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 power-operated chaff cutter with $2$ cutting knives mounted on a flywheel rotates at $N = 420\text{ rpm}$. The feed throat opening is $w = 200\text{ mm}$ wide and $h = 100\text{ mm}$ high. The fodder is advanced at a speed of $v_f = 0.35\text{ m/s}$. The compressed bulk density of green fodder in the throat is $\rho = 250\text{ kg/m}^3$. The green fodder throughput capacity of the chaff cutter in $\text{t/h}$ (tonnes per hour) is ________ (round off to 2 decimal places).
Answer Key:
6.30
Step-by-Step Solution & Explanation
```
Chaff Cutter Throat Cross-Section:
Width: w = 200 mm = 0.20 m
Height: h = 100 mm = 0.10 m
Feed Speed: v_f = 0.35 m/s
```
**Step-by-step Calculation:**
1. Cross-sectional area of throat ($A$):
$A = w \times h = 0.20\text{ m} \times 0.10\text{ m} = 0.020\text{ m}^2$
2. Volumetric throughput rate ($Q$):
$Q = A \times v_f = 0.020\text{ m}^2 \times 0.35\text{ m/s} = 0.007\text{ m}^3/\text{s}$
3. Mass throughput rate ($\dot{m}$):
$\dot{m} = Q \times \rho = 0.007\text{ m}^3/\text{s} \times 250\text{ kg/m}^3 = 1.75\text{ kg/s}$
4. Capacity in tonnes per hour ($C$):
$C = \frac{1.75\text{ kg/s} \times 3600\text{ s/h}}{1000\text{ kg/t}} = \frac{6300\text{ kg/h}}{1000} = 6.30\text{ t/h}$