Question

What is the settling velocity of a discrete particle in a wide body of water when the relevant Reynold's number is less than 0.5? The diameter and specific gravity of the particle are $2\times {10}^{-3}$ cm and 2.65, respectively. Water temperature is ${20}^{\circ }.$ (Kinematic viscosity $=2\times {10}^{-2}c{m}^2/sec$)

• A. $0.025cm/sec$
• B. $0.018cm/sec$
• C. $0.25cm/sec$
• D. $0.0018cm/sec$

Answer 1

The correct option is B $0.018cm/sec$

For Re < 5, we apply Stokes's law equation

$V_s=\frac{g}{18}(G-1)\frac{d^2}{v}$

$=\frac{9.81}{18}(2.65-1)\times \frac{(2\times {10}^{-3}{)}^2}{2\times {10}^{-2}}\frac{m}{se{c}^2}\times \frac{c{m}^2\times sec}{c{m}^2}$

$=\frac{9.81}{18}\left(1.65\right)\times \frac{4\times {10}^{-6}}{2\times {10}^{-2}}\frac{m}{sec}$

$=0.018cm/sec$