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Questions
With what terminal velocity will an air bubble 0.4 mm in diameter rise in a liquid of viscosity 0.1 Ns/m2 and specific gravity 0.9? Density of air is 1.29 kg/m3.
Calculate the terminal velocity with which an air bubble of diameter 0.4 mm rise through a liquid of viscosity 0.1 Ns/m2 and density 900 kg/m3. Density of air is 1.29 kg/m3.
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Solution
Given: d = 0.4mm,
η = 0.1Pa·s,
ρL = 0.9 × 103 kg/m3 = 900 kg/m3,
ρair = 1.29 kg/m3,
g = 9.8 m/s2
To find: Terminal velocity of the air bubble.
At terminal velocity, the downward viscous force is equal in magnitude to the net upward force.
Viscous force = Buoyant force − The gravitational force
∴ `6πηrv_t = 4/3 pir^3 (rho_"air" - rho_L)`g
∴ `v_t= (2r^2g(rho_"air" - rho_L))/(9η)`
`= (2(2 xx 10^-4)^2 (9.8 )(1.29 - 900))/(9(0.1))`
`= (2 xx 4 xx 9.8 xx (-898.7) xx 10^-8)/0.9`
= −7.829 × 104 × 10−8
= −7.829 × 10−4 m/s ...[The negative sign indicates that the bubble rises up]
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