Question

an air bubble of radius 0.4 mm rises up in water determine the terminal speed of the bubble density of air is negligible​

Answer 1

terminal speed of bubble is 0.348 m/s

terminal speed is given by,

v = 2/9 gr² (ρ - σ)/η

coefficient of viscosity of water, η = 1 × 10^-3 kg/ms

density of water, ρ = 10³ kg/m³

density of Air, σ = 0 kg/m³

radius of air bubble ,r = 0.4 mm = 4 × 10^-4 m

acceleration due to gravity, g = 9.8m/s²

so, v = 2/9 × 9.8 × (4 × 10^-4)² (10³ - 0)/(1 × 10^-3)

= 2/9 × 9.8 × 16 × 10^-8 × 10^6

= 19.6/9 × 16 × 10^-2

= 0.348 m/s

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Answer 2

$\huge\bold\purple{Answer:-}$

terminal speed is given by,

v = 2/9 gr² (ρ - σ)/η

coefficient of viscosity of water, η = 1 × 10^-3 kg/ms

density of water, ρ = 10³ kg/m³

density of Air, σ = 0 kg/m³

radius of air bubble ,r = 0.4 mm = 4 × 10^-4 m

acceleration due to gravity, g = 9.8m/s²

so, v = 2/9 × 9.8 × (4 × 10^-4)² (10³ - 0)/(1 × 10^-3)

= 2/9 × 9.8 × 16 × 10^-8 × 10^6

= 19.6/9 × 16 × 10^-2

= 0.348 m/s