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Calculating sprinkler precipitation rates

 

The rate of precipitation (ROP) of a sprinkler is the amount of water it distributes over a given area and amount of time. It is most commonly expressed in millimetres per hour (mm/hr). We use the ROP to calculate how long to run our irrigation zones in order to apply a specific amount of water to our garden. For example, if our ROP is 20 mm/h and we need to apply 10mm to our garden we would run the system for 30 minutes. Most manufacturers will provide an operating specifications sheet which will give you the ROP of a sprinkler under certain installation conditions. In some cases you may need to calculate the ROP, especially when your design doesn’t fit the exact criteria in the operating specifications sheet. In this article we will discuss how to calculate ROP from first principles.

 

 

The rate of precipitation (ROP) of a sprinkler is the amount of water it distributes over a given area and amount of time. It is most commonly expressed in millimetres per hour (mm/hr). We use the ROP to calculate how long to run our irrigation zones in order to apply a specific amount of water to our garden. For example, if our ROP is 20 mm/h and we need to apply 10mm to our garden we would run the system for 30 minutes. Most manufacturers will provide an operating specifications sheet which will give you the ROP of a sprinkler under certain installation conditions. In some cases you may need to calculate the ROP, especially when your design doesn’t fit the exact criteria in the operating specifications sheet. In this article we will discuss how to calculate ROP from first principles.

 

The ROP is dependent on 3 criteria:

  1. Sprinkler type. There are many different sprinkler types, including rotary sprinklers, cone sprayers (normal pop-ups and stand pipes), micro misters, and drip. Each of these has its own range of precipitation rates, depending on the choice of nozzle. A typical cone sprinkler has a ROP of about 40mm/h while a mico mister may have a ROP as low as 5mm/h.
  2. Pressure. Typically the lower the pressure the higher the ROP. This may sound counter intuitive, but there is a good reason for it. As the pressure drops two things happen to the sprinkler. First of all it uses less water (its flow rate decreases). Secondly the radius the sprinkler sprays reduces which means a smaller area is being watered. The key here is that the area the sprinkler covers reduces faster than the flow rate reduces. Therefore we have proportionately more water on a smaller area and the result is a higher ROP.
  3. Sprinkler Spacing. In general the further sprinklers are spaced from each other the lower the ROP (more area being watered with the same amount of water). In addition to this it is important to note whether the irrigation system was designed using square spacing or triangular spacing. Triangular spacing yields a higher ROP than square spacing. (for more information on spacing see here)

 

Once we know which sprinkler type we have, what pressure it is operating at and how far apart sprinklers are spaced from one another we can calculate ROP. The formulas for calculating ROP is as follows:

 

Square Spacing
ROP = _litre per hour = mm/hr
         spacing x spacing

 

Triangular Spacing
ROP =           litres per hour                     = mm/hr
               spacing x spacing x 0.866

 

 

For example let’s calculate the precipitation rate of a 15 series nozzle. The operating specifications in the catalogue are as follows:

 

15F Nozzle 

Pressure (bar) Radius (m) Flow Rate (l/hr)
1.0 3.4 590
1.4 3.7 680
1.7 4.3 750
2.1 4.6 840

 

A typical irrigation system should operate near the top end of the operating range so we will assume in this example that the system is operating at 2.1 bar. If we substitute the variables into our formula we get the following:

 

Square Spacing
ROP =    _ 840               = 40mm/hr
          4.6 x 4.6

 

Triangular Spacing
ROP    = __840__           = 46mm/hr
         4.6 x 4.6 x 0.866

 

As mentioned earlier, triangular spacing gives a higher ROP than square spacing. The impact of this is important to note when setting controller run times. The square spaced zone will have to run for about 15% longer to apply the same amount of water as a triangular zone.
If you mix square spacing and triangular spacing on the same zone, a good practice is to spread the triangular spaced sprinklers out slightly further to bring the precipitation rate down to 40mm/hr. You would need to space the sprinklers at about 4.92 metres to get 40mm per hour.


ROP = ___840___ = 40mm/hr
4.92 x 4.92 x 0.866