Chapter 2, Problem 2.5P

Interpretation Introduction

Interpretation: The volume of the continuous gravity decanter to separate the chlorobenzene from the wash liquid is to be calculated.

Concept introduction: A continuous gravity decanter is a system that separates 2 immiscible liquids of different densities. The volume of the two components differing in densities are given as

For Component-1,

  ${\text{V}}_{\text{1}}\text{=}\frac{{\text{<mover accent="true"> <mo>m</mo><mo>˙</mo></mover>}}_{\text{1}}}{{\text{ρ}}_{\text{1}}}\text{×t}\mathrm{......}\text{(1)}$

For Component-2,

  ${\text{V}}_{\text{2}}\text{=}\frac{{\text{<mover accent="true"> <mo>m</mo><mo>˙</mo></mover>}}_{\text{2}}}{{\text{ρ}}_{\text{2}}}\text{×t}\mathrm{......}\text{(2)}$

The notations used in the above formulae are,

  $\begin{array}{l}{\text{V}}_{\text{1}}\text{and}{\text{V}}_{\text{2}}\text{are}\text{the}\text{volumes}\text{of}\text{component-1}\text{and}\text{component-2}\text{respectively}\\ {\text{<mover accent="true"> <mo>m</mo><mo>˙</mo></mover>}}_{\text{1}}\text{and}{\text{<mover accent="true"> <mo>m</mo><mo>˙</mo></mover>}}_{\text{2}}\text{are}\text{the}\text{mass}\text{flow}\text{rates}\text{of}\text{component-1}\text{and}\text{component-2}\text{respectively}\text{.}\\ {\text{ρ}}_{\text{1}}\text{and}{\text{ρ}}_{\text{2}}\text{are}\text{the}\text{densities}\text{of}\text{component-1}\text{and}\text{component-2}\text{respectively}\\ \text{t}\text{=}\text{Separation}\text{time}\end{array}$

Separation time is the time required to separate the two fluids of different densities and is given by the following formula,

  $\begin{array}{l}\text{t}\text{=}\frac{\text{100μ}}{{\text{ρ}}_{\text{1}}\text{-}{\text{ρ}}_{\text{2}}}\mathrm{......}\text{(3)}\\ \text{μ}\text{=}\text{Viscosity}\text{of}\text{the}\text{continous}\text{phase}\text{in}\text{cP}\text{.}\end{array}$