In the design of deep grain silos, Janssen's equation demonstrates that with increasing grain depth, the lateral pressure against the silo wall:
Options:
(A) Increases linearly without bound
(B) Approaches an asymptotic maximum limiting value
(C) Decreases exponentially to zero
(D) Remains strictly equal to hydrostatic liquid pressure
Answer Key:
B
Step-by-Step Solution & Explanation
Janssen's equation accounts for friction between the grain and the bin wall ($L = \frac{w R}{\mu'} [1 - e^{-k \mu' y / R}]$). As depth $y \to \infty$, the exponential term decays to zero and lateral pressure approaches an asymptotic upper limit $\frac{w R}{\mu'}$, unlike fluids which increase linearly.