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Scaling Chemical Processes by Jonathan Worstell

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Chapter 2

Dimensional Analysis

Abstract

This chapter provides the foundation for using a matrix-based procedure for identifying and defining dimensionless parameters.

Keywords

Dimension; fundamental dimension; derived dimension; unit systems; Dimension table; Dimension matrix; Total matrix

Introduction

To ensure that a prototype chemical process behaves similarly to its model chemical process, we must establish the relationships

ΠMGeometric=ΠPGeometricΠMStatic=ΠPStaticΠMKinematic=ΠPKinematicΠMDynamic=ΠPDynamicΠMThermal=ΠPThermalΠMChemical=ΠPChemical (2.1)

image (2.1)

where each ΠMi and ΠPi is a dimensionless parameter for the model M and the prototype P. The ...

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