GATE 2020 AG – Question 63
A cylindrical silo has diameter3 m, height/diameter5 and contains60 metric tons wheat of bulk density725 kg/m³. Wall friction coefficient0.42 and lateral/vertical stress ratio0.5. Find bottom vertical pressure in kPa (two decimals), with g=9.81 m/s².
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Correct answer: 23.50 to 25.50
Explanation
Use the actual grain depth z=m/(ρA)=60000/[725π(3²)/4]≈11.71 m, less than silo height15 m. Hydraulic radius Rh=A/perimeter=D/4=0.75 m. Janssen pressure is σv=ρgRh/(μK)[1−exp(−μKz/Rh)]. Substituting gives approximately24.4 kPa. Wall friction limits pressure below the hydrostatic value.