Question

A reservoir with a live storage of 300 million cubic meters (1 hectare = \(10^4 \, \text{m}^2\)) of a crop with two fillings of the reservoir. If the base period of the crop is 120 days, the duty for this crop (in hectares per cumec, round off to integer) will then be \(\underline{\hspace{1cm}}\).

Hint:

The duty of a crop is calculated by dividing the area irrigated by the total discharge and the base period.

Answer 1

Correct Answer: 689

The duty is defined as the area of land (in hectares) that can be irrigated per unit discharge (in cumecs). The formula for duty is given by: \[ D = \frac{A}{Q \times B}, \] where:
- \( A = 300 \times 10^6 \, \text{m}^3 \) is the total volume of water,
- \( Q = \frac{A}{\text{Base Period}} = \frac{300 \times 10^6}{120 \times 86400} \approx 34.72 \, \text{cumecs} \),
- \( B = 2 \) is the number of fillings.
Thus, the duty is: \[ D = \frac{300 \times 10^6}{34.72 \times 120} \approx 689 \, \text{hectares per cumec}. \] Thus, the duty is \( \boxed{689} \, \text{hectares per cumec} \).