Question

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

• A. $\text{4.8 m}$
• B. $\text{9.6 m}$
• C. $\text{6.0 m}$
• D. $\text{2.9 m}$

Answer 1

The correct option is A $\text{4.8 m}$

Volumetric flow rate through circular opening is given by-
$Q=Av$
[where $Q=$ water flow rate, $A=$ area of opening and $v=$ velocity through opening]
$\Rightarrow \frac{0.74}{60}=\pi r^{2}v=(\pi \times 4\times {10}^{-4})\times \sqrt{2gh}$
$\Rightarrow \sqrt{2gh}=\frac{74\times 100}{240\pi }\Rightarrow \sqrt{2gh}=\frac{740}{24\pi }$
$\Rightarrow 2gh=\frac{740\times 740}{24\times 24\times 10}(\because {\pi }^2=10)$
$\Rightarrow h=\frac{74\times 74}{2\times 24\times 24}\approx 4.8m$

i.e., The depth of the centre of the opening from the level of water in the tank is close to $4.8\text{m}$