First slide

Viscosity

Question

A gas bubble of diameter D rises steadily through a solution of density $ρ$ at the rate of v. The coefficient of viscosity of the solution is

Moderate

A

$\frac{D^{2} g ρ}{9 v}$
B

$\frac{D^{2} g ρ}{18 v}$
C

$\frac{2 D^{2} g ρ}{9 v}$
D

$\frac{D^{2} g ρ}{v}$

Solution

$\begin{array}{l} V = \frac{2}{9} r^{2} \frac{(ρ - σ)}{η} g \\ \Rightarrow η = \frac{2}{9} r^{2} \frac{(ρ - σ)}{v} g \\ \Rightarrow η = \frac{2}{9} \frac{{(\frac{D}{2})}^{2} ρ . g}{v} [n e g l e c t i n g σ] \\ \Rightarrow η = \frac{D^{2} ρ . g}{18 v} \end{array}$

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