How to Calculate and Solve for Required Discharge of Each Sprinkler | Irrigation Water Requirement

The image above represents the required discharge of each sprinkler. To calculate the required discharge of each sprinkler, three essential parameters are needed, and these parameters are the Spacing of the Sprinkler along the Interval (Sl), the Spacing of the Sprinkler along the Main Pipe (Sm), and the Optimum Water Application Rate (l).

The formula for calculating the required discharge of each sprinkler:

q = ^{S_l . S_m . I} / ₃₆₀₀

Where:

q = Required Discharge of Each Sprinkler
S_l = Spacing of Sprinkler along the Interval
S_m = Spacing of Sprinkler along the Main Pipe
I = Optimum Water Application Rate

Let’s solve an example;
Find the required discharge of each sprinkler when the spacing of sprinkler along the interval is 21, the spacing of sprinkler along the main pipe is 24 and the optimum water application rate is 19.

This implies that;

S_l = Spacing of Sprinkler along the Interval = 21
S_m = Spacing of Sprinkler along the Main Pipe = 24
I = Optimum Water Application Rate = 19

q = ^{S_l . S_m . I} / ₃₆₀₀
That is, q = ^{(21) . (24) . (19)} / ₃₆₀₀
q = ⁹⁵⁷⁶ / ₃₆₀₀
q = 2.66

Therefore, the required discharge of each sprinkler is 2.66.

Calculating the Spacing of the Sprinkler along the Interval when the Required Discharge of each Sprinkler, the Spacing of the Sprinkler along the Main Pipe, and the Optimum Water Application Rate are Given

S_l = ^{q x 3600} / _{Sm x l}

Where;

S_l = Spacing of Sprinkler along the Interval
q = Required Discharge of Each Sprinkler
S_m = Spacing of Sprinkler along the Main Pipe
I = Optimum Water Application Rate

Let’s solve an example;
Find the spacing of sprinkler along the interval when the required discharge of each sprinkler is 24, the spacing of sprinkler along the main pipe is 14 and the optimum water application rate is 20.

This implies that;

q = Required Discharge of Each Sprinkler = 24
S_m = Spacing of Sprinkler along the Main Pipe = 14
I = Optimum Water Application Rate = 20

S_l = ^{q x 3600} / _{Sm x l}
Then, S_l = ^{24 x 3600} / _{14 x 20}
S_l = ⁸⁶⁴⁰⁰ / ₂₈₀
S_l = 308.5

Therefore, the spacing of sprinkler along the interval is 308.5.

Read more: How to Calculate and Solve for Capacity of the Sprinkler System | Irrigation Water Requirement

Calculating the Spacing of Sprinkler along the Main Pipe when the Required Discharge of each Sprinkler, the Spacing of Sprinkler along the Interval and the Optimum Water Application Rate are Given

S_m = ^{q x 3600} / _{Sl x l}

Where;

S_m = Spacing of Sprinkler along the Main Pipe
q = Required Discharge of Each Sprinkler
S_l = Spacing of Sprinkler along the Interval
I = Optimum Water Application Rate

Let’s solve an example;
Find the spacing of sprinkler along the main pipe when the required discharge of each sprinkler is 7, the spacing of sprinkler along the interval is 10 and the optimum water application rate is 6.

This implies that;

q = Required Discharge of Each Sprinkler = 7
S_l = Spacing of Sprinkler along the Interval = 10
I = Optimum Water Application Rate = 6

S_m = ^{q x 3600} / _{Sl x l}
S_m = ^{7 x 3600} / _{10 x 6}
Hence, S_m = ²⁵²⁰⁰ / ₆₀
S_m = 420

Therefore, the spacing of sprinkler along the main pipe is 420.

Calculating the Optimum Water Application Rate when the Required Discharge of each Sprinkler, the Spacing of Sprinkler along the Main Pipe and the Spacing of Sprinkler along the Interval are Given

l = ^{q x 3600} / _{Sl x Sm}

Where;

I = Optimum Water Application Rate
q = Required Discharge of Each Sprinkler
S_l = Spacing of Sprinkler along the Interval
S_m = Spacing of Sprinkler along the Main Pipe

Let’s solve an example;
Find the optimum water application rate when the required discharge of each sprinkler is 15, the spacing of the sprinkler along the interval is 4, and the spacing of the sprinkler along the main pipe is 8.

This implies that;

q = Required Discharge of Each Sprinkler = 15
S_l = Spacing of Sprinkler along the Interval = 4
S_m = Spacing of Sprinkler along the Main Pipe = 8

l = ^{q x 3600} / _{Sl x Sm}
So, l = ^{15 x 3600} / _{4 x 8}
l = ⁵⁴⁰⁰⁰ / ₃₂
l = 1687.5

Therefore, the optimum water application rate is 1687.5.

How to Calculate the Required Discharge of Each Sprinkler Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the required discharge of each sprinkler.

To get the answer and workings of the required discharge of each sprinkler, use the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 2,000 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Agricultural under Engineering.

Now, Click on Irrigation Water Requirement under Agricultural

Now, Click on Required Discharge of Each Sprinkler under Irrigation Water Requirement

The screenshot below displays the page or activity to enter your values, to get the answer for the required discharge of each sprinkler according to the respective parameters which is the Spacing of Sprinkler along the Interval (S_l), Spacing of Sprinkler along the Main Pipe (S_m) and Optimum Water Application Rate (l).

Now, enter the values appropriately and accordingly for the parameters as required by the Spacing of Sprinkler along the Interval (S_l) is 21, Spacing of Sprinkler along the Main Pipe (S_m) is 24 and Optimum Water Application Rate (l) is 19.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the required discharge of each sprinkler and presents the formula, workings and steps too.