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A cylindrical vessel of height 500 mm has a small orifice at its base. The orifice is kept closed while water is poured in up to a height H. The top of the vessel is then sealed airtight with a cap and the orifice is opened. Some water escapes and the level settles at a steady height of 200 mm of water. Find the drop (in mm) in the water level caused by opening the orifice. [Atmospheric pressure = 1.0e5 N/m², water density = 1000 kg/m³, g = 10 m/s²; ignore surface tension.]
- 6 mm
- 12 mm
- 8 mm
- 10 mm
Correct answer: 6 mm
Solution
After sealing, the air column above the water is trapped. As water leaves, the air expands and its pressure drops. Flow ceases when the pressure at the orifice equals atmospheric, letting you find H from the trapped-air relation.
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