First slide

Pressure in a fluid-mechanical properties of fluids

Question

When a large bubble rises from the bottom of a lake to the surface. Its radius doubles. If atmospheric pressure is equal to that of column of water height H, then the depth of lake is

Moderate

A

H
B

2H
C

7H
D

8H

Solution

$P_{1} V_{1} = P_{2} V_{2} \Rightarrow (P_{0} + hρg) \times \frac{4}{3} {πr}^{3} = P_{0} \times \frac{4}{3} π (2 r)^{3}$
Where, h = depth of lake
$\Rightarrow hρg = 7 P_{0} \Rightarrow h = 7 \times \frac{Hρg}{ρg} = 7 H$

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