Question

The total discharge of a drip system is 150 m$^3$/hr and discharge of Individual dripper is 8 liters per hour. Find out the number of emitters per plant if plant water requirement is 15 litres per day and also find out the area of field if the drippers plant spacing is 1 m x 1 m. (Assume the time of operation as 1 hr).

• A. 9152 m$^2$
• B. 8439 m$^2$
• C. 9375 m$^2$
• D. 7253 m$^2$

Hint:

To easily solve:
1. Find total drippers: \( 150,000 / 8 = 18,750 \).
2. Daily emitter output is 8 liters. Since requirement is 15 liters, we need 2 emitters per plant.
3. Total plants = \( 18,750 / 2 = 9375 \). Since spacing is \( 1 \text{ m}^2 \), area = \( 9375 \text{ m}^2 \).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We must calculate the total number of emitters in the drip system, determine the number of emitters required per plant, and use the plant spacing to find the total irrigated area of the field.
Key Formula or Approach:
1. Total emitters ($N$) = $\frac{\text{Total discharge } (Q)}{\text{Individual dripper discharge } (q)}$
2. Emitters per plant = $\frac{\text{Plant water requirement}}{\text{Emitter discharge } \times \text{operating time}}$
3. Number of plants ($P$) = $\frac{\text{Total emitters } (N)}{\text{Emitters per plant}}$
4. Area of field ($A$) = $P \times \text{plant spacing area}$

Step 2: Detailed Explanation:
Given values:
- Total system discharge ($Q$) = $150 \text{ m}^3\text{/hr} = 150,000 \text{ liters/hr}$
- Emitter discharge ($q$) = $8 \text{ liters/hr}$
- Plant water requirement = $15 \text{ liters/day}$
- Operating time = $1 \text{ hour/day}$
- Plant spacing = $1 \text{ m} \times 1 \text{ m} = 1 \text{ m}^2\text{/plant}$
Calculate Total Emitters ($N$):
\[ N = \frac{150,000 \text{ liters/hr}}{8 \text{ liters/hr}} = 18,750 \text{ emitters} \] Calculate Emitters per Plant:
Each emitter delivers $8 \text{ liters}$ in the $1 \text{ hour}$ of daily operation.
To meet the $15 \text{ liters/day}$ requirement:
\[ \text{Emitters per plant} = \frac{15 \text{ liters}}{8 \text{ liters/emitter}} = 1.875 \text{ emitters/plant} \] To simplify field installation, this is practically rounded to ______2 emitters per plant______.
Calculate Number of Plants ($P$) using exactly 2 emitters per plant:
\[ P = \frac{18,750 \text{ emitters}}{2 \text{ emitters/plant}} = 9375 \text{ plants} \] Calculate Field Area ($A$):
Since each plant occupies $1 \text{ m}^2$:
\[ A = 9,375 \text{ plants} \times 1 \text{ m}^2\text{/plant} = 9375 \text{ m}^2 \]

Step 3: Final Answer:
The area of the field is 9375 m$^2$, corresponding to option (C).