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Fluid Mechanics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsFluid Mechanics1 Mark
MCQ
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 v.
  • A
    The water level in the tank will keep on rising.
  • B
    No water can be stored in the tank.
  • ✓
    The water level will rise to a height $\frac{\text{v}^2}{2\text{g}}$ and then stop.
  • D
    The water level will oscillate.
✓

Answer

Correct option: C.
The water level will rise to a height $\frac{\text{v}^2}{2\text{g}}$ and then stop.
From the principle of continuity and Bernoulli's equation, ​we have:
$\text{v}^2=2\text{gh}$
$\Rightarrow\text{h}=\frac{\text{v}^2}{2\text{g}}$
So, h is the maximum height up to which the water level will rise if the water is ejected at a speed v.

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