Find the terminal velocity with which an air bubble of density `1 kg m^(-3)` and 0.6 mm in diameter will rise in a liquid of viscosity `0.15 Nm^(-2)s` and of specific gravity 0.9 ? What is the teminal velocity of the same bubble in water of coefficient of viscosity `10^(-3) Nm^(-2)s`?

Explanation

Here, `rho = 1 kg m^(-3)`
`r = 0.3 mm = 3 xx 10^(-4)m`,
`eta = 0.15 Nm^(-2)s , sigma = 0.9 xx 10^(3) kg m^(-3)`
Terminal velocity of air bubble is
`upsilon = (2 r^(2) (rho-sigma)g)/(9 eta)`
`=(2 xx (3 xx 10^(-4))^(2) [1-0.9 xx 10^(3)]xx9.8)/(9xx0.15)`
`=-0.0012ms^(-1)`
Here negative sign shows that the air bubble will rise up.
Now we will take terminal velocity of air bubble in water.
here, `rho = 1 kg m^(-3) , sigma = 1000 kg m^(-3)`,
`eta = 10^(-3) Nm^(-2)s`
Terminal velocity
`upsilon = (2 r^(2) (rho-sigma)g)/(9 eta)`
`=(2 xx (3 xx 10^(-4))^(2) [1-1000]xx9.8)/(9xx10^(-3))`
`= -0.196 ms^(-1)`.