Question

An air bubble of radius $r=3mm$ moves up in a viscous liquid with a constant velocity $v=0.7cm/s$ and the density of the liquid is $1.75g/cc$. If viscosity of liquid (in poise) is given by $10x$ then $x$ will be (Neglect the density of air in comparision to that of the liquid.)

Answer 1

For the bubble, the buoyant force is balanced by the gravitational force,
$B=mg$
$B={\rho }_{l}Vg$
$6\pi \eta rv=\frac{4}{3}\pi r^3{\rho }_{l}g$
$\eta =\frac{2}{9}{r}^2\frac{{\rho }_{l}g}{v}$
$g$ in $CGS$ system is $1000cm/s^2$
$\eta =\frac{2}{9}\times \frac{(0.3{)}^2\times 1.75\times 1000}{0.7}=50\text{poise}$