest ow demand, then calculate the
required head pressure otherwise we can use the minimum sprinkler pressure
in step 1
4 Calculate the pressure loss in the pipe
5 Add the head pressure to the pressure loss in step 4 to determine the pressure
at the next sprinkler
6 Use the k-factor formula to determine the ow from the sprinkler head
7 Repeat step 4 to 6 until you do not have any more sprinklers or pipes
K-Factor formula (/tag/k-factor-formula.html) ,
Hayes William pressure loss formula (/tag/hayes-william-pressure-loss-formula.html) ,
Hydraulic calculations for sprinkler systems (/tag/hydraulic-calculations-for-sprinkler-systems.html)
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