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12/10/2018 (https://twitter.com/canutesoft) How to calculate a fire sprinkler system (skype:canutesoft.com?chat) +44 (0)113 328 0350 (tel:+44(0)1133280350) info@canutesoft.com (mailto:info@canutesoft.com) Mon - Fri - 9:00 - 17:00 (/) 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 kfactor 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 summarises the pipe data which we will need for the calculation for this example: https://www.canutesoft.com/how-to-calculate-a-fire-sprinkler-system.html 1/9 12/10/2018 How to calculate a fire sprinkler system Node Ref Pipe Size ID (mm) Length (m) C-factor 130-120 27.30 3.20 120 120-110 27.30 3.20 120 110-100 36.00 3.20 120 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 m2 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 Sprinkler k-factor Sprinkler minimum Head area (m2) (mm/min) pressure (Bar) 130 7.50 70 0.5 10.20 120 7.50 70 0.5 10.20 110 7.5 70 0.5 10.20 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 this by multiplying the design density (/supporttopmenu/support-basichydraulics/54-design-density.html) by the head area: https://www.canutesoft.com/how-to-calculate-a-fire-sprinkler-system.html 2/9 12/10/2018 How to calculate a fire sprinkler system Equation 1: q1 = (design density) x (area per sprinkler) In this example, this gives: q1 = 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 KFactor and the minimum head pressure by using the standard K-Factor formula (/support-topmenu/support-basichydraulics/27-k-factor-formula.html): Equation 2: q = kp0.5 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 0.50.5 = 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 this by using equation Equation p = (q/k)2 In the example, this gives: p = (76.50 / 70)0.5 = 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 https://www.canutesoft.com/how-to-calculate-a-fire-sprinkler-system.html 3/9 12/10/2018 How to calculate a fire sprinkler system Hazen-Williams pressure loss formula (/support-topmenu/supportbasichydraulics/26-the-hazen-williams-formula-for-use-in- re-sprinklersystems.html) Equation 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 this we will use the K-Factor formula Equation https://www.canutesoft.com/how-to-calculate-a-fire-sprinkler-system.html 4/9 12/10/2018 How to calculate a fire sprinkler system This gives 70 x 1.2800.5 = 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 this we will use the Hazen-Williams pressure loss, formula 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 this by using the k-factor given in equation as we now know the pressure at node [110] is 1.597 bar, this gives 70 x 1.5970.5 = 88.50 L/min from the sprinkler head at node [110]. We now 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. https://www.canutesoft.com/how-to-calculate-a-fire-sprinkler-system.html 5/9 12/10/2018 How to calculate a fire sprinkler system 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 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 Design Density (mm/min) Pressure Flow from (Bar) sprinkler (L/min) Head Area (m2) Actual Design Density 130 [MRH] 7.50 1.194 76.50 10.20 7.50 120 7.50 1.280 79.20 10.20 7.76 130 7.50 1.597 88.50 10.20 8.68 https://www.canutesoft.com/how-to-calculate-a-fire-sprinkler-system.html 6/9 12/10/2018 How to calculate a fire sprinkler system Sprinkler calculation step by step Calculate minimum ow from the MRH with the sprinkler minimum pressure and k-factor Calculate the minimum ow given the system design density and sprinkler head area If the calculation in step is the highest ow demand, then calculate the required head pressure otherwise we can use the minimum sprinkler pressure in step Calculate the pressure loss in the pipe Add the head pressure to the pressure loss in step to determine the pressure at the next sprinkler Use the k-factor formula to determine the ow from the sprinkler head Repeat step to until you 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) (http:/(http:/ /www.facebook.com/share (https:/ /twitter.com/share? 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