Discharge Calculation for Distributary

The problem asks us to find the required discharge at the head of a distributary based on given irrigation data for the Rabi season. We are given the Gross Commanded Area (GCA), the percentage of GCA that is culturable irrigable, the intensity of irrigation for the Rabi season, and the corresponding average duty at the head of the distributary.

Understanding Irrigation Terms

• Gross Commanded Area (GCA): The total area that can be theoretically irrigated by a canal system.
• Culturable Commanded Area (CCA): The portion of GCA that is suitable for cultivation. Area within GCA where cultivation is possible.
• Intensity of Irrigation: The percentage of the CCA that is actually irrigated during a specific season (like Rabi or Kharif).
• Duty: The area (usually in hectares) that can be irrigated by one unit of discharge (usually 1 cumec) flowing continuously throughout the base period of a crop. It represents the efficiency of water usage.
• Discharge: The volume of water flowing through a channel per unit time (usually in cumec or cubic meters per second).

Steps to Calculate Discharge

To find the discharge required at the head of the distributary for the Rabi season, we need to follow these steps:

1. Calculate the Culturable Commanded Area (CCA).
2. Calculate the actual area irrigated during the Rabi season based on the intensity of irrigation.
3. Use the calculated irrigated area and the given duty to find the required discharge.

Given Data

Let's list the given information:

• Gross Commanded Area (GCA) = 8000 hectares
• Percentage of GCA that is Culturable Irrigable = 60%
• Intensity of Irrigation for Rabi season = 60%
• Average Duty at the head of the distributary for Rabi = 2000 hectares/cumec

Calculating Culturable Commanded Area (CCA)

The CCA is 60% of the GCA.

$\text{CCA} = \text{GCA} \times \left( \frac{\text{Percentage of Culturable Irrigable Area}}{100} \right)$

$\text{CCA} = 8000 \text{ hectares} \times \left( \frac{60}{100} \right)$

$\text{CCA} = 8000 \times 0.60$

$\text{CCA} = 4800 \text{ hectares}$

Calculating Area Irrigated in Rabi Season

The area actually irrigated during the Rabi season is determined by the intensity of irrigation applied to the CCA.

$\text{Area Irrigated in Rabi} = \text{CCA} \times \left( \frac{\text{Intensity of Irrigation (Rabi)}}{100} \right)$

$\text{Area Irrigated in Rabi} = 4800 \text{ hectares} \times \left( \frac{60}{100} \right)$

$\text{Area Irrigated in Rabi} = 4800 \times 0.60$

$\text{Area Irrigated in Rabi} = 2880 \text{ hectares}$

Calculating Required Discharge

The relationship between Duty, Area Irrigated, and Discharge is given by the formula:

$\text{Duty} = \frac{\text{Area Irrigated}}{\text{Discharge}}$

We need to find the Discharge, so we can rearrange the formula:

$\text{Discharge} = \frac{\text{Area Irrigated}}{\text{Duty}}$

Substituting the values we calculated and the given duty:

$\text{Discharge} = \frac{2880 \text{ hectares}}{2000 \text{ hectares/cumec}}$

$\text{Discharge} = \frac{2880}{2000} \text{ cumec}$

$\text{Discharge} = 1.44 \text{ cumec}$

Thus, the discharge required at the head of the distributary from average demand considerations for the Rabi season is 1.44 cumec.

Summary of Calculation Steps

The calculated discharge is 1.44 cumec.