Question

A circular mild steel storage bin of 8 m height contains wheat having bulk density of 800 \(\text{kg.m}^{-3}\). The coefficient of static friction between wheat grain and bin wall is 0.40 and hydraulic radius of the bin is 1 m. Equivalent diameter of the bin, in m, is

• A. 4
• B. 8
• C. 1
• D. 2

Hint:

For a circular bin, the hydraulic radius equals the diameter divided by four.

Answer 1

The Correct Option is A

For grain bin design, hydraulic radius links the cross-section shape to a single characteristic length, and for a circle that link is fixed at one quarter of the diameter.

1. 4: comes directly from $D = 4R_h = 4 \times 1$, matching the circular bin relation $R_h = D/4$.
2. 8: this is the bin height value, mistakenly carried over instead of using the hydraulic radius relation.
3. 1: this just repeats the hydraulic radius itself, not the diameter.
4. 2: would follow only if $R_h = D/2$, which is the relation for a different cross-section, not a circle.

Applying $D = 4R_h$ for the circular bin gives 4 m, so option A is correct.