What is the rate at which a trapped bubble of 2 mm diameter rises slightly through a solution of density `13.6 xx 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` .

Options

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

Answer

A

Explanation

Emperical formula for velocity of small bubbles rising through a fluid is
` V_"terminal" = 1.15 ( (gd (rho_f - rho_g) )/(eta_f) ) xx 10^(-2)`
where , d = mean diameter , `rho_f` - density of fluid, `rho_y` = density of gas bubble and `eta_f` = viscosity index of fluid
` v = (1.15 xx 10 xx 2 xx 10^(-3) xx 1.3 xx 10^3 xx 10^(-2) )/(1.5 xx 10^(-2) )`
` = 19.99 ms^(-1) = 20 ms^(-1)`