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# Fire sprinkler hydraulic calculations and design density

One of the most important concepts in fire sprinkler design is the principle of design density, yet many fire sprinkler system design engineers do not fully understand the concept. This short instruction will hopefully full fill this requirement.

We often refer to Design Density in lazy preference to Design Density of Discharge which, in turn, is a short way of saying the Density of Application of Water. This is an unusual use of the word 'density' since we know, of course, that the density of water is 1. However, the density of application means how much water we apply over a certain area, much the same as pressure is a force applied over a unit area.

Therefore, we are talking about a volume of water spread over a certain area in a unit of time.

Volume can be measured in litres
The area can be measured in m2
Time can be measured in minutes

The density of water application would be measured thus:

Volume / Area x Time or Litre / m3 x min

It is necessary to bring this formula to a manageable state by changing the units. A Litre of water is defined as a cubic decimetre which is 10 centimetres × 10 centimetres × 10 centimetres (1 L ≡ 1 dm3 ≡ 1000 cm3). Hence 1 L ≡ 0.001 m3 ≡ 1000 cm3 and 1 m3 (i.e. a cubic metre, which is the S.I. unit for volume) is exactly 1000 L.

Therefore, we can rewrite the formula:

dm x dm x dm / 10dm x 10dm x min

This can be simplified by cancelling out

dm / 100min = 100mm / 100min = 1mm / 1min = mm/min

The density of application can, therefore, be measured in millimetres per minute (mm/min).

Whichever route you take, it is essential to realise that when we use this strange, apparently linear unit, we are talking about a volume of water discharged over an area of 1m2 in 1 min.

In the case of Ordinary Hazard Installations (EN 12845) with a Density of Discharge of 5.0 mm/min, bearing in mind that this really means 5 L/min2/min then we are applying less than half a bucket full of water on every square metre each minute.

The art, of course, is how you tell it or, in this case, how you apply it. The sprinkler head distributes the water in an even pattern so that in the case of OH3, each of the 12m2 covered by the head receives its share of water. When testing a sprinkler head, the floor is covered with 1m2 trays, and after a discharge for 1 minute, there should be water in each tray to a depth of 5mm. The volume of water in the tray would be 5mm x 1000 mm x 1000 mm = 5,000,000 mm3 since there are (100 x 100 x 100) i.e. 1,000,000mm3 in 1dm3, the volume of water will, of course, be 5dm3 or 5 litres.

Taking OH3 as an example, if we design for a maximum of 18 sprinkler heads operating, each capable of covering 12m2, then the maximum area of operation will be (18 x 12)m2 = 216m2.  If each of the 18 sprinkler heads discharges 5dm3/m2 every minute, we will require a flow of (5 x 18 x 12) dm3/min = 1080 dm3/min. In calculating pipe sizes, this is approximated to 1000dm3/min.

Now we know the theory of 'Design Density' we can use it in fire sprinkler hydraulic calculations to find the quantity of water required to flow from a fire sprinkler. If we know the area a sprinkler head is covering and the required design density, then we can use the following formula:

Area x Density = Quantity

Therefore if we have a fire sprinkler head which is covering 8m2 and we require 12.5 mm/min

8m2 x 12.5 mm/min = 100 Litres/min

This would be the minimum flow rate required for the sprinkler head to prove the correct Design Density.  The specific design density to be used for design purposes is determined by reference to the occupancy fire hazard of the building once this is known the applicable design standard such as EN 12845, BS 9251 or NFPA 13 will have tables of occupancies from which you can find the required design density.

### A practical design density example

Let’s take an example, if we are designing a fire sprinkler system and we know that we require a design density of 15.0 mm/min over the design area, then this is the starting point for our fire sprinkler hydraulic calculation.

We now need to take the first most remote fire sprinkler on the branch line (range pipe) and find the actual area the fire sprinkler is covering let’s assume it’s 7.5m2 for this example. We can now calculate the minimum flow rate from the fire sprinkler to provide the required design density, this can be found in the equation:

Q = D x A

When:

Q = flow rate from the fire sprinkler
D = Design density
A = Area of coverage for the fire sprinkler

For our example:

15 mm/min x 7.5 m2 = 112.50 L/min

We now know that the most remote fire sprinkler must have a flow rate equal to or greater than 112.50 L/min. The next step in the calculation is to check that we can get this flow rate from the fire sprinkler and what pressure will be required.

We hope you have found this short introduction to water design density informative and will help you understand one of the fundamental concepts of sprinkler system design.

##### Footnotes:

The litre is the SI derived unit for volume which is the volume of a cube with 10 cm sides and has the symbol L or l. A decimeter (dm3) is 1,000 cubic centimetres (cm3) or 1/1000 of a cubic metre.

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