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:
An air-assisted orchard sprayer employs an axial-flow fan delivering an airflow rate of $Q = 9.0\text{ m}^3/\text{s}$ at an air discharge velocity of $v = 30\text{ m/s}$. The ambient air density is $\rho = 1.20\text{ kg/m}^3$. If the total efficiency of the fan is $\eta = 60\%$, the mechanical shaft power required to drive the sprayer fan in $\text{kW}$ is ________ (round off to 2 decimal places).
Answer Key:
8.10
Step-by-Step Solution & Explanation
```
Axial Blower Fan Schematic:
Drive Shaft ===>[ Axial Fan ] ===> Air Jet (Q = 9 m^3/s, v = 30 m/s)
```
**Step-by-step Calculation:**
1. Kinetic energy of air discharged per second (air power $P_{\text{air}}$):
$P_{\text{air}} = \frac{1}{2} \dot{m} v^2 = \frac{1}{2} (\rho Q) v^2$
$\rho = 1.20\text{ kg/m}^3, \quad Q = 9.0\text{ m}^3/\text{s}, \quad v = 30\text{ m/s}$
$P_{\text{air}} = 0.5 \times (1.20 \times 9.0) \times (30)^2 = 0.5 \times 10.8 \times 900 = 4860\text{ W} = 4.86\text{ kW}$
2. Mechanical shaft power required with fan efficiency $\eta = 60\% = 0.60$:
$P_{\text{shaft}} = \frac{P_{\text{air}}}{\eta} = \frac{4.86\text{ kW}}{0.60} = 8.10\text{ kW}$