According to Janssen's formula, the asymptotic maximum horizontal wall pressure $p_{h,\infty}$ at infinite depth in a deep bin is given by:
Options:
(A) $p_{h,\infty} = \frac{\rho g R}{\mu'}$, where $R$ is hydraulic radius and $\mu'$ is wall friction coefficient
(B) $p_{h,\infty} = \rho g H$
(C) $p_{h,\infty} = 0$
(D) $p_{h,\infty} = \frac{\mu'}{\rho g R}$
Answer Key:
A
Step-by-Step Solution & Explanation
At large depth, vertical gradient $\frac{dp_v}{dz} \rightarrow 0$. Vertical equilibrium between downward gravity $\rho g A dz$ and upward wall friction $\mu' p_h U dz = \mu' k p_v U dz$ yields $p_{h,\infty} = \frac{\rho g R}{\mu'}$.