A single-cylinder 4-stroke agricultural diesel engine operates at a mean speed of $N = 1500\text{ rpm}$ (mean angular speed $\omega = 157.08\text{ rad/s}$). The maximum fluctuation of energy per cycle is $\Delta E = 1250\text{ J}$. If the permissible coefficient of fluctuation of speed is $C_s = 0.02$, the required mass moment of inertia ($I$) of the flywheel in $\text{kg}\cdot\text{m}^2$ is ________ (round off to 2 decimal places).
Answer Key:
2.53
Step-by-Step Solution & Explanation
The relationship for flywheel energy fluctuation is:
$\Delta E = I \omega^2 C_s$
Where:
• $\Delta E = 1250\text{ J}$
• $\omega = 157.08\text{ rad/s}$
• $C_s = 0.02$
$I = \frac{\Delta E}{\omega^2 C_s} = \frac{1250}{(157.08)^2 \times 0.02} = \frac{1250}{24,674.1 \times 0.02} = \frac{1250}{493.48} \approx 2.533\text{ kg}\cdot\text{m}^2 \approx 2.53\text{ kg}\cdot\text{m}^2$