Question

The top of a water tank is open to air and its water level is maintained. It is giving out $0.74m^3$ water per minute through a circular opening of $2cm$ radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to :

• A. 9.6 m
• B. 4.8 m
• C. 2.9 m
• D. 6.0 m

Answer 1

Answer: (B)

In flow volume = outflow volume
$\Rightarrow \frac{0.74}{60}=\left(\pi \times 4\times 10^{-4}\right)\times \sqrt{2gh}$
$\Rightarrow \sqrt{2gh}=\frac{74\times 100}{240\pi }$
$\Rightarrow \sqrt{2gh}\frac{740}{24\pi }$
$\Rightarrow 2gh=\frac{740\times 740}{24\times 24\times 10}\left({\pi }^2=10\right)$
$\Rightarrow h=\frac{74\times 74}{2\times 24\times 24}$
$\Rightarrow h\approx 4.8m$