Question
An air bubble of radius 5mm rises through a vat of syrup at a steady speed of 4mm/s. If the syrup has a density of 1.4×103kg/m3, what is its viscosity?
Answer: Option D
:
D
In this case the terminal velocity is upward. Since σ>ρ, the density of the air
inside the bubble may be neglected completely.
From equation
v=2a2(σ−ρ)ggη=2a2ρg9η⇒η=2a2ρg9v
where, a = 5mm,ρ=1.4×103kg/m3,v=4mm/s
∴η=2×25×10−6×1.4×103×9.89×4×10−3kg/m−s=19.05kg/m−s
Hence, (D) is correct.
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:
D
In this case the terminal velocity is upward. Since σ>ρ, the density of the air
inside the bubble may be neglected completely.
From equation
v=2a2(σ−ρ)ggη=2a2ρg9η⇒η=2a2ρg9v
where, a = 5mm,ρ=1.4×103kg/m3,v=4mm/s
∴η=2×25×10−6×1.4×103×9.89×4×10−3kg/m−s=19.05kg/m−s
Hence, (D) is correct.
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