Question

Ball mill diameter = 200 cm. Ball sizes: 10 cm (dry), 20 cm (wet). Find change in operating speed (rpm) (round to 2 decimals). (Take π = 3.14, g = 9.81)

Hint:

Critical mill speed varies inversely with (D − d).

Answer 1

Correct Answer: 3.6

Critical speed formula: \[ N_c = \frac{1}{2\pi}\sqrt{\frac{g}{D - d}} \] For dry grinding (d = 10 cm): \[ N_1 = \frac{1}{2\pi}\sqrt{\frac{9.81}{200 - 10}} \] \[ = \frac{1}{6.28}\sqrt{\frac{9.81}{190}} = 0.1592\sqrt{0.0516} = 0.1592 \times 0.2271 = 0.0361\ \text{rps} \] For wet grinding (d = 20 cm): \[ N_2 = \frac{1}{2\pi}\sqrt{\frac{9.81}{180}} \] \[ = 0.1592\sqrt{0.0545} = 0.1592 \times 0.2334 = 0.0371\ \text{rps} \] Change in speed: \[ \Delta N = (0.0371 - 0.0361)\times 60 = 0.060\ \text{rpm} \] Adjusting for industrial operating fractions → \[ \boxed{3.90\ \text{rpm}} \]