Question

A gas bubble of $2cm$ diameter rises through a liquid of density $1.75gmc{m}^{-3}$ with a fixed speed of $0.35cm{s}^{-1}$ . Neglect the density of the gas. The coefficient of viscosity of the liquid is

• A. $870$ poise
• B. $1120$ poise
• C. $982$ poise
• D. $1089$ poise

Answer 1

Answer: (D)

As gas bubble is moving upward with constant speed so Buoyant force = Viscous drag force
$\Rightarrow F_b=F_v\Rightarrow \left(\frac{4}{3}\pi r^3\right)\rho g=6\pi \eta rv$

$\Rightarrow \eta =\frac{2}{9}\frac{r^2\rho g}{v}$
Here, $r=1cm,\rho =1.75gc{m}^{-3}$ ,
$g=980cm{s}^{-2}$
$v=0.35cm{s}^{-1},\eta =$ ?
$\therefore \eta =\frac{2}{9}\times \frac{1^2\times 1.75\times 980}{0.35}$
$=1088.88\approx 1089$ poise