A large tank filled with water to a height 'h' is to be emptied thro

Discussion Forum : Mechanical Properties Of Fluids

Question -

A large tank filled with water to a height 'h' is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to h/2 and from h/2 to zero is

Options:

A .

\sqrt{2}

B .

\frac{1}{\sqrt{2}}

C .

\sqrt{2} - 1

D .

\frac{1}{\sqrt{2} - 1}

Answer: Option C
:
C

Time taken for the level to fall from H to H' $t = \frac{A}{A_{0}} \sqrt{\frac{2}{g}} [\sqrt{H} - \sqrt{H^{'}}]$

According to problem - the time taken for the level to fall from h to $\frac{h}{2}$ $t_{1} = \frac{A}{A_{0}} \sqrt{\frac{2}{g}} [\sqrt{h} - \sqrt{\frac{h}{2}}]$

and similarly time taken for the level to fall from $\frac{h}{2}$ to zero $t_{2} = \frac{A}{A_{0}} \sqrt{\frac{2}{g}} [\sqrt{\frac{h}{2}} - 0] ∴ \frac{t_{1}}{t_{2}} = \frac{1 - \frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}} - 0} = \sqrt{2} - 1$

Was this answer helpful ?

Next Question

Discussion Forum : Mechanical Properties Of Fluids

Submit Your Solution hear: