The diameter of an air bubble which was initially 2 mm , rises steadily through a solution of density 1750 kg / m 3 at the rate of 0.35 cm / s . Coefficient of viscosity of the solution is ______ (Ass

Question

The diameter of an air bubble which was initially 2 mm , rises steadily through a solution of density 1750 kg / m 3 at the rate of 0.35 cm / s . Coefficient of viscosity of the solution is ______ (Assume mass of the bubble to be negligible) (Answer in Poise to the nearest integer)

TestHub · Accepted Answer

As the bubble is rising steadily the net force acting on it will be zero.
(Because of density of air is negligible, so the value of $m g$ can be neglected)
So, the force of buoyancy $B$ is equal to the weight of the displaced liquid acting upward is equal to the viscous force acting downward, i.e., $B = F$ .
$\Rightarrow \frac{4 π}{3} R^{3} ρ g = 6 π η R v$
Putting $R = 1 mm = 10^{- 3} m$ , $ρ = 1.75 \times 10^{3} kg m^{- 3}$ , $g = 10 m s^{- 2}$ and $v = 0.35 \times 10^{- 2} m s^{- 1}$
$η = \frac{10}{9} = 1 \cdot 11$
In SI unit, $η = 11$ poise $(CGS)$ .

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