Physics
Fluid-Mechanics
Easy

Question

There is a hole of area 1 over 25 cm squared  in the bottom of a cylindrical vessel containing fluid up to height h. The liquid flows out in time t. If the liquid were filled in the vessel up to height 4 h, then it would flow out in time

  1. t
  2. 2 t
  3. 4 t
  4. t over 2

The correct answer is: 2 t


    table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell text  Then,  end text A open parentheses negative fraction numerator d h over denominator d t end fraction close parentheses equals alpha v equals a square root of 2 g h end root end cell row cell text  or  end text minus fraction numerator d h over denominator square root of h end fraction equals fraction numerator alpha square root of 2 g end root over denominator A end fraction d t end cell row cell negative integral subscript A superscript 0   fraction numerator 1 over denominator square root of h end fraction d h equals fraction numerator a square root of 2 g end root over denominator A end fraction integral subscript 0 superscript g   d t end cell row cell negative left parenthesis negative 2 square root of h right parenthesis equals fraction numerator alpha square root of 2 g end root over denominator A end fraction t end cell row cell text  or  end text t equals A over alpha fraction numerator 1 over denominator square root of 2 g end root end fraction cross times 2 square root of h text  or  end text t equals A over alpha square root of fraction numerator 2 h over denominator g end fraction end root end cell end table
    When h is quadrupled, t is doubled

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