Question

An irrigation canal is to be designed to deliver 10 cumec to meet the peak demand of 7500 hectare of cropped area. The estimated canal losses are 50 % of the head discharge. The duty (in hectare/cumec) on capacity of this canal is

• A. 375
• B. 1125
• C. 1500
• D. 1875

Hint:

Separate the discharge delivered to the field (10 cumec) from the discharge the canal must carry at its head, using the fact that 50% of the head discharge is lost in transit.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The canal must deliver 10 cumec of water at the field/outlet so that the peak crop-water demand of 7500 hectares is met. Along the way from the canal head to the field, 50% of the head discharge is lost (seepage and other conveyance losses). We need the duty measured on the canal's capacity, that is, using the discharge at the head of the canal, not the discharge that actually reaches the field.

Step 2: Key Formula or Approach:
Duty is the area that can be irrigated per unit discharge:
\[ \text{Duty} = \frac{\text{Area irrigated}}{\text{Discharge}} \]
Duty can be quoted either at the field (using field discharge) or at the head/capacity (using head discharge), and these two numbers differ whenever there are conveyance losses in between. Here canal losses are 50% of the head discharge, so:
\[ Q_{field} = Q_{head} - \text{losses} = Q_{head} - 0.5\,Q_{head} = 0.5\,Q_{head} \]

Step 3: Detailed Explanation:
The 10 cumec stated in the question is the discharge that must reach the field to meet the peak demand of 7500 hectares, so \(Q_{field} = 10\) cumec.
Using the loss relation from Step 2:
\[ Q_{field} = 0.5\,Q_{head} \implies Q_{head} = \frac{Q_{field}}{0.5} = \frac{10}{0.5} = 20 \text{ cumec} \]
This \(Q_{head} = 20\) cumec is the design capacity of the canal at its head.
The duty on capacity uses this head discharge, not the field discharge:
\[ \text{Duty on capacity} = \frac{\text{Area}}{Q_{head}} = \frac{7500}{20} = 375 \text{ hectare/cumec} \]

Step 4: Final Answer:
The duty on capacity of this canal is 375 hectare/cumec. \[ \boxed{375 \text{ ha/cumec}} \]