Chapter 7, Problem 7.6P

Interpretation Introduction

Interpretation: The pressure drop for different gas velocities for individual fibers of a demister pad is to be calculated using the concept of drag coefficients.

Concept introduction: Just like friction factor in fluid flow through pipes and channels, its analogous is drag coefficient which is used in immersed solids.

It is given as,

  ${\text{C}}_{\text{D}}\text{=}\frac{{\text{F}}_{\text{D}}\text{/A}}{\frac{\text{1}}{\text{2}}{\text{ρ<mover accent="true"><mo>v </mo><mo>¯</mo></mover>}}^{\text{2}}}\mathrm{.......}\text{(1)}$

In the above formula, the notations used are,

  $\begin{array}{l}{\text{C}}_{\text{D}}\text{=}\text{Drag}\text{coefficient}\\ {\text{F}}_{\text{D}}\text{=}\text{Total}\text{drag}\text{force}\\ \text{A}\text{=}\text{Projected}\text{area}\text{of}\text{drag}\\ \text{ρ}\text{=}\text{Density of fluid}\\ \text{<mover accent="true"><mo>v </mo><mo>¯</mo></mover> = Average}\text{Velocity of stream}\end{array}$

The Reynolds number for the fluid is given as,

  $\text{Re}\text{=}\frac{\text{ρ<mover accent="true"><mo>v </mo><mo>¯</mo></mover> D}}{\text{μ}}\mathrm{.......}\text{(2)}$

  $\text{μ}\text{is the viscosity of fluid}$

D is the diameter of the fibers

The volume of the pad is given as,

  $\begin{array}{l}\text{V}\text{=}\text{St(1-ε)}\mathrm{.......}\text{(3)}\\ \text{V is the volume of fiber}\\ \text{S = Area of demister pad}\\ \text{t = Thickness of pad}\\ \text{ε}\text{=}\text{Average}\text{Porosity}\end{array}$

The average velocity is related to superficial velocity as,

  $\begin{array}{l}\text{<mover accent="true"><mo>v </mo><mo>¯</mo></mover> = }\frac{\text{u}}{\text{ε}}\mathrm{.......}\text{(4)}\\ \text{u}\text{=}\text{Superficial}\text{velocity}\text{of}\text{gas}\end{array}$

The pressure drop through the individual fibers is given as,

  $\begin{array}{l}\text{ΔP}\text{=}\frac{{\text{F}}_{\text{D}}}{\text{S}}\mathrm{.......}\text{(5)}\\ \text{ΔP}\text{=}\text{Pressure}\text{drop}\end{array}$