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

Step 1: Recall the hydraulic radius definition for a circular bin.
Hydraulic radius is defined as cross-sectional area divided by wetted perimeter, \(R_h = \dfrac{A}{P}\).
For a circular bin of diameter \(D\), \(A = \dfrac{\pi D^2}{4}\) and \(P = \pi D\), so \(R_h = \dfrac{D}{4}\).

Step 2: Solve for the diameter.
Rearranging gives \(D = 4 R_h\).
With \(R_h = 1\) m, \(D = 4 \times 1 = 4\) m.

Step 3: Note the unused data.
The bin height, bulk density, and coefficient of friction are needed for Janssen's pressure equations, not for finding the equivalent diameter from hydraulic radius.

Final Answer:
The equivalent diameter of the bin is 4 m. \[ \boxed{D = 4 \text{ m}} \]