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Standard XII

Physics

Wave Equation

An air bubble...

Question

An air bubble of radius $1 m m$ is allowed to rise through a long cylindrical column of a viscous liquid of radius $5 c m$ and travels at a steady rate of $2.1 c m$ per second. If the density of the liquid is $1.47 g / c c$ , find its viscosity. Assume $g = 980 c m / s^{2}$ and neglect the density of air.

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Solution

R.E.F image
solution At steady state,
$a_{n e t}$ of air bubble = 0
Also,
Stokes's force = Buoyant force
$\Rightarrow 6 π n r v = f g (\frac{4}{3} π r^{3})$
$\Rightarrow n = \frac{2 f g r^{2}}{9 v}$
$\Rightarrow n = \frac{2}{9} \frac{(1.47 \times 10^{3} k g / m^{3}) (9.8 m / s^{2}) (\frac{1 m}{1000})^{2}}{(\frac{2.1}{100} m / s)}$
$\Rightarrow n = 0.1524 m^{2} / s$

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An air bubble of radius 1 mm is allowed to rise through a long cylindrical column of a viscous liquid of radius 5 cm and travels at a steady rate of 2.1 cm per second. If the density of the liquid is 1.47 g/cc, find its viscosity. Assume g=980 cm/s2 and neglect the density of air.

R.E.F imagesolution At steady state,anet of air bubble = 0Also,Stokes's force = Buoyant force⇒6πnrv=fg(43πr3)⇒n=2fgr29v⇒n=29(1.47×103kg/m3)(9.8m/s2)(1m1000)2(2.1100m/s)⇒n=0.1524m2/s