Question

In an area of 100 hectares, maize and wheat crops are grown which can tolerate 8 m mhos conductivity in the drainage water. Yearly consumptive use of crop is 200 cm and yearly rainfall is 100 cm. The conductivity of irrigation water is 2 m mhos. Calculate the water requirement for the year.

• A. 133 cm
• B. 33 cm
• C. 13.33 cm
• D. 3.33 cm

Hint:

To remember this formula easily:
$\text{Irrigation Depth} = \frac{\text{Net Deficit (ET - Rain)}}{\text{Fraction of water remaining (1 - LR)}}$.
This ensures you apply enough water to cover both crop consumption and salt leaching.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In irrigated agriculture, salts present in irrigation water accumulate in the root zone as water is consumed by transpiration and evaporation.
To maintain a favorable salt balance, a fraction of the applied water must pass through the root zone to leach these salts.
This fraction is called the Leaching Requirement ($LR$).
The total irrigation water required must satisfy both the crop consumptive use (evapotranspiration) and this leaching requirement.
Key Formula or Approach:
The Leaching Requirement ($LR$) is given by: \[ LR = \frac{EC_i}{EC_d} \] where: - $EC_i$ is the electrical conductivity of the irrigation water.
- $EC_d$ is the tolerable electrical conductivity of the drainage water.
The water balance equation for the root zone (assuming no change in soil moisture storage and ignoring surface runoff) is: \[ D_i + P = ET + D_d \] where: - $D_i$ is the depth of irrigation water applied.
- $P$ is the yearly precipitation (rainfall).
- $ET$ is the yearly evapotranspiration (consumptive use).
- $D_d$ is the depth of drainage water.
Since $LR = \frac{D_d}{D_i}$, we can substitute $D_d = LR \times D_i$ into the water balance equation: \[ D_i + P = ET + LR \times D_i \] \[ D_i (1 - LR) = ET - P \] \[ D_i = \frac{ET - P}{1 - LR} \]

Step 2: Detailed Explanation:
Let us plug the given values into these equations:
- Area $= 100\text{ ha}$
- tolerable $EC_d = 8\text{ m mhos/cm}$
- $EC_i = 2\text{ m mhos/cm}$
- $ET = 200\text{ cm}$
- $P = 100\text{ cm}$
First, calculate the leaching requirement: \[ LR = \frac{2}{8} = 0.25 \] Next, calculate the irrigation water depth required: \[ D_i = \frac{200\text{ cm} - 100\text{ cm}}{1 - 0.25} \] \[ D_i = \frac{100\text{ cm}}{0.75} = 133\text{ cm} \] Therefore, the depth of irrigation water required to meet the crop's consumptive needs while preventing soil salinization is $133\text{ cm}$.

Step 3: Final Answer:
The annual irrigation water requirement for the area is $133\text{ cm}$.
Hence, the correct option is (A).