Understanding the Duty of Irrigation Water

The question asks about the conditions under which the duty of irrigation water will be less. To answer this, we need to understand what duty of water means in the context of irrigation.

What is Duty of Water?

Duty of water is a measure of the efficiency of an irrigation system. It represents the area of land that can be irrigated by a unit discharge of water running for the entire duration of the base period of the crop. It is typically expressed in hectares per cumec (ha/cumec) or acres per cusec.

Mathematically, duty (D) can be related to the base period (B) and the total depth of water required by the crop (Δ) by the formula:

\( D = \frac{8.64 \times B}{\Delta} \)

Where:

• \(D\) is the Duty (in ha/cumec)
• \(B\) is the Base Period (in days) - the time from the first watering to the last watering of a crop.
• \(\Delta\) is the Total water depth required by the crop (in meters) during its base period.

Alternatively, Duty can be understood as the ratio of the area irrigated (A) to the discharge (Q) used to irrigate that area over a certain time. While not the standard definition linking to base period and delta, a higher discharge required for a given area means a lower duty, and vice versa.

\( D \propto \frac{\text{Area Irrigated}}{\text{Water Supply (Discharge)}} \)

Let's analyze the given options based on these relationships.

Analyzing the Options

Option 1: area irrigated is more

If the area irrigated increases while the water supply (discharge) remains the same, the duty (Area / Discharge) increases. This means duty is more, not less.

Option 2: water supply required is more

If the water supply required (Discharge, Q) for a certain area (A) is more, then the ratio A/Q decreases. Thus, the duty is less. Also, if the crop requires more water depth ($\Delta$) for the entire base period, the duty \(D = \frac{8.64B}{ \Delta}\) will be less because $\Delta$ is in the denominator. A higher water supply required usually indicates a higher $\Delta$. This option suggests duty will be less.

Option 3: water supply required is less

If the water supply required (Discharge, Q) for a certain area (A) is less, then the ratio A/Q increases. Thus, the duty is more. Also, if the crop requires less water depth ($\Delta$), the duty \(D = \frac{8.64B}{ \Delta}\) will be more because $\Delta$ is in the denominator. A lower water supply required indicates a lower $\Delta$. This option suggests duty will be more.

Option 4: None of the above

Based on the analysis, option 2 leads to a lower duty, so this option is incorrect.

Conclusion

The duty of irrigation water is inversely proportional to the total depth of water required by the crop ($\Delta$) for its base period, and also inversely related to the discharge needed to irrigate a certain area. Therefore, if the water supply required is more (implying a higher $\Delta$ or a higher Q for a given A), the duty will be less.

The duty of irrigation water will be less if the water supply required is more.

Revision Table: Key Irrigation Concepts

Additional Information on Factors Affecting Duty

Several factors influence the duty of irrigation water. Understanding these factors helps in efficient water management:

• Type of Crop: Different crops have different water requirements. Crops requiring more water (higher $\Delta$) will have lower duty.
• Climate Conditions: Hot, dry, and windy climates lead to higher evaporation and transpiration (higher water loss), increasing the water requirement ($\Delta$) and thus reducing duty.
• Soil Type: Soil properties like permeability and water-holding capacity affect water losses (percolation). Highly permeable soils lead to more losses and lower duty. Heavy clay soils with high water retention tend to have higher duty.
• Rainfall: Effective rainfall during the crop period supplements irrigation water, reducing the net water requirement from irrigation sources. Higher effective rainfall increases duty.
• Irrigation Method: Efficient irrigation methods like drip or sprinkler irrigation minimize water losses compared to traditional flood irrigation, leading to higher duty.
• Efficiency of Irrigation System: Losses in canals (seepage, evaporation) and at the field (application losses) reduce the water available to the crop. Higher efficiencies lead to higher duty.
• Preparation of Land: Proper land leveling and preparation help in uniform water application and reduce losses, increasing duty.
• Quality of Water: Saline water might require more frequent leaching, increasing water requirement and reducing duty.
• Skill of the Irrigator: An experienced irrigator can apply water more efficiently, leading to higher duty.

All these factors essentially influence either the water requirement ($\Delta$) or the losses, thereby affecting the water supply (Q) needed for a given area and ultimately impacting the duty.