Question

A tubewell operating 10 hours per day discharges water at a rate of \(25\ \text{m}^3.\text{h}^{-1}\). The average irrigation depth is 80 mm, and the irrigation interval is 20 days. If the intensity of irrigation is 80%, the culturable command area (in hectares) is ________. (Rounded off to two decimal places)

Hint:

Start by finding the total volume the tubewell delivers over one irrigation interval.

Answer 1

Correct Answer: 7.81

Step 1: Find the volume of water pumped in one irrigation interval.
The tubewell discharges water at \(25\ \text{m}^3/\text{h}\) and runs for 10 hours each day.
Volume pumped per day \(= 25 \times 10 = 250\ \text{m}^3\).
Over one irrigation interval of 20 days, total volume \(= 250 \times 20 = 5000\ \text{m}^3\).

Step 2: Find the area that gets wetted by this volume.
The average irrigation depth applied is 80 mm, which is \(0.08\ \text{m}\).
Area actually irrigated \(= \dfrac{\text{Volume}}{\text{depth}} = \dfrac{5000}{0.08} = 62500\ \text{m}^2\).
Convert to hectares: \(62500\ \text{m}^2 = 6.25\ \text{ha}\).

Step 3: Scale up to the full culturable command area using the irrigation intensity.
An intensity of irrigation of 80% means only 80% of the culturable command area (CCA) gets watered in this interval.
So \(0.80 \times \text{CCA} = 6.25\ \text{ha}\), which gives \(\text{CCA} = \dfrac{6.25}{0.80} = 7.8125\ \text{ha}\).

Final Answer:
The culturable command area works out close to 7.81 hectares. \[ \boxed{CCA \approx 7.81\ \text{ha}} \]