### Introduction to Sprinkler Design

This article will show you how to calculate and determine the size of a sprinkler system. We will use a scenario with three sprinkler heads as an example, which is part of a larger sprinkler system known as a "tree" configuration. The tree system is identified as an 'end feed' system, where water is provided from a single direction, unlike a grid or loop system where water can come from various directions to reach the sprinkler head. These calculations are relevant for any system that uses a k-factor.

In order to perform these calculations, you need to have the internal diameter of the pipe, its length, and the C factor, as demonstrated in the example below:

Note: Further information on types of pipes and corresponding C-factor values can be found in the table below:

For pipe types and inner diameter see attached link.

Below is a table containing further crucial information about the various types of sprinkler heads:

It should be noted that sprinkler heads are the same for simplicity in calculations, although this may not always be true.

### Pressure Drop Calculation Methodology

Next, you need to determine the minimum flow rate necessary for the farthest sprinkler in the index run to meet the design density of 7.5mm/min.

To calculate the necessary flow rate, multiply the design density by the area that the sprinkler head is protecting.

The next step involves determining the sprinkler's flow rate by taking into account the K-factor and head pressure mentioned earlier.

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 drop in the initial pipe is 0.0242 Bar/m, resulting in a total pressure drop of 0.0845bar in the pipe.

Node 2's pressure is calculated as 1.2bar + 0.0845bar = 1.28bar.

Our next task involves determining the flow rate for the second sprinkler head at node 2. This will be achieved by applying the K-Factor formula previously referenced in the preceding calculations.

After considering the information provided, the revised flow rate in the pipe connecting node 2 to node 3 is 79.33 + 76.5 l/min = 155.835 l/min.

The pressure drop in the second pipe (node 2-3) amounts to 0.315 bar.

The pressure at node 3 is calculated as 1.28 bar + 0.315 bar = 1.597 bar.

Next, we must determine the flow rate for the sprinkler at node 3. This is done using the same k-factor formula and the pressure of 1.597 bar. The result is 70 x 1.597^0.5 = 88.50 L/min from the sprinkler at node 3.

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

To determine the pressure drop in the third pipe connecting node 3 to the main branch, we once again apply the Hazen-Williams pressure loss formula. With an internal diameter of 36.66 mm, this pipe results in a pressure loss of 0.19 bar.

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

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.

**Disclaimer:**

The information provided in these posts is for informational purposes only and should not be considered design advice, specifications, or a calculation template. We assume no responsibility or liability for the use of the information presented. For professional advice or design services, please contact us via our __contact form__.