Question

An air bubble of 1cm radius is rising at a steady rate of 2mm /sec through a liquid of density 1.5 gm per cm cube neglect density of air , if g is 1000 cm /sec square , then the coffecient of viscosity of the liquid is ????????????????????????????????

Answer 1

An air bubble of 1cm radius is rising at a steady rate of $2\frac{mm}{s}$ through a liquid of density $1.5\frac{g}{cm^3}$ neglect density of air, if $g$ is $1000\frac{cm}{s^2}$, then the coefficient of viscosity of the liquid is?

Force of viscosity equals (Stokes' law):

$$F _ {v} = 6 \pi \mu v r$$

where $v$ – speed of the bubble, $\mu$ – coefficient of viscosity

Buoyant force that is exerted on bubble equals:

$$F _ {b} = \rho g V = \rho g \frac {4}{3} \pi r ^ {3}$$

Newton's first law of motion:

$$F _ {b} = F _ {v}$$ $$6 \pi \mu v r = \rho g \frac {4}{3} \pi r ^ {3}$$ $$\mu = \frac {\rho g \frac {4}{3} \pi r ^ {3}}{6 \pi v r} = \frac {2 \rho g r ^ {2}}{9 v} \cong 167 \frac {kg}{m * s}$$

Answer: $167\frac{kg}{m*s}$