A large cylindrical tank of cross-sectional are $1 m^{2}$ is filled with water. It has a small hole at a height of $1 m$ from the bottom. A movable piston of mass 5kg is fitted on top of the tank such that it can slide in the tank freely. A load of 45kg is applied on the top of water piston as shown in figure. Find the value of v when piston is 7m above the bottom( $g = 10 m / s^{2}$ )

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Solution

Applying Bernaulis theorem on upper and lower part of the vessel
$P_{0} + 50 \times 10 \times 1 + 1000 \times 10 \times 7 = \frac{1}{2} ρ v^{2} + P_{0} v = \sqrt{\frac{(500 + 70000) 2}{1000}} v = \sqrt{\frac{705}{5}} v = \sqrt{352.5} v = 18.8 m / s$

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