GATE ME 2023 Set 1 — Question 40
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Fluid Mechanics → Fluid Properties & Statics → Pressure in Static Fluids
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Question
The figure shows a thin-walled open-top cylindrical vessel of radius and wall thickness . The vessel is held along the brim and contains a constant-density liquid to height from the base. Neglect atmospheric pressure, the weight of the vessel and bending stresses in the vessel walls. Which one of the plots depicts qualitatively CORRECT dependence of the magnitudes of axial wall stress () and circumferential wall stress () on ?
Correct answer
(A) [figure]
Solution
1.Circumferential (Hoop) Stress (): The pressure at a depth from the free surface (brim) is . The hoop stress is given by . This is a linear function of that is zero at the brim () and maximum at the base ().
2.Axial Stress (): Since the vessel is held at the brim, the wall at any depth must support the total weight of the liquid and the base below it. The total weight of the liquid is . Neglecting the vessel's weight, the axial force in the wall is constant throughout its height: . The axial stress is . This is constant with respect to .
3.Intersection: Setting gives .
Thus, plot (A) correctly depicts a constant and a linearly increasing that intersect at .Continue learning with Success Tracker
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