The area of cross-section of a large tank is 0.5 m2. It has a narrow… | JEE Main 2022 (27 Jun, Shift 1)

Q17JEE Main 2022 · 27 JUN · SHIFT 1Medium

Velocity of Efflux (Torricelli)

The area of cross-section of a large tank is 0.5 m2. It has a narrow opening near the bottom having area of cross-section 1 cm2. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40 cm above the bottom, will be ___________ cms ${}^{-1}$ . [Take g = 10 ms ${}^{-2}$ ]

Numerical answer type. Work it out, then open the answer.

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Answer: 300

Extra pressure from the load: $\frac{mg}{A} = \frac{25 \times 10}{0.5} = 500\text{ Pa}$
Bernoulli: $\frac{1}{2}\rho v^2 = \frac{mg}{A} + \rho g h = 500 + 1000(10)(0.4) = 4500$
$v^2 = 9 \Rightarrow v = 3\text{ m/s} = 300\text{ cm/s}$

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