Question

A air bubble of radiuas 1mm is allowed to rise throigh a long cylindrical column of a viscous liquid of radius 5cm and travelsat a steady rate 2.1 cm per seconds if the density of the liquid is 1.47 g cc find its visxosity

Answer 1

Hey mate,

# Answer-
η = 0.155 Pa.s

## Explanation-
# Given-
r = 1 mm = 10^-3 m
R = 5 cm = 0.05 m
v = 2.1 cm/s = 2.1×10^-2 m/s
d = 1.47 gm/cm^3 = 1470 kg/m^3

# Solution-
Here, we can calculate-
a) Buoyant force-
Fb = mg = 4/3 πr^3d g
b) Viscous force-
Fv = 6πηrv

For bubble to move with steady speed, buoyant force must be balanced by viscous force.
Fb = Fv
4/3 πr^3dg = 6πηrv

Rearranging,
η = 2/9 r^2dg / v
η = 2/9 × (10^-3)^2 × 1470 × 10 / 2.1×10^-2
η = 0.155 Pa.s

Viscosity of the liquid is 0.155 Pa.s

Hope that was useful...