A cylindrical silo (3.0 m diameter, height:diameter ratio 5:1) holds 60 metric tons of wheat (bulk density 725 kg/m³). Wall friction coefficient = 0.42; lateral:vertical pressure ratio = 0.5. Find the vertical pressure at the bottom of the silo (kPa). [1 kgf = 9.81 N] (Rounded to 2 decimal places)
Official Answer Key:
23.50 to 25.50
Step-by-Step Solution & Explanation
Grain volume = 60,000/725 = 82.76 m³; silo cross-section area = π(1.5)² = 7.069 m² ⇒ fill height z = 82.76/7.069 = 11.71 m (less than the full 15 m silo height). Janssen's equation: pv = (γR/μk)[1−e^(−μkz/R)], with R=D/4=0.75 m, γ=725×9.81=7112.25 N/m³, μk=0.42×0.5=0.21. pv = (7.112×0.75/0.21)×[1−e^(−0.21×11.71/0.75)] = 25.40×(1−0.0378) ≈ 24.44 kPa.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.