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 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to :

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

Answer 1

The correct option is B $4.8m$

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