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PhysicsFluidBernoulli's theorem and applicationsMedium2 minPYQ_2018

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When an air bubble of radius $r$ rises from the bottom to the surface of a lake, its radius becomes $\frac{5 r}{4}$ . Taking the atmospheric pressure to be equal to $10 m$ height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature):

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Answer:

Solution:

Using $P_{1} V_{1} = P_{2} V_{2}$ $(P_{1}) \frac{4}{3} π r^{3} = (P_{2}) \frac{4}{3} π \frac{125 r ^{3}}{64} \frac{ρ g ( 10 ) + ρ g h}{ρ g ( 10 )} = \frac{125}{64} 640 + 64 h = 1250$ On solving we get $h = 9.5 m$

Stream:JEESubject:PhysicsTopic:FluidSubtopic:Bernoulli's theorem and applications

⏱ 2mℹ️ Source: PYQ_2018

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