Question

A powder comprising particles of various sizes is stirred up in a vessel filled to a height of 10 cm with water. Assuming the particles to be spherical, find the size of the largest particle that will remain in suspension after 1 h (density of powder = 4 $g/c{m}^3$, viscosity of water = 0.01 poise).

Answer 1

Terminal velocity of the largest particle which is just about to settle at the bottom of the
Vessel is $v_r=\frac{10\times {10}^{-2}}{3600}m/s$
Let r be the radius of that particle. Then
$v_r=\frac{2}{9}{r}^2\frac{(\sigma -\rho )}{\eta }g$
where $\sigma =4\times {10}^{3}kg/m^{2}and\eta =\frac{0.01}{10}Ns/m^3$
After solving, we get r = 2.0 $\times {10}^{-6}$ m.