GATE 2021 AG – Question 63
A 4 m diameter,16 m high paddy bin has grain bulk density640 kg/m³,grain–wall friction angle30° and horizontal/vertical pressure ratio .4. By what multiple does lateral pressure rise when fill depth increases4→16 m? Give two decimals.
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Correct answer: 1.60 to 1.70
Explanation
Janssen pressure is proportional to $1-e^{-4\mu Kh/D}$ with μ=tan30°,K=.4,D=4. The multiplier is $[1-e^{-(.57735)(.4)(16)}]/[1-e^{-(.57735)(.4)(4)}]=\mathbf{1.62}$ approximately. Density and the saturation-pressure prefactor cancel. Pressure does not grow fourfold because wall friction carries increasing load.