39.2.2. Mathematical Expression

Duty (D) is the area of land that can be irrigated with a unit discharge of water flowing continuously during the entire base period of a crop.

Duty (D) is a critical concept in irrigation engineering that describes how much land can be effectively watered with a specific amount of water discharge. It is expressed in hectares per cubic meter per second (hectares/cumec) and indicates the irrigation efficiency of a system. Essentially, it helps farmers and engineers understand the relationship between water supply and agricultural land.

Imagine you have a garden where you want to grow vegetables. If you have a hose that can provide water at a certain flow rate, duty tells you how large your garden can be while still receiving enough water. If your hose can deliver enough for just a small garden but you have a large area, the plants may not get enough water, causing stunted growth.

A D= Q Where: • D = Duty (hectares/cumec) • A = Area irrigated (hectares) • Q = Discharge (cumec or cubic metre per second)

The mathematical expression for Duty is represented as D = A / Q. In this formula:

• D represents the duty, which measures how many hectares can be watered per cumec of discharge.
• A indicates the area of land that is being irrigated in hectares.
• Q is the discharge rate, which is the volume of water flowing per second in cubic meters. This equation allows engineers to calculate the area that can be effectively irrigated based on the water they have available.

Think of the duty formula like a recipe. If you have a certain number of ingredients (discharge), you can only make a limited number of dishes (irrigated area). If you have more ingredients, you can make more dishes. Similarly, with a higher discharge (more water), you can water a larger area of land.

Units: • Commonly expressed in hectares/cumec (i.e., hectare per cubic metre per second).

Duty is primarily measured in hectares/cumec. This unit indicates how many hectares can be watered for every cubic meter of water that flows per second. Understanding the units helps in comparing the efficacy of different irrigation systems and in planning appropriate water management strategies.

You can think of the unit 'hectares/cumec' similar to a car's fuel efficiency, which tells you how far you can go on a certain amount of fuel. In this case, the 'distance' refers to the area of land that can be irrigated instead of a geographical distance.

1. Gross Duty: Refers to water measured at the head of the canal system.
2. Net Duty: Refers to water available at the field level after losses in conveyance.

There are two main types of duty: Gross Duty and Net Duty. Gross Duty refers to the total amount of water measured at the source (like the head of an irrigation canal) before any losses, such as evaporation or leakages. On the other hand, Net Duty considers only the water that actually reaches the field after losses have occurred in the system. Understanding both is important for effective irrigation management.

Imagine a large pitcher of water (Gross Duty) that you pour into smaller cups (Net Duty). If some water spills out while pouring, the amount left in each cup is less than what was initially poured. Thus, the 'Net Duty' is what really counts for watering plants that receive this water.

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