2019 Mechanical Properties of FluidsSurface Tension – Excess Pressure in a Soap Bubble Hard Question 20 of 34 in Mechanical Properties of Fluids

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of $2.5\times10^{-2}\ N/m$. The pressure inside the bubble equals at a point $Z_0$ below the free surface of water in a container. Taking $g=10\ m/s^2$, density of water $=10^3\ kg/m^3$, the value of $Z_0$ is:

A 100 cm
B 10 cm
C 1 cm
D 0.5 cm

The answer is C.

Solution

Excess pressure inside a soap bubble $=\frac{4T}{R}$; gauge pressure at depth $Z_0$ in water $=\rho gZ_0$. $P_0+\frac{4T}{R}=P_0+\rho gZ_0\Rightarrow Z_0=\frac{4T}{R\rho g}$ $Z_0=\frac{4\times2.5\times10^{-2}}{10^{-3}\times1000\times10}\ m=10^{-2}\ m$ $Z_0=1\ cm$

Concept depth of water with pressure equal to that inside a bubble

Mechanical Properties of Fluids in past papers

34 questions from this chapter have appeared across 14 exam years.