Question

If the net amount of irrigation requirement is 8 cm and the field efficiency is 75 per cent, the gross amount to be applied to the field is

• A. 6.66 cm
• B. 8.66 cm
• C. 10.66 cm
• D. 12.66 cm

Hint:

Gross is always larger than Net: $\text{Gross} = \frac{\text{Net}}{\text{Efficiency}} = \frac{8}{0.75} = 10.67\text{ cm}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Field water application efficiency is the ratio of the net depth of water stored in the crop root zone to the gross depth of water delivered to the field.
Key Formula or Approach:
\[ \eta_a = \frac{d_{\text{net}}}{d_{\text{gross}}} \times 100\% \implies d_{\text{gross}} = \frac{d_{\text{net}}}{\eta_a / 100} \]

Step 2: Detailed Explanation:
Given parameters:
- Net irrigation requirement: \(d_{\text{net}} = 8\text{ cm}\)
- Field application efficiency: \(\eta_a = 75\% = 0.75\)
Calculating gross irrigation depth:
\[ d_{\text{gross}} = \frac{8\text{ cm}}{0.75} = \frac{8}{3/4} = \frac{32}{3} = 10.666\dots\text{ cm} \approx 10.66\text{ cm} \]

Step 3: Final Answer:
Thus, the gross amount to be applied is 10.66 cm, matching option (C).