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 $1.4\times {10}^{3}kg/m^3$, what is its viscosity?

• A. 1.15 kg/m-s
• B. 15kg/m-s
• C. 2.25 kg/m-s
• D. 19.05 kg/m-s

Answer 1

The correct option is D

19.05 kg/m-s

In this case the terminal velocity is upward. Since $\sigma >\rho$, the density of the air

inside the bubble may be neglected completely.

From equation

$v=\frac{2a^2(\sigma -\rho )g}{g\eta }=\frac{2a^2\rho g}{9\eta }\Rightarrow \eta =\frac{2a^2\rho g}{9v}$

where, a = 5mm, $\rho =1.4\times {10}^{3}kg/m^3,v=4mm/s$

$\therefore \eta =\frac{2\times 25\times {10}^{-6}\times 1.4\times {10}^3\times 9.8}{9\times 4\times {10}^{-3}}kg/m-s=19.05kg/m-s$

Hence, (D) is correct.