Special bacterias of radius 1 × 10–6 m and density 1.1 × 103 kg m–3 is allowed to settle uniformly at terminal speed in an aqueous suspension. Density of water is 103 kg m–3, viscosity of water 1 × 10–3 Pa-s and depth of settlement 1 × 10

Engineering

Physics

Liquid Pressure

Viscosity and Terminal Velocity New

Forces and Types of Forces

Question

Special bacterias of radius 1 × 10^–6 m and density 1.1 × 10³ kg m^–3 is allowed to settle uniformly at terminal speed in an aqueous suspension. Density of water is 10³ kg m^–3, viscosity of water 1 × 10^–3 Pa-s and depth of settlement 1 × 10^–2 m. The time for settlement is

settlement will not occur without centrifuge

10 hrs 25 min

12 hrs 30 min

11 hrs 10 min

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$y_{t} = \frac{2}{9} \frac{r^{2} g (ρ - σ)}{η}$

$= \frac{2}{9} \times \frac{10^{- 12} \times 10 \times 10^{2}}{10^{- 3}} = \frac{2}{9} \times 10^{- 6} m / s$

$t = \frac{10^{- 2}}{\frac{2}{9} \times 10^{- 6}} = 4 .5 \times 10^{4} \sec$

$= \frac{45000}{3600} = 12 .5 Hrs . = 12 hrs . 30 \min$