Chapter 7, Problem 7.16P

(a)

Interpretation Introduction

Interpretation:

The terminal velocity for different size of particles is to be calculated.

Concept Introduction:

The terminal velocity is the constant velocity which a particle attains when moving in a fluid at the zero acceleration.

For very small Reynolds number, Stokes law is applied to calculate the terminal velocity and equation for the same is given as,

  ${\text{u}}_{\text{t}}\text{=}\frac{{\text{gD}}_{\text{p}}{}^{\text{2}}{\text{(ρ}}_{\text{p}}\text{-ρ)}}{\text{18μ}}\mathrm{.......}\text{(1)}$

The notations used are,

  $\begin{array}{l}{\text{u}}_{\text{t}}\text{=}\text{Terminal}\text{velocity}\text{of}\text{particle}\\ \text{g}\text{=}\text{Acceleration}\text{due}\text{to}\text{gravity}\\ {\text{D}}_{\text{p}}\text{=}\text{Particle}\text{diameter}\\ \text{μ}\text{=}\text{Viscosity}\text{of}\text{air}\\ {\text{ρ}}_{\text{p}}\text{=}\text{Density}\text{of}\text{particle}\\ \text{ρ}\text{=}\text{Density}\text{of}\text{air}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The residence time to settle the dust is to be calculated.

Concept Introduction:

The residence time is the time required by the dust particles to settle down in the rectangular chamber. It is given by,

  $\text{t}\text{=}\frac{\text{d}}{{\text{u}}_{\text{t}}}\mathrm{.......}(2)$

t is the residence time

d is the depth of the rectangular chamber