Question

An air bubble of radius 1mm is allowed to raise through a long cylindrical column of a viscous liquid of radius 5cm and travels at a steady rate of 2.1cm/sec. If the density of liquid if 1.5gm/cm3. Find its viscosity

Answer 1

Given,

Radius of bubble = 1 mm =0.001m

Density of liquid = 1.5g/cc= 1500kg/m^3

Velocity =2.1cm/s= 0.021m/s

Volume of bubble = (4/3)*π*r^3 = 4.1887*10^-9 m^3

Here, buoyant force = weight of liquid displaced by bubble.

Weight displaced = (volume of bubble * density of liquid * acceleration due to gravity) = 6.1573*10^-5 N

By stokes law,

Viscous force = 6πnrv, where v = velocity and n = viscosity

On equating Viscous force to buoyant force we get,

6πnrv = 0.06165 N  

On solving by substituting the respective values in the above equation,

∴ Viscosity, n = 0.1564 Nm/s^2.