Question

What is the rate at which a trapped bubble of $2\, mm$ diameter rises slightly through a solution of density $13.6 \times 10^{3} \,kg / m ^{3}$ and coefficient of viscosity $1.5$ centipoise? Assume, the density of air is negligible and $g=10 \,m / s ^{2}$.

• A. 20 m / s
• B. 2 m / s
• C. 0.2 m / s
• D. 0.02 m / s

Answer 1

Answer: (A)

Emperical formula for velocity of small bubbles rising through a fluid is
$v_{\text {terminal }}=1.15\left(\frac{g d\left(\rho_{f}-\rho_{g}\right)}{\eta_{f}}\right) \times 10^{-2}$
where, $d=$ mean diameter, $\rho_{f}=$ density of fluid, $\rho_{g}=$ density of gas of bubble and $\eta_{f}=$ viscosity index of fluid.
$v =\frac{1.15 \times 10 \times 2 \times 10^{-3} \times 1.3 \times 10^{3} \times 10^{-2}}{1.5 \times 10^{-2}} $
$=19.99 \,ms ^{-1}=20 \,ms ^{-1}$