The tank is shown in the figure. A small capped hole with cross-sectional area 0.1 m2 is located 10 m below the surface of water as shown. If the cap is removed, the velocity of water just outside the tank is approximately [Density of water = 103 kg m

Engineering

Physics

BernoulIis Equation and Equation of Continuity

Question

The tank is shown in the figure. A small capped hole with cross-sectional area 0.1 m² is located 10 m below the surface of water as shown. If the cap is removed, the velocity of water just outside the tank is approximately [Density of water = 10³ kg m^–3 ]

5 ms^–1

14 ms^–1

20 ms^–1

10 ms^–1

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This problem applies Torricelli's theorem, which states that the speed of efflux from a small hole in a tank is the same as the speed an object would attain in free fall from the same height. The velocity is given by the equation:

$v = \sqrt{2 g h}$

where $g = 10 m / s^{2}$ and the height $h = 10 m$ . The cross-sectional area and water density are not needed for this calculation.

Substituting the values: $v = \sqrt{2 \times 10 \times 10} = \sqrt{200} = 14.14 m / s$ , which is approximately 14 m/s.

Final Answer: 14 ms^–1