A cylindrical silo, 3 m in diameter and 20 m high, is filled with barley having bulk density of 625 kg m⁻³. Coefficient of friction between grain and the bin wall is 0.45 and the ratio of lateral pressure to vertical pressure is 0.4. The lateral pressure at the base of the bin in kPa will be __________.
Official Answer Key:
10.1 to 10.2
Step-by-Step Solution & Explanation
• Janssen’s equation for vertical pressure at depth h in a silo: σv = (γR)/(μk) × [1 – exp(–μkh/R)], where R = hydraulic radius = D/4 (for a circular silo), γ = unit weight of grain, μ = wall friction coefficient, k = lateral/vertical pressure ratio.
• γ = 625 × 9.81 = 6131.25 N/m³. R = 3/4 = 0.75 m. μk = 0.45×0.4 = 0.18.
• μkh/R = 0.18×20/0.75 = 4.8. exp(–4.8) ≈ 0.00823.
• σv = (6131.25×0.75/0.18)×(1–0.00823) = 25,546.9 × 0.99177 ≈ 25,336.8 Pa.
• Lateral pressure = k × σv = 0.4 × 25,336.8 ≈ 10,135 Pa ≈ 10.13 kPa, inside the accepted range 10.1–10.2.
Section 7 — Dairy and Food Engineering
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