Chapter 34, Problem 34.12QAP

Interpretation Introduction

Interpretation:

The value of the diameter and the density are 9.5 $\text{μm}$ and 1.06 ${\text{g cm}}^{-3}$ respectively in a particular batch of polystyrene microspheres. The setting velocity of particles in 1G gravitational field at $20°\text{C}$ and the time required to 10 mm sediment of particlesis to be determined. The water density is ${\rho }_F=0.998{\text{ g cm}}^{-3}$.

Concept introduction:

The following formula will be used for the calculation of the settling velocity-

$u=\frac{(\rho -{\rho }_F)g}{18\eta }{d}^2$ …… (1)

Here,

$u$ = velocity of particle

$\rho$ = density of particle

${\rho }_F$ = density of fluid

$\eta$ = viscosity of the medium

$d$ = diameter of the particle

g = acceleration due to gravity

Also,

$t=\frac{h}{u}$

Here,

h = sedimentation distance

u = velocity of the particle

t = time