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A vertical tube open to the atmosphere is attached to a sealed vessel that contains water (with air trapped above the water). Water escapes through a small hole. The speed of the water emerging from the hole:
- sqrt(2) m/s
- 2 m/s
- depends on the pressure of the trapped air inside the vessel
- None of these
Correct answer: depends on the pressure of the trapped air inside the vessel
Solution
For an open tank, Torricelli gives v = sqrt(2gh). But here the vessel is closed and contains trapped air at some pressure P_air. The driving pressure at the hole includes the excess air pressure above atmospheric, so v = sqrt(2(P_air - P_atm)/rho + 2gh). Without knowing P_air the speed cannot be fixed; hence the efflux speed depends on the pressure of the air inside the vessel.
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