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An air bubble of radius 1 mm is allowed to rise through a long

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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 $5 c m$ and travels at a steady rate of $2.1 c m$ per second. If the density of the liquid is $1.47 g / cc$ , find its viscosity. Assume $g = 980 c m / s^{2}$ and neglect the density of air.

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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 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 / cc

, find its viscosity. Assume

g = 980 c m / s^{2}

and neglect the density of air.

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Text solutionVerified

R.E.F image

solution At steady state,

a_{n e t}

of air bubble = 0

Also,

Stokes's force = Buoyant force

\Rightarrow 6 πn 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 1 0 ^{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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Question Text	An air bubble of radius $1 mm$ 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 $1.47 g / cc$ , find its viscosity. Assume $g = 980 c m / s^{2}$ and neglect the density of air.
Answer Type	Text solution:1
Upvotes	154