In centrifugal discharge bucket elevators, clean discharge at the head pulley depends on the balance between gravitational force ($m g$) and centrifugal force ($m v^2 / r$). The critical head pulley speed where centrifugal force equals weight occurs when:
Options:
(A) $v = \sqrt{g r}$
(B) $v = g r$
(C) $v = \sqrt{g / r}$
(D) $v = g / r^2$
Answer Key:
A
Step-by-Step Solution & Explanation
At critical velocity $v_c = \sqrt{g r}$, the centrifugal acceleration equals gravitational acceleration ($v^2 / r = g$), enabling grain to cleanly discharge tangentially into the discharge chute without backlegging.