Subtopic: Controlled and modified atmosphere storage
Question Statement:
Storage Systems: Controlled and modified atmosphere storage; perishable food storage, godowns, bins and grain silos, packaging material and machines.
Angle of internal friction of a certain grain (bulk density = 650 kg/m³) is 30°. A bin filled with this grain experiences a pressure of 60 kPa at its base. Ignoring the factor of safety, the safe height (m) to which water (density = 1000 kg/m³) can be filled in this bin (rounded to 2 decimals) is ______.
Official Answer Key:
2.00 to 2.10
Step-by-Step Solution & Explanation
The 60 kPa given is the vertical pressure the grain exerts at the bin base. The bin wall/base is designed to withstand the corresponding lateral pressure the grain exerts (this is the actual structural design pressure for a bin, via Rankine's active earth pressure coefficient):
Ka = (1 − sinφ)/(1 + sinφ) = (1 − sin30°)/(1 + sin30°) = (1−0.5)/(1+0.5) = 0.5/1.5 = 0.3333.
Lateral (design) pressure = Ka × vertical pressure = 0.3333 × 60 = 20 kPa.
The safe height of water hw is the height at which hydrostatic pressure equals this same design pressure (bin designed to safely hold this maximum lateral pressure, whether from grain or a fluid):
ρw·g·hw = 20,000 Pa ⟹ hw = 20,000/(1000×9.81) = 2.039 ≈ 2.04 m. Answer: within 2.00–2.10.
Section 7 — Dairy and Food Engineering
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