Subtopic: Functional requirements, principles of working, construction and operation of manual, animal, tractor and renewable energy operated equipment for tillage, sowing, planting, fertilizer application, inter-cultivation, spraying, mowing, chaff cutting, harvesting and threshing
Question Statement:
A vacuum precision planter uses a vertical rotating disc with suction holes of diameter $d = 2.5\text{ mm}$. The mass of an individual hybrid maize seed is $m = 0.32\text{ g}$. Taking acceleration due to gravity $g = 9.81\text{ m/s}^2$ and a design factor of safety of $n = 3.0$ against seed detachment under machine vibrations, the minimum vacuum suction pressure (gauge pressure) required across the plate in $\text{kPa}$ is ________ (round off to 2 decimal places).
Answer Key:
1.92
Step-by-Step Solution & Explanation
```
Pneumatic Suction Hole Geometry:
Vacuum Pressure (P_v)
<====== [ Suction Hole (d = 2.5 mm) ]
[ Seed (m = 0.32 g) ]
| Weight W = m*g
v
```
**Step-by-step Calculation:**
1. Area of circular suction hole ($A$):
$A = \frac{\pi}{4} d^2 = \frac{\pi}{4} (0.0025\text{ m})^2 = 4.9087 \times 10^{-6}\text{ m}^2$
2. Weight of a single seed ($W$):
$W = m \times g = (0.32 \times 10^{-3}\text{ kg}) \times 9.81\text{ m/s}^2 = 3.1392 \times 10^{-3}\text{ N}$
3. Required holding force with safety factor $n = 3.0$:
$F_{\text{hold}} = n \times W = 3.0 \times 3.1392 \times 10^{-3} = 9.4176 \times 10^{-3}\text{ N}$
4. Suction vacuum pressure ($\Delta P$):
$\Delta P = \frac{F_{\text{hold}}}{A} = \frac{9.4176 \times 10^{-3}\text{ N}}{4.9087 \times 10^{-6}\text{ m}^2} = 1918.55\text{ Pa} = 1.92\text{ kPa}$