Question

A Persian wheel with an average discharge of 230 litres/minute irrigates 1 ha of wheat crop in 50 hrs. What is the average depth of irrigation?

• A. 3.6 cm
• B. 4 cm
• C. 5 cm
• D. 6.9 cm

Hint:

Ensure that all units are consistent:
\[ Q \times t = A \times d \] \[ \frac{230 \times 10^{-3} \text{ m}^3/\text{min} \times (50 \times 60) \text{ min}}{10,000 \text{ m}^2} = 0.069\text{ m} = 6.9\text{ cm} \]

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The average depth of irrigation is the total volume of water supplied divided by the total surface area of the irrigated land.

Step 2: Key Formula or Approach:
1. Calculate the total volume of water \(V\) supplied in cubic meters (\(\text{m}^3\)):
\[ V = \text{Discharge Rate } (Q) \times \text{Irrigation Time } (t) \] 2. Convert the crop area from hectares (ha) to square meters (\(\text{m}^2\)):
\[ 1 \text{ ha} = 10,000 \text{ m}^2 \] 3. Find the depth of irrigation \(d\):
\[ d = \frac{V}{A} \]

Step 3: Detailed Explanation:
1. Calculate the total water volume \(V\):
Given discharge rate \(Q = 230\text{ litres/min}\). Since \(1000\text{ litres} = 1\text{ m}^3\):
\[ Q = 0.23 \text{ m}^3/\text{min} \] Given time \(t = 50\text{ hours} = 50 \times 60 = 3000\text{ minutes}\).
\[ V = 0.23 \text{ m}^3/\text{min} \times 3000 \text{ min} = 690 \text{ m}^3 \] 2. Convert the irrigated area:
\[ A = 1\text{ ha} = 10,000\text{ m}^2 \] 3. Calculate the irrigation depth \(d\):
\[ d = \frac{690\text{ m}^3}{10000\text{ m}^2} = 0.069\text{ m} \] Convert the depth to centimeters:
\[ d = 0.069 \times 100 = 6.9\text{ cm} \]

Step 4: Final Answer:
The correct option is 4, which corresponds to 6.9 cm.