An air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m³ at a speed of 0.5 cm/s. Find the coefficient of viscosity of the liquid in Poise.

For an air bubble rising through a liquid, Stokes' Law gives:

v = (2r²ρg)/(9η)

where:

• r = radius of bubble
• ρ = density of liquid
• η = coefficient of viscosity
• v = terminal velocity

Given:

Diameter = 2 mm

Radius = 1 mm = 10^-3 m

Density = 2000 kg/m³

Velocity = 0.5 cm/s

= 0.005 m/s

Substituting:

η = (2 × (10^-3)² × 2000 × 10) / (9 × 0.005)

η = 0.888 SI unit

Since:

1 Pa·s = 10 Poise

η = 8.88 Poise

Final Answer

8.88 Poise