JEE PYQ: Mechanical Properties Of Fluids Question 30
Question 30 - 2019 (09 Jan 2019 Shift 2)
The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m$^3$ 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:
(1) 6.0 m
(2) 4.8 m
(3) 9.6 m
(4) 2.9 m
Show Answer
Answer: (2) 4.8 m
Solution
Here, volumetric flow rate $= \frac{0.74}{60} = \pi r^2 v = (\pi \times 4 \times 10^{-4}) \times \sqrt{2gh}$ $\Rightarrow \sqrt{2gh} = \frac{74 \times 100}{240\pi} \Rightarrow \sqrt{2gh} = \frac{740}{24\pi}$ $\Rightarrow 2gh = \frac{740 \times 740}{24 \times 24 \times 10} \quad (\therefore \pi^2 \approx 10)$ $\Rightarrow h = \frac{74 \times 74}{2 \times 24 \times 24} \approx 4.8$ m
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