Subtopic: Centrifugal vs gravity discharge in bucket elevator
Question Statement:
In a vertical centrifugal-discharge bucket elevator, the critical head pulley speed occurs when centrifugal force equals the gravitational weight of the grain in the bucket, corresponding to:
Options:
(A) $\frac{v^2}{r} = g \implies v = \sqrt{g r}$
(B) $v = g r$
(C) $\frac{v}{r} = 2 g$
(D) $v = \sqrt{2 g r}$
Answer Key:
A
Step-by-Step Solution & Explanation
At the top of the head pulley of radius $r$, the condition where centrifugal force matches gravity is $m \frac{v^2}{r} = m g \implies v = \sqrt{g r}$. Speeds slightly above this critical speed project grain cleanly into the discharge chute by centrifugal force.