Fluid MechanicsMedium
Question
If an air bubble of diameter 2 mm rises steadily through a liquid of density $2000\text{ }kg/m^{3}$ at a rate of $0.5\text{ }cm/s$, then the coefficient of viscosity of liquid is $\_\_\_\_$ Poise. (Take $g = 10\text{ }m/s^{2}$ )
Options
A.0.88
B.8.8
C.88.8
D.0.088
Solution
Sol. [Key Concept: Terminal rise: buoyancy $=$ viscous drag, $\frac{4}{3}\pi\ R^{3}\rho\ g = 6\pi\eta\ Rv$.]
For constant speed
$${F_{B} = F_{V} }{\Rightarrow \rho_{\mathcal{l}}\frac{4}{3}\pi R^{3}\text{ }g = 6\pi\eta Rv }{\frac{2}{9}\frac{\rho_{\mathcal{l}}R^{2}g}{V} = \eta }{\Rightarrow \frac{2}{9} \times \frac{2000 \times 10^{- 6} \times 10}{5 \times 10^{- 3}} = \eta }{\Rightarrow \eta = \frac{8}{9} \times 10 }$$$\Rightarrow \eta = \frac{80}{9}$ Poise $= 8.88$
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