PhysicsA large cylindrical tank has a hole of area A at its bottom. Water is poured in the tank by a tube of equal cross-sectional area A ejecting water at the speed u.

A large cylindrical tank has a hole of area A at its bottom. Water is poured in the tank by a tube of equal cross-sectional area A ejecting water at the speed u.

  1. A

    The water level in the tank will keep on rising

  2. B

    No water can be stored in the tank

  3. C

    The water level will rise to a height v2/2g and then stop

  4. D

    The water level will oscillate

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    Solution:

    The water going out will initially be less than the water flowing in. As a result, the water level will continue to rise. When the water level is h, the efflux velocity = 2gh. The level will stabilize when this reaches the inflow velocity since the filling tube's and the hole's cross sections have the same cross sectional area. Torricelli's theorem provides this height,

    v=2gh

    v22g=h

    Hence the correct answer is The water level will rise to a height v2/2g and then stop.

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