Question

A cylindrical storage bin with an internal diameter of 4 m and a height of 16 m is completely filled with paddy having bulk density of 640 kg·m\(^3\). The angle of internal friction between grain and bin wall is \(30^\circ\) and the ratio of horizontal to vertical pressures is 0.4. When the grain filling rises from 4 m to 16 m in height, the lateral pressure increases by a multiple of \(\underline{\hspace{1cm}}\).

Hint:

Pressure increases with depth in granular materials, and the increase is proportional to the ratio of vertical to horizontal pressures.

Answer 1

Correct Answer: 1.6

The relationship between the lateral pressure (\(p_h\)) and vertical pressure (\(p_v\)) is given by the ratio of the pressures: \[ \frac{p_h}{p_v} = 0.4 \] Since the internal friction angle is \(30^\circ\), the lateral pressure at height \(h\) is:
\[ p_h = p_v \times \left(\frac{h}{h_0}\right) \times \tan(\theta) \] The grain's weight increases with depth, and we are required to calculate the increase in lateral pressure. By applying the pressure-volume relation: For a height increase from 4 m to 16 m, the pressure increase is: \[ \text{Increase in lateral pressure} = 1.6 \times \text{pressure increase at 4 m} \] Thus, the lateral pressure increases by a multiple of \( \boxed{1.6} \).