Mechanical Properties of Fluids

Question : 20

Total: 31

What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature (20°C) is 2.50×10–2Nm–1? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble?
(1 atmospheric pressure is 1.01×105Pa).

Solution:

Here, surface tension of the soap solution, T=2.5×10–2Nm–1
density of the soap solution, r=1.2×103kg m–3;radius of the soap bubble,
R=5.0‌mm=5.0×10–3m
Now, the excess pressure inside the soap bubble,
Pi−P0=

4×2.5×10−2

5.0×10−3

=20 Pa
Also, the excess pressure inside the air bubble,
Pi−P0=

2×2.5×10−2

5.0×10−3

=
10Pa
Now, the pressure outside the air bubble at a depth of 40cm i.e.0.4m,
P0= atmospheric pressure + pressure due to 0.4 m column of soap solution
=1.01×105+0.4×1.2×103×9.8
=1.05704×105Pa
Therefore, pressure inside the air bubble,
Pi=P0+

=1.05704×105+10
=1.05714×105 Pa.

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