# Scale-up Engineering

Johann Stichlmair
Department of Chemical Engineering at the Technical University of Munich, Lehrstuhl A für Verfahrenstechnik Arcisstr. 21, D- 0333 Munchen, Germany

## Description

Scale-up Engineering is an extremely effective tool for engineers of all disciplines. It is based on the description of technical objects by complete sets of dimensionless numbers. The scale-up laws are very helpful in solving engineering problems by simple or small-scale experiments. Thus, the dimensionless numbers and scale-up laws are used in many fields of natural and engineering sciences. Classical fields of applications are fluid mechanics, heat and mass transfer, mechanics (statics, dynamics, stress and strain), and aeronautics. Novel fields of applications are reaction engineering, acoustics and space sciences.

220 pages,
© 2001

## Table of Contents:

1 Description of Physical Phenomena

1.2 Formulation of Physical Relationships

1.3 Principle of Invariance

1.4 Mathematical Formulation of Physical Relationships with Quantities

1.5 Quantity Equations, Modified Quantity Equations, Numerical Equations

1.6 Conversion of Numerical Equations into Other Units

2 Dimensionless Numbers, Dimensionless Groups

2.1 Structure of Dimensionless Numbers

2.2 Derivation of Sets of Dimensionless Numbers from Algebraic Equations

2.3 Derivation of Dimensionless Numbers from Differential Equations

2.4 Derivation of Complete Sets of Dimensionless Numbers from Relevance Lists

2.4.1 Calculation Procedure

2.4.2 Equivalence Transformations

2.4.3 Examples for the Calculation Procedure

2.4.4 Derivation of Different Sets of Dimensionless Numbers

2.4.5 Derivation of Short Sets of Dimensionless Numbers

2.5 Derivation of Modified Sets of Dimensionless Numbers from a Given Set

2.6 Maximum Number of Equivalent Sets of Dimensionless Groups

3 Application of Dimensionless Numbers for the Investigation of Natural Phenomena

3.1 Relationships Described by Algebraic Equations

3.2 Relationships Described by Differential Equations

3.3 Empirical Relationships

3.3.1 Flow Through Beds of Solid Particles

4 Similarity in Engineering Science

4.3 Application of Model Laws at Total Similarity

4.3.1 Terminal Velocity of a Glass Body in Acetylene

4.3.2 Pressure Drop of Liquid Sodium in a Pipe

4.3.3 Convective Heat Transfer from Sulfuric Acid to a Wall

4.3.4 Convective Heat Transfer from Liquid Sodium to a Wall

4.3.6 Spraying of Liquid Oxygen in a Nozzle

4.3.9 Resistance of a Dam to Earthquakes

4.3.10 Oscillations of a Building in a Storm

4.3.11 Deformations of a Steel Beam

4.3.12 Acoustics of a Concert Hall

4.3.13 Landing Stability of the Lunar Excursion Module

5.1 Problems Arising in the Application of Similarity Laws

5.2 Application of Model Laws at Partial Similarity

5.2.1 Deformations of a Steel Beam

5.2.2 Splashdown of a Solid Rocket Booster

5.2.3 Convective Heat Transfer of Concentrated Sulfuric Acid

5.2.4 Power Consumption and Heat Transfer in an Agitated Vessel

5.2.5 Suspending Particulate Matter in an Agitated Vessel

5.2.6 Production of Glassware