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Terminal Velocity

With what ter...

Question

With what terminal velocity will an air bubble of diameter $0.8 m m$ rise in a liquid of density $900 k g m^{- 3}$ and viscosity $0.15 N s m^{- 2}$ ? What will be the terminal velocity of the same bubble in water? Ignore density of air.

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Solution

Terminal velocity is given as
$V_{T} = \frac{2}{9} r^{2} \frac{(δ - σ) g}{h}$
$∵$ no density of air $ρ = 0$

$V_{T} = \frac{2}{9} r^{2} \frac{(σ) g}{h}$

$= \frac{2}{9} \frac{(0.4 \times 10^{- 3})^{2} (900) \times 9.8}{0.15}$

$= 0.0020 m / s$

$V_{T} = 0.20 c m / s$

For water
$(V_{T})_{l i q} = (V_{T})_{w a t e r}$

$\frac{(V_{T})_{l i q}}{{V_{T}}_{(H_{2} O)}} = \frac{σ_{1}}{σ_{2}}$

$V_{T (H_{2} O)} = V_{T (l i q)} \times \frac{σ_{2}}{σ_{1}} = 0.002 \times \frac{900}{997}$

$V_{T (H_{2} O)} = 0.18 c m / s$

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