Question

Sweet sorghum with an initial average particle size of 4.0 mm was pulverized using a burr mill at two different gap settings between stones. The average feed rate of the material is 200 kg h$^{-1$. The resultant flour was analyzed by IS sieves for particle size determination and was found to be 0.336 mm and 0.306 mm for the first and second gap settings, respectively. Using Kick’s law, if the power required to grind the sorghum at first setting is 7.2 kW, the power requirement in kW with the second setting is _____.} \textit{[Round off to two decimal places]}

Hint:

Using Kick's law, the power required for grinding is proportional to the logarithm of the ratio of particle sizes.

Answer 1

Correct Answer: 7.4

According to Kick's law, the power required for grinding is proportional to the logarithm of the ratio of the initial and final particle sizes: \[ P_2 = P_1 \times \log \left( \frac{d_1}{d_2} \right) \] where: - \( P_1 = 7.2 \, \text{kW} \) is the power at the first setting, - \( d_1 = 0.336 \, \text{mm} \) and \( d_2 = 0.306 \, \text{mm} \) are the initial and final particle sizes, - \( P_2 \) is the power at the second setting. Substitute the values into the formula: \[ P_2 = 7.2 \times \log \left( \frac{0.336}{0.306} \right) \] \[ P_2 = 7.2 \times \log(1.098) = 7.2 \times 0.0414 = 7.46 \, \text{kW}. \] Thus, the power requirement with the second setting is approximately \( \boxed{7.46} \, \text{kW} \) (rounded to two decimal places).