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  2. I need help with 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 :
# Engineering

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)

    \frac{2A}{\pi a^{2}}\sqrt{\frac{h}{g}}

  • Option 2)

    \frac{\sqrt{2}A}{\pi a^{2}}\sqrt{\frac{h}{g}}

  • Option 3)

    \frac{2\sqrt{2}A}{\pi a^{2}}\sqrt{\frac{h}{g}}

  • Option 4)

    \frac{A}{\sqrt{2}\pi a^{2}}\sqrt{\frac{h}{g}}

 

Answers (1)
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)

\frac{2A}{\pi a^{2}}\sqrt{\frac{h}{g}}

Option 2)

\frac{\sqrt{2}A}{\pi a^{2}}\sqrt{\frac{h}{g}}

Option 3)

\frac{2\sqrt{2}A}{\pi a^{2}}\sqrt{\frac{h}{g}}

Option 4)

\frac{A}{\sqrt{2}\pi a^{2}}\sqrt{\frac{h}{g}}

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