First slide

Pressure in a fluid-mechanical properties of fluids

Question

The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercury, the depth of the lake is

Moderate

A

5 m
B

10 m
C

15 m
D

20 m

Solution

$\begin{array}{l} P_{1} V_{1} = P_{2} V_{2} \Rightarrow (P_{0} + hρg) V = P_{0} \times 3 V \\ \Rightarrow hρg = 2 P_{0} \Rightarrow h = \frac{2 \times 75 \times 13 .6 \times g}{\frac{13 .6}{10} \times g} = 15 m \end{array}$

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