GATE 2022 AG – Question 61
A 3 m internal-diameter,10 m deep cylindrical metal silo holds maize of bulk density720 kg/m³. Grain internal-friction angle24°, grain–wall friction angle22°,g=9.81 m/s². Using Airy’s theory, find lateral pressure at the bottom in kPa, to two decimals.
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Correct answer: 23.80 to 24.50
Explanation
Let $\mu=\tan22^\circ=.40403$ and $\mu^{\prime}=\tan24^\circ=.44523$. The keyed Airy wedge calculation uses $K_A=[\sqrt{\mu^{\prime}(\mu^{\prime}+\mu)}+\sqrt{1+(\mu^{\prime})^2}]^{-2}=.3422$ and $p=\rho ghK_A$,giving **about 24.17 kPa**,within the official23.80–24.50 range. This is the shallow-wedge form. Its critical-depth criterion is about 3.71 m for the stated3 m width, so applying it at 10 m is an implicit source convention rather than a general deep-silo design recommendation. See the [Airy pressure equations](https://www.jstage.jst.go.jp/article/kona/41/0/41_2024013/_html/-char/en).