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  4. A cylindrical vessel contains a liquid of density ρ up to a height h . The liquid is closed by a piston of mass m and area of cross-section A . There is a small hole at the bottom of the vessel. The speed v with which the liquid comes out of the hole is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-5mosxxrifocb.png />

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Q. A cylindrical vessel contains a liquid of density $\rho $ up to a height $h$ . The liquid is closed by a piston of mass m and area of cross-section $A$ . There is a small hole at the bottom of the vessel. The speed $v$ with which the liquid comes out of the hole is

Question

NTA AbhyasNTA Abhyas 2020

Solution:

Applying Bernoulli's theorem at 1 and 2 : difference in pressure energy between 1 and $2 \, =$ difference in kinetic energy between 1 and 2

Solution
or $\rho gh \, + \, \frac{m g}{A} \, = \, \frac{1}{2}\rho v^{2}$
or $v=\sqrt{2 g h + \frac{2 m g}{\rho A}}= \, \sqrt{2 \left(g h + \frac{m g}{\rho A}\right)}$