Question

Considering acceleration due to gravity as 9.81 m.s\(^{-2}\) and \( \pi \) as 3.14, the critical speed of a ball mill having 3600 mm mill diameter and 160 mm ball diameter is _________ rpm. (Answer in integer)

Hint:

To calculate the critical speed of a ball mill, use the formula involving the radius of the mill and the acceleration due to gravity. Convert all units to meters before substituting into the formula.

Answer 1

Formula: \[ N_c = \frac{42.3}{\sqrt{D - d}} \] Where: $N_c$ = critical speed in rpm $D$ = mill diameter in meters $d$ = ball diameter in meters
Given: \[ D = 3600\ {mm} = 3.6\ {m}, \quad d = 160\ {mm} = 0.16\ {m} \] \[ N_c = \frac{42.3}{\sqrt{3.6 - 0.16}} = \frac{42.3}{\sqrt{3.44}} \approx \frac{42.3}{1.8547} \approx 22.8 \] \[ \boxed{N_c \approx 23\ {rpm}} \]