Subtopic: Mechanics and energy requirement in size reduction of agriculture produce
Question Statement:
A crusher requires $15.0\text{ kW}$ to crush grain from $8.0\text{ mm}$ to $2.0\text{ mm}$ at a feed rate of $3.0\text{ t/h}$. Assuming Rittinger's law applies ($P \propto [1/d_2 - 1/d_1]$), the power required to crush the same material from $2.0\text{ mm}$ to $1.0\text{ mm}$ at the same feed rate is ________ $\text{kW}$ (in integer).
Answer Key:
20
Step-by-Step Solution & Explanation
Rittinger's Law:
$P_1 = C \left(\frac{1}{2} - \frac{1}{8}\right) = C \left(\frac{3}{8}\right) = 15.0 \implies C = \frac{15 \times 8}{3} = 40.0$
$P_2 = C \left(\frac{1}{1} - \frac{1}{2}\right) = 40.0 \times 0.50 = 20.0\text{ kW}$
Hence, the power is **20** $\text{kW}$.