GATE 2025 AG – Question 65
A concrete silo of internal diameter 6 m and height 24 m holds rough rice of bulk density 635 kg/m³. Wall-friction angle is 30° and lateral/vertical pressure ratio .4. Find the lateral-pressure ratio at depths 10 m and 5 m, to two decimals.
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Correct answer: 1.44 to 1.48
Explanation
Janssen’s pressure law is $p_h(z)=K\gamma R_h/(K\mu)[1-e^{-K\mu z/R_h}]$,where $R_h=A/P=D/4=1.5$ m and $\mu=\tan30^\circ$. Constant prefactors cancel in the ratio. Therefore $$\frac{p_h(10)}{p_h(5)}=\frac{1-e^{-.4\tan30^\circ(10)/1.5}}{1-e^{-.4\tan30^\circ(5)/1.5}}=1.4631055\ldots.$$ Answer **1.46**. Total fill height exceeds both depths and does not enter this local ratio.