Question

A Persian wheel discharges water at the rate of 11,000 lph and works for 8 hours each day. Estimate the area commanded by the water lift if the average depth of irrigation is 8 cm and irrigation interval is 15 days.

• A. 1.5 ha
• B. 2.0 ha
• C. 1.65 ha
• D. 1.75 ha

Hint:

To perform volume calculations quickly, convert discharge rates to \( \text{m}^3/\text{hour} \) early by dividing the value in litres by 1,000:
\[ 11,000 \text{ lph} = 11 \text{ m}^3/\text{hour} \]
This keeps the numerical values manageable and reduces calculation errors.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The command area of a water-lifting device is the total land area that can be irrigated within a given irrigation interval.
This area depends on the total volume of water discharged by the device during the interval and the depth of water required for each irrigation.
Key Formula or Approach:
1. Total water discharged per day (\( V_{\text{day}} \)):
\[ V_{\text{day}} = Q \times t \]
where \( Q \) is the discharge rate and \( t \) is the daily working hours.
2. Total water discharged over the irrigation interval (\( T \)):
\[ V_{\text{total}} = V_{\text{day}} \times T \]
3. Relationship between total water volume, commanded area (\( A \)), and irrigation depth (\( d \)):
\[ V_{\text{total}} = A \times d \]
4. Rearranging to solve for the area (\( A \)):
\[ A = \frac{V_{\text{total}}}{d} \]
Note: \( 1 \text{ m}^3 = 1000 \text{ litres} \) and \( 1 \text{ hectare} = 10,000 \text{ m}^2 \).

Step 2: Detailed Explanation:
Let us perform the calculations step-by-step:
1. Identify the given parameters:
- Discharge rate, \( Q = 11,000 \text{ litres/hour} = 11 \text{ m}^3/\text{hour} \).
- Daily working hours, \( t = 8 \text{ hours/day} \).
- Depth of irrigation, \( d = 8 \text{ cm} = 0.08 \text{ m} \).
- Irrigation interval, \( T = 15 \text{ days} \).
2. Calculate the volume of water discharged in one day:
\[ V_{\text{day}} = 11 \text{ m}^3/\text{hour} \times 8 \text{ hours/day} = 88 \text{ m}^3/\text{day} \]
3. Calculate the total water volume discharged over the 15-day interval:
\[ V_{\text{total}} = 88 \text{ m}^3/\text{day} \times 15 \text{ days} = 1320 \text{ m}^3 \]
4. Calculate the commanded area:
\[ A = \frac{1320 \text{ m}^3}{0.08 \text{ m}} = 16,500 \text{ m}^2 \]
5. Convert the area to hectares:
\[ \text{Area in ha} = \frac{16,500}{10,000} = 1.65 \text{ ha} \]
The estimated area commanded by the Persian wheel is \( 1.65 \text{ ha} \).

Step 3: Final Answer:
The area commanded by the water lift is 1.65 ha.