Project ForgeA cylindrical container of radius R=1m, wall thickness 1mm, is filled with water to a depth of 2m and suspended along its upper rim (self-weight of the cylinder negligible). Density of water=1000 kg/m³, g=10 m/s². The axial and circumferential stress (σa, σc) experienced by the cylinder wall at mid-depth (1m) are
- A(10, 10) MPa
- (5, 10) MPa
- C(10, 5) MPa
- D(5, 5) MPa
Explanation
Circumferential (hoop) stress at mid-depth: p=ρg(1m)=1000×10×1=10000 Pa; σc=pR/t=10000×1/0.001=10 MPa. Axial stress: the wall carries in tension, up to the rim, the weight of all water BELOW that cross-section (1m of water, cross-section area πR²): W=ρg(πR²×1)=1000×10×π×1≈31,416 N. σa=W/(2πRt)=31416/(2π×1×0.001)≈5 MPa.
Source: GATE ME 2008 (2008)
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