GATE AG 2009 • Q46 MCQ • 1 Mark

Section 6: Agricultural Process Engineering

Storage Systems

Subtopic: Controlled and modified atmosphere storage

Question Statement:

The diameter of a grain storage bin is 4 m and the depth is 16 m. It is completely filled with wheat having bulk density of 800 kg m⁻³. The angle of friction between wheat and wall is 24°. The ratio of lateral and vertical pressure intensity is 0.4. The lateral pressure intensity of wheat in kPa on the bin wall at 2 m depth is

Options:

  • (A) 2.85
  • (B) 5.28
  • (C) 8.25
  • (D) 8.52

Official Answer Key:

B

Step-by-Step Solution & Explanation

Deep-bin (Janssen) vertical pressure: Pv = (w·R)/(μK)·[1 − e^(−μKz/R)], where w = ρg = 800×9.81 = 7848 N/m³, R = hydraulic radius = Area/Perimeter = (πD²/4)/(πD) = D/4 = 4/4 = 1.0 m, μ = tan(24°) = 0.4452, K = 0.4, z = 2 m. Pv = (7848×1.0)/(0.4452×0.4) × [1 − e^(−0.4452×0.4×2/1.0)] = 44,032 × [1 − e^(−0.3562)] = 44,032 × 0.2999 = 13,205 Pa. Lateral pressure Ph = K·Pv = 0.4 × 13,205 = 5282 Pa = 5.28 kPa, matching option (B).

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