What is the rate at which a trapped bubble of 2 mm diameter rises slightly through a solution of density 13.6 × 103 kg / m 3 and coefficient of viscosity 1.5 centipoise? Assume, the density of air is negligible and g=10 m / s 2.

Question

What is the rate at which a trapped bubble of 2 mm diameter rises slightly through a solution of density 13.6 × 103 kg / m 3 and coefficient of viscosity 1.5 centipoise? Assume, the density of air is negligible and g=10 m / s 2. (A) 20 m / s (B) 2 m / s (C) 0.2 m / s (D) 0.02 m / s

Tardigrade Admin · Accepted Answer

Emperical formula for velocity of small bubbles rising through a fluid is

v_{terminal} = 1.15 (\frac{g d ( ρ _{f} - ρ _{g} )}{η _{f}}) \times 1 0^{- 2}

where,

d =

mean diameter,

ρ_{f} =

density of fluid,

ρ_{g} =

density of gas of bubble and

η_{f} =

viscosity index of fluid.

v = \frac{1.15 \times 10 \times 2 \times 1 0 ^{- 3} \times 1.3 \times 1 0 ^{3} \times 1 0 ^{- 2}}{1.5 \times 1 0 ^{- 2}}

= 19.99 m s^{- 1} = 20 m s^{- 1}

Q. What is the rate at which a trapped bubble of 2mm diameter rises slightly through a solution of density 13.6×103kg/m3 and coefficient of viscosity 1.5 centipoise? Assume, the density of air is negligible and g=10m/s2.

20 m / s

2 m / s

0.2 m / s

0.02 m / s

Q. What is the rate at which a trapped bubble of $2 mm$ diameter rises slightly through a solution of density $13.6 \times 1 0^{3} k g / m^{3}$ and coefficient of viscosity $1.5$ centipoise? Assume, the density of air is negligible and $g = 10 m / s^{2}$ .