A cylindrical vessel of cross-section A contains water to a height h.There is a hole in the bottom of radius 'a'.The time in which it will be emptied is : Option 1) Option 2) Option 3) Option 4)

S SudhirSol

As we have learned

Torricelli's Theorem / Velocity of Efflux -

In fluid dynamics relating the speed of fluid flowing out of an orifice.

- wherein

Velocity of eflux of water = $\sqrt { 2gh }$

$\frac{dV}{dt}=-A\frac{dh}{dt}= \pi a^2 \sqrt { 2gh }$

$\int_{h}^{0}\frac{dh}{h}= - \pi \frac{a^2\sqrt {2g}}{A} \int_{0}^{t_0}dt$

$t = \frac{A}{\pi a^2}\cdot \sqrt{\frac{2h}{g}}$

Option 1)

Option 2)

Option 3)

Option 4)

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