Question

A lateral has 12 sprinklers spaced 14 metres apart. The laterals are spaced 20 metres on the main line. Determine the amount of fertilizer to be applied at each setting when the recommended fertilizer dose is 80 kg/ha.

• A. 22 kg
• B. 20 kg
• C. 27 kg
• D. 30 kg

Hint:

To perform this quickly without pen and paper:
\[ 12 \times 14 \times 20 = 3360 \text{ m}^2 \] Multiplying \(3360 \times 80\) is \(268,800\).
Dividing by \(10,000\) yields \(26.88\text{ kg}\), which rounds closest to \(27\text{ kg}\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Fertilizer application through a sprinkler irrigation system (fertigation) requires calculating the exact land surface area covered during one single operation (setting) of the sprinkler lateral.

Step 2: Key Formula or Approach:
1. The area covered per setting (\(A_s\)) is given by:
\[ A_s = N \times S_e \times S_m \] where:
\(N\) = number of sprinklers on the lateral
\(S_e\) = spacing between individual sprinklers along the lateral
\(S_m\) = spacing between laterals along the main line
2. Convert this area from square meters (\(\text{m}^2\)) to hectares (ha).
3. Calculate the weight of fertilizer \(W\) required for this area:
\[ W = \text{Recommended Dose } (\text{kg/ha}) \times A_s \text{ (ha)} \]

Step 3: Detailed Explanation:
Given values:
- Number of sprinklers (\(N\)) = \(12\)
- Sprinkler spacing (\(S_e\)) = \(14\text{ m}\)
- Lateral spacing (\(S_m\)) = \(20\text{ m}\)
- Recommended dose = \(80\text{ kg/ha}\)
First, calculate the area \(A_s\) covered during one setting of the lateral:
\[ A_s = 12 \times 14 \text{ m} \times 20 \text{ m} \] \[ A_s = 168 \text{ m} \times 20 \text{ m} = 3360 \text{ m}^2 \] Convert the calculated area to hectares:
\[ A_s = \frac{3360}{10000} = 0.336 \text{ ha} \] Now, calculate the quantity of fertilizer to be added for this setting:
\[ W = 80 \text{ kg/ha} \times 0.336 \text{ ha} \] \[ W = 26.88 \text{ kg} \approx 27 \text{ kg} \]

Step 4: Final Answer:
The correct option is 3, which corresponds to 27 kg.