Project ForgeFluid Mechanics
Mechanical Operations
GATE 2017
Hard
A gas bubble (ρg=2 kg/m³, D=10⁻⁴m) rises through water (ρ=1000 kg/m³, μ=0.001 Pa·s). dv/dt=−g(ρg−ρ)/ρg−(18μ/(ρgD²))v, g=9.81 m/s². The terminal rising velocity (cm/s), rounded to 2 decimal places, is
0.54 cm/s(± 0.03 accepted)
Explanation
At terminal velocity, dv/dt=0: v=−g(ρg−ρ)D²/(18μ)=9.81×998×10⁻⁸/0.018=0.00544 m/s=0.544 cm/s.
Source: GATE CH 2017 (2017)
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