Chemical Engineering > GATE 2017 > Bubble Dynamics
A gas bubble (gas density ρg = 2 kg/m3; bubble diameter D = 10-4 m) is rising vertically through water (density ρ = 1000 kg/m3; viscosity μ = 0.001 Pa.s). Force balance on the bubble leads to the following equation,
dv/dt = (ρ - ρg)g / ρg - 18μv / (ρgD2)
where v is the velocity of the bubble at any given time t. Assume that the volume of the rising bubble does not change. The value of g = 9.81 m/s2. The terminal rising velocity of the bubble (in cm/s), rounded to 2 decimal places, is
dv/dt = (ρ - ρg)g / ρg - 18μv / (ρgD2)
where v is the velocity of the bubble at any given time t. Assume that the volume of the rising bubble does not change. The value of g = 9.81 m/s2. The terminal rising velocity of the bubble (in cm/s), rounded to 2 decimal places, is
Correct : 0.54
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