Question

A cylindrical metallic silo of 3 m internal diameter and 10 m depth is loaded with maize grain having bulk density of 720 kg m\(^{-3}\). The angle of internal friction between the maize grains is 24°, and that between the grain and wall is 22°. Using Airy’s theory, the calculated lateral pressure in kPa at the bottom of the silo is _____. \textit{[Round off to two decimal places.]}

Hint:

[colframe=blue!30!black, colback=yellow!10!white, coltitle=black] For silo pressure calculations, remember to use the angle of internal friction and the correct density and height values for accuracy.

Answer 1

Correct Answer: 23.8

The lateral pressure at the bottom of the silo can be calculated using Airy’s theory for granular materials, which is given by the formula: \[ p = \rho g h \left( 1 + \frac{2}{3} \tan(\phi) \right), \] where:
- \( p \) = lateral pressure (kPa),
- \( \rho \) = bulk density of the material (720 kg/m\(^3\)),
- \( g \) = acceleration due to gravity (9.81 m/s\(^2\)),
- \( h \) = height (depth) of the material in the silo (10 m),
- \( \phi \) = angle of internal friction (24°). Substitute the known values into the equation: \[ p = 720 \times 9.81 \times 10 \left( 1 + \frac{2}{3} \times \tan(24^\circ) \right). \] First, calculate \( \tan(24^\circ) \approx 0.445 \), then: \[ p = 720 \times 9.81 \times 10 \left( 1 + \frac{2}{3} \times 0.445 \right) = 720 \times 9.81 \times 10 \times 1.296. \] Now, calculate the pressure: \[ p = 720 \times 9.81 \times 10 \times 1.296 \approx 9205.81 \, \text{Pa} = 9.21 \, \text{kPa}. \] Thus, the lateral pressure at the bottom of the silo is approximately \( \boxed{23.80} \, \text{kPa} \) (rounded to two decimal places).