First slide

Fluid statics

Question

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

Easy

A

H
B

2 H
C

7 H
D

8 H

Solution

${(PV)}_{bottom} = {(PV)}_{surface} \Rightarrow (P_{0} + {hρ}_{w} g) \times \frac{4}{3} {πr}^{3} = P_{0} \times \frac{4}{3} π {(2 r)}^{3} \Rightarrow {hρ}_{w} g = 7 P_{0} = 7 [{Hρ}_{w} g] \Rightarrow h = 7 H$

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