With what terminal velocity will an air bubble of density `1 kg m^(-3)` and `0.6` mm diameter rise in a liquid of viscosity `0.15 Ns m^(-2)` and specific gravity `0.9` ? What is the terminal velocity of the same bubble in water of `eta=1xx10^(-3) Ns m^(-2)` ?

Explanation

Here, `r=0.6//2=0.3 mim=0.3xx10^(-3)m`
`3xx10^(-4) m`
`eta=0.15, g=9.8 ms^(-2)`
Density of liquid (i.e. ,medium)`sigma`
`=` sp. Gravity of liquid x density of water
`0.9xx10^(3) kg m^(-3) =900 kg m^(-3)`
Density of air bubble, `rho= kg m^(-3)`
Terminal velocity of air bubble is
`v=(2r^(2)(rho-sigma)g)/(9 eta) =(2xx(3xx10^(-4))^(2)[1-900])/(9xx0.15)`
`=-0.00012 ms^(-1)`
Here negative sign indicates that the air bubble rises up.
Terminal velocity of air bubble in water
Here, `sigma=10^(3) kg//m^(3) , eta=10^(3) Ns m^(2)`
`v_(g)=(2xx(3xx10^(-4))^(2)xx9.8(1-10^(3)))/(9xx10^(3))`
`=-0.196 ms^(-1)`