Grain Storage: Silos, Bins & Pressure Distribution
Subtopic: Maximum asymptotic vertical pressure in deep silo
Question Statement:
A circular deep grain silo of internal diameter $D = 6.0\text{ m}$ (hydraulic radius $R = D/4 = 1.50\text{ m}$) is filled with wheat of unit weight $\gamma = 7.5\text{ kN/m}^3$. The coefficient of friction between grain and silo wall is $\mu' = 0.40$ and the ratio of lateral to vertical pressure is $k = 0.50$. According to Janssen's theory, the theoretical maximum asymptotic vertical pressure that can ever develop at great depths is ________ $\text{kPa}$ (round off to two decimal places).
Answer Key:
56.25
Step-by-Step Solution & Explanation
The asymptotic vertical pressure in Janssen's silo theory is given by:
$P_{v,\max} = \frac{\gamma R}{\mu' k}$
Substituting $\gamma = 7.5\text{ kN/m}^3$, $R = 1.50\text{ m}$, $\mu' = 0.40$, and $k = 0.50$:
$P_{v,\max} = \frac{7.5 \times 1.50}{0.40 \times 0.50} = \frac{11.25}{0.20} = 56.25\text{ kPa}$