### Introduction

In this article, we will demonstrate how to perform calculations and sizing for a sprinkler system. Our example will focus on a branch of three sprinkler heads, which is a segment of a larger "tree" sprinkler system configuration. A tree system is characterized as an 'end feed' system, where water is supplied from a single direction, unlike a grid or loop system where water can reach the sprinkler head from multiple directions. These calculations apply to any system utilizing a k-factor.

To conduct these calculations, it's necessary to know the internal diameter of the pipe, its length, and the C factor, as illustrated in the following example:

Note: More about types of pipes and C-factor values as per the below table:

For pipe types and inner diameter see attached link.

Additional important details regarding the types of sprinkler heads are provided in the table below:

Note: Sprinkler heads are identical for the ease of calculation. This is not always the case.

### Pressure Drop Calculation Methodology

The next step is to calculate the minimum flow rate which will be required at the most remote located sprinkler in the index run. The minimum flow rate will have to satisfy the design density of 7.5mm/min.

The required flow rate is calculated by multiplying the design density with the area the head is covering.

The second stage is to calculate the flow rate for the sprinkler considering the above K - factor and head pressure.

Where

p = the required pressure k = the discharge coefficient of the sprinkler (k-factor)

From the above, it results that the minimum required flow rate is bigger than what the sprinkler head can provide. The solution for this is to consider the sprinkler flow rate equal to the minimum required flow rate, keep the same k factor, and find out the required pressure from the equation.

We have now determined the minimum pressure and flow for the first sprinkler at the first node which will be 76.50 L/min @ 1.2 bar. The next step is to calculate the pressure drop in the pipe between nodes 1 and 2 and for this, we will use the **Hazen-Williams pressure loss formula.**

Where

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

## Download our __FREE Calculation Sheet__ for the sprinkler pressure drop

__FREE Calculation Sheet__

The pressure loss in the first pipe is 0.0242 Bar/m and the total pressure loss in the pipe is 0.0845bar.

The pressure at node 2 is equal to 1.2bar+0.0845bar=1.28bar.

The next step is to find the flow rate for the second sprinkler head at node 2. To do this we will use the K-Factor formula mentioned before in the above calculations.

Considering the above the new flow rate in the pipe connecting node 2 with node 3 is 79.33+76.5l/min=155.835l/min

The pressure loss in the second pipe (node 2-3) is equal to 0.315bar

The pressure at node 3 is equal to 1.28 bar+0.315 bar=1.597 bar.

We now need to find the flow rate for the sprinkler at node 3. We do this by using the same k-factor formula and the 1.597 bar pressure. This gives 70 x 1.5970.5 = 88.50 L/min from the sprinkler head at node 3.

**The total flow rate resulted for the 3 sprinkler heads is 155.835+88.50l/min=244.33l/min. **

The last step is to find the pressure loss in the third pipe connecting node 3 with the main branch by again using the Hazen-Williams pressure loss formula. However, the last pipe has an internal diameter of 36.66 mm so this gives us a pressure loss of 0.19bar.

**The total pressure at the branch level is 1.597+0.19bar=1.787bar**

The most remote sprinkler head will match the minimum flow requirement whereas the rest of the sprinkler heads will have a higher pressure, discharging more water.

Please note that this document is not a guide for sizing a sprinkler system. Instead, it serves as an illustrative example of how to apply specific literature and principles in this context. For actual system sizing and installation, __professional guidance__ and adherence to relevant codes and standards are strongly recommended.

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