Question

The main drive wheel diameter of a 7$\times$20 cm seed-drill is 140 cm. During calibration, the total weight of grain collected after 20 revolution of drive wheel is 0.154 kg. Calculate the seed rate in kg per hectare for the seed-drill neglecting wheel slippage.

• A. 10.0
• B. 12.5
• C. 20.0
• D. 25.0

Hint:

To simplify seed-drill calculations, use the consolidated formula:
\[ \text{Seed Rate (kg/ha)} = \frac{10,000 \times w}{n \times \pi \times D \times W} \]
This helps avoid rounding errors at intermediate steps.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Calibration of a seed-drill is performed to determine the quantity of seed sown per unit area (seed rate) before taking the machine to the field.
This ensures the seed-drill is adjusted to deliver the recommended seed rate.
Key Formula or Approach:
1. Total working width (\( W \)) of the seed-drill:
\[ W = N \times S \]
where \( N \) is the number of openers and \( S \) is the spacing between openers.
2. Distance traveled (\( L \)) in \( n \) revolutions of the drive wheel:
\[ L = n \times \pi D \]
where \( D \) is the diameter of the drive wheel.
3. Area covered (\( A \)) during calibration:
\[ A = W \times L \]
4. Seed rate (SR) in kg/ha:
\[ \text{SR} = \frac{\text{Weight of seed collected (kg)}}{\text{Area covered (ha)}} \]
Note: \( 1 \text{ hectare} = 10,000 \text{ m}^2 \).

Step 2: Detailed Explanation:
Let us perform the calculations step-by-step:
1. Identify the given values:
- Seed-drill specification: \( 7 \times 20 \text{ cm} \) (implies \( N = 7 \) and \( S = 20 \text{ cm} = 0.2 \text{ m} \)).
- Total working width, \( W = 7 \times 0.2 \text{ m} = 1.4 \text{ m} \).
- Drive wheel diameter, \( D = 140 \text{ cm} = 1.4 \text{ m} \).
- Number of revolutions, \( n = 20 \).
- Weight of grain collected, \( w = 0.154 \text{ kg} \).
2. Calculate the distance traveled in 20 revolutions:
\[ L = 20 \times \pi \times 1.4 = 28\pi \text{ m} \approx 87.965 \text{ m} \]
3. Calculate the area covered during the test:
\[ A = W \times L = 1.4 \text{ m} \times 87.965 \text{ m} = 123.151 \text{ m}^2 \]
4. Convert the area from square meters to hectares:
\[ A_{\text{ha}} = \frac{123.151}{10,000} = 0.012315 \text{ ha} \]
5. Calculate the seed rate:
\[ \text{SR} = \frac{0.154 \text{ kg}}{0.012315 \text{ ha}} \approx 12.505 \text{ kg/ha} \]
The calculated seed rate is approximately \( 12.5 \text{ kg/ha} \).

Step 3: Final Answer:
The seed rate of the seed-drill is 12.5 kg/ha.