Question

If the lateral pressure at a certain height in a grain storage structure is calculated to be \(2000 \text{ kg}\cdot\text{m}^{-2}\); then the vertical pressure will be (given K = 0.5)

• A. \(1000 \text{ kg}\cdot\text{m}^{-2}\)
• B. \(2000 \text{ kg}\cdot\text{m}^{-2}\)
• C. \(4000 \text{ kg}\cdot\text{m}^{-2}\)
• D. \(1500 \text{ kg}\cdot\text{m}^{-2}\)

Hint:

Since the lateral pressure coefficient (\(K\)) is always less than 1 (typically ranging from 0.3 to 0.6 for grains), the lateral pressure is always less than the vertical pressure. This means the vertical pressure must be greater than 2000, which immediately rules out options (A), (B), and (D).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When granular material (such as grains) is stored in a bin or silo, it exerts both vertical pressure on the floor and lateral pressure on the side walls.
The relationship between these two pressures is defined by the lateral pressure coefficient (\(K\)).
Key Formula or Approach:
The lateral pressure coefficient (\(K\)) is the ratio of lateral pressure (\(P_L\)) to vertical pressure (\(P_V\)) at any given depth:
\[ K = \frac{P_L}{P_V} \] Rearranging this formula to solve for vertical pressure gives:
\[ P_V = \frac{P_L}{K} \]

Step 2: Detailed Explanation:
Let us perform the calculations using the given values:
- Lateral pressure (\(P_L\)) = \(2000 \text{ kg}\cdot\text{m}^{-2}\)
- Lateral pressure coefficient (\(K\)) = 0.5
Substitute these values into the rearranged formula:
\[ P_V = \frac{2000 \text{ kg}\cdot\text{m}^{-2}}{0.5} \] \[ P_V = 2000 \times 2 = 4000 \text{ kg}\cdot\text{m}^{-2} \] The vertical pressure in the grain storage structure is \(4000 \text{ kg}\cdot\text{m}^{-2}\).

Step 3: Final Answer:
The correct option is (C).