Question

Ten sprinklers are spaced equally at 10 meters on a lateral. The laterals are spaced 1000 cm on the main line. The recommended fertilizer dose is 120 kg/ha. The amount of fertilizer to be applied at each setting is

• A. 0.12 kg
• B. 1.20 kg
• C. 12.0 kg
• D. 120 kg

Hint:

Fast shortcut: $\text{Area} = 10 \times (10 \times 10) = 1000\text{ m}^2 = 0.1\text{ ha}$. Fertilizer $= 0.1 \times 120 = 12.0\text{ kg}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Fertigation dosing in pressurized sprinkler irrigation systems calculates chemical fertilizer quantity based on the instantaneous command area per lateral setting.
Key Formula or Approach:
\[ A_{\text{setting}} = N_{\text{sprinklers}} \times S_e \times S_l \]
\[ \text{Fertilizer Mass (kg)} = A_{\text{setting}} (\text{ha}) \times \text{Application Dose (kg/ha)} \]

Step 2: Detailed Explanation:
Given parameters:
- Number of operating sprinklers: \(N = 10\)
- Sprinkler spacing along lateral: \(S_e = 10\text{ m}\)
- Lateral spacing along mainline: \(S_l = 1000\text{ cm} = 10\text{ m}\)
- Recommended fertilizer dose: \(D = 120\text{ kg/ha}\)

Step 1: Calculate wetted area covered per sprinkler:
\[ A_{\text{sprinkler}} = S_e \times S_l = 10\text{ m} \times 10\text{ m} = 100\text{ m}^2 \]
Calculate total area covered per setting (10 sprinklers):
\[ A_{\text{setting}} = 10 \times 100\text{ m}^2 = 1000\text{ m}^2 \]
Convert to hectares (\(1\text{ ha} = 10,000\text{ m}^2\)):
\[ A_{\text{setting}} = \frac{1000}{10,000} = 0.1\text{ ha} \]

Step 2: Compute fertilizer amount to inject per setting:
\[ \text{Fertilizer Mass} = 0.1\text{ ha} \times 120\text{ kg/ha} = 12.0\text{ kg} \]

Step 3: Final Answer:
Hence, the amount of fertilizer to apply at each setting is 12.0 kg, corresponding to option (C).