The pressure drop through a chromatographic column is to be calculated in different units. Concept introduction: The pressure drop through the chromatographic column is calculated by the Ergun equation which is a combination of the Kozeny-Carman equation and Burke-Plummer equation. The Kozeny-Carman equation is applicable for the particles in a bed whose Reynolds number is less than 1. It is given as, ΔP L = 150 V ¯ 0 μ(1-ε) 2 ϕ s 2 D p 2 ε 3 ....... ( 1 ) In the above formula, the notations used are, ΔP = Pressure drop through packed tubes L = Length of tube V ¯ 0 = Superficial velocity μ = Viscosity of fluid ε = Bed porosity D p = Pellet diameter ϕ s = Sphericity of particles The Burke Plummer equation is applicable for the particles in a bed whose Reynolds number is more than 1000. It is given as, ΔP L = 1 .75 V ¯ 0 2 ρ(1-ε) ϕ s D p ε 3 ....... (2) ρ= Density of water Ergun equation can be derived by combining equation (1) and equation (2): ΔP L = 150 V ¯ 0 μ(1-ε) 2 ϕ s 2 D p 2 ε 3 + 1 .75 V ¯ 0 2 ρ(1-ε) ϕ s D p ε 3 ....... (3)

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Chapter 7, Problem 7.18P

(a)

Interpretation Introduction

Interpretation: The pressure drop through a chromatographic column is to be calculated in different units.

Concept introduction: The pressure drop through the chromatographic column is calculated by the Ergun equation which is a combination of the Kozeny-Carman equation and Burke-Plummer equation.

The Kozeny-Carman equation is applicable for the particles in a bed whose Reynolds number is less than 1. It is given as,

ΔPL=150V¯0μ(1-ε)2ϕs2Dp2ε3 ....... (1)

In the above formula, the notations used are,

ΔP = Pressure drop through packed tubesL = Length of tubeV¯0 = Superficial velocityμ = Viscosity of fluidε = Bed porosityDp = Pellet diameterϕs = Sphericity of particles

The Burke Plummer equation is applicable for the particles in a bed whose Reynolds number is more than 1000. It is given as,

ΔPL=1.75V¯02ρ(1-ε)ϕsDpε3 ....... (2)

ρ= Density of water

Ergun equation can be derived by combining equation (1) and equation (2):

ΔPL=150V¯0μ(1-ε)2ϕs2Dp2ε3 +1.75V¯02ρ(1-ε)ϕsDpε3 ....... (3)

(b)

Interpretation Introduction

Interpretation:

Sensitivity with particular void fraction should be calculated.

Concept Introduction:

The pressure drop through the chromatographic column is calculated by the Ergun equation which is a combination of the Kozeny-Carman equation and Burke-Plummer equation.

The Kozeny-Carman equation is applicable for the particles in a bed whose Reynolds number is less than 1. It is given as,

ΔPL=150V¯0μ(1-ε)2ϕs2Dp2ε3 ....... (1)

In the above formula, the notations used are,

ΔP = Pressure drop through packed tubesL = Length of tubeV¯0 = Superficial velocityμ = Viscosity of fluidε = Bed porosityDp = Pellet diameterϕs = Sphericity of particles

The Burke Plummer equation is applicable for the particles in a bed whose Reynolds number is more than 1000. It is given as,

ΔPL=1.75V¯02ρ(1-ε)ϕsDpε3 ....... (2)

ρ= Density of water

Ergun equation can be derived by combining equation (1) and equation (2):

ΔPL=150V¯0μ(1-ε)2ϕs2Dp2ε3 +1.75V¯02ρ(1-ε)ϕsDpε3 ....... (3)

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