Question

If net irrigation for a crop is 8 cm and field efficiency is 75%, then gross irrigation depth to be applied will be

• A. 10.66 cm
• B. 9.82 cm
• C. 8.75 cm
• D. 12 cm

Hint:

To verify your calculation quickly, remember that the Gross depth must always be larger than the Net depth because of water application losses. Dividing the net depth by a decimal less than $1$ (like $0.75$) will always yield a larger value.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
When water is applied to a field during irrigation, some of it is lost to surface runoff and deep percolation below the root zone.
To ensure that the root zone receives its required net depth of water ($d_n$), a larger gross depth of water ($d_g$) must be applied to the field surface.
The relationship between these depths is determined by the field application efficiency.
Key Formula or Approach:
The relationship between gross irrigation depth and net irrigation depth is: \[ d_g = \frac{d_n}{\eta_f} \] where: - $d_g$ is the gross irrigation depth to be applied.
- $d_n$ is the required net irrigation depth.
- $\eta_f$ is the field application efficiency, expressed as a decimal.

Step 2: Detailed Explanation:
Let us plug the given values into the equation:
- Net irrigation depth ($d_n$) $= 8\text{ cm}$
- Field application efficiency ($\eta_f$) $= 75\% = 0.75$
Calculate the gross irrigation depth: \[ d_g = \frac{8\text{ cm}}{0.75} \] \[ d_g = \frac{8}{\frac{3}{4}} = \frac{32}{3} \approx 10.666\text{ cm} \] Rounding to two decimal places, this gives $10.66\text{ cm}$.

Step 3: Final Answer:
The gross irrigation depth that must be applied to the field is $10.66\text{ cm}$.
Hence, the correct option is (A).