Question

A bubble of gas whose diameter is 2 cm is travelling in a liquid with constant velocity of 0.90 cm/s. The density of the gas is negligible and density of the liquid is 1.5 $gm/c{m}^3$. Calculate the value of $\eta$.

Answer 1

Given, $v_t=90cm{s}^{-1};r=\frac{2}{2}=1cm$;

$g=980cm{s}^{-2}$

$p=0;\sigma =1.5c{m}^{-3};\eta =?$

$\therefore v_t=\frac{2r^2(p-\sigma )g}{9\eta }$

$\therefore 90=\frac{2\times (1{)}^2(0-1.5)980}{9\eta }=\frac{2\times 1\times 1.5\times 980}{9\eta }$

Here, (-ve) sign indicates that the bubble is moving in the upward direction

$\therefore \eta =\frac{2\times 1.5\times 980}{9\times 90}=3.6296$

$\eta =3.63Poise$