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Copyright © 1997 CRC Press, LLC

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Library of Congress Cataloging-in-Publication Data

Handbook of food engineering practice / edited by Enrique Rotstein,
R. Paul Singh, and Kenneth J. Valentas.
p. cm.
Includes bibliographical references and index.
ISBN 0-8493-8694-2 (alk. paper)
1. Food industry and trade Handbooks, manuals, etc.
I. Rotstein, Enrique. II. Singh, R. Paul. III. Valentas, Kenneth
J., 1938- .
TP370.4.H37 1997
664 dc21 96-53959

CIP
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Copyright © 1997 CRC Press, LLC


The Editors

Enrique Rotstein, Ph.D.,

is Vice President of Process Technology of the Pillsbury Company,
Minneapolis, Minnesota. He is responsible for corporate process development, serving all
the different product lines of his company.
Dr. Rotstein received his bachelor’s degree in Chemical Engineering from Universidad
del Sur, Bahia Blanca, Argentina. He obtained his Ph.D. from Imperial College, University
of London, London, U.K. He served successively as Assistant, Associate, and Full Professor
of Chemical Engineering at Universidad del Sur. In this capacity he founded and directed
PLAPIQUI, Planta Piloto de Ingenieria Quimica, one of the leading Chemical Engineering
teaching and research institutes in Latin America. During his academic career he also taught
at the University of Minnesota and at Imperial College, holding visiting professorships. He
worked for DuPont, Argentina, and for Monsanto Chemical Co., Plastics Division. In 1987
he joined The Pillsbury Company as Director of Process Analysis and Director of Process
Engineering. He assumed his present position in 1995.
Dr. Rotstein has been a member of the board of the Argentina National Science Council,
a member of the executive editorial committee of the

Latin American Journal of Chemical
Engineering and Applied Chemistry

, a member of the internal advisory board of Drying
Technology, and a member of the editorial advisory boards of

Advances in Drying, Physico
Chemical Hydrodynamics Journal


, and

Journal of Food Process Engineering

. Since 1991 he
has been a member of the Food Engineering Advisory Council, University of California,
Davis. He received the Jorge Magnin Prize from the Argentina National Science Council, was
Hill Visiting Professor at the University of Minnesota Chemical Engineering and Materials
Science Department, was keynote lecturer at a number of international technical conferences,
and received the Excellence in Drying Award at the 1992 International Drying Symposium.
Dr. Rotstein is the author of nearly 100 papers and has authored or co-authored several books.

R. Paul Singh, Ph.D.,

is a Professor of Food Engineering, Department of Biological and
Agricultural Engineering, Department of Food Science and Technology, University of Cali-
fornia, Davis.
Dr. Singh graduated in 1970 from Punjab Agricultural University, Ludhiana, India, with
a degree in Agricultural Engineering. He obtained an M.S. degree from the University of
Wisconsin, Madison, and a Ph.D. degree from Michigan State University in 1974. Following
a year of teaching at Michigan State University, he moved to the University of California,
Davis, in 1975 as an Assistant Professor of Food Engineering. He was promoted to Associate
Professor in 1979 and, again, to Professor in 1983.
Dr. Singh is a member of the Institute of Food Technologists, American Society of
Agricultural Engineers, and Sigma Xi. He received the Samuel Cate Prescott Award for
Research, Institute of Food Technologies, in 1982, and the A. W. Farrall Young Educator
Award, American Society of Agricultural Engineers in 1986. He was a NATO Senior Guest
Lecturer in Portugal in 1987 and 1993, and received the IFT International Award, Institute
of Food Technologists, 1988, and the Distinguished Alumnus Award from Punjab Agricultural
University in 1989, and the DFISA/FPEI Food Engineering Award in 1997.

Dr. Singh has authored and co-authored nine books and over 160 technical papers. He
is a co-editor of the

Journal of Food Process Engineering.

His current research interests are
in studying transport phenomena in foods as influenced by structural changes during processing.

Copyright © 1997 CRC Press, LLC

Kenneth J. Valentas, Ph.D.,

is Director of the Bioprocess Technology Institute and Adjunct
Professor of Chemical Engineering at the University of Minnesota. He received his B.S. in
Chemical Engineering from the University of Illinois and his Ph.D. in Chemical Engineering
from the University of Minnesota.
Dr. Valentas’ career in the Food Processing Industry spans 24 years, with experience in
Research and Development at General Mills and Pillsbury and as Vice President of Engi-
neering at Pillsbury-Grand Met. He holds seven patents, is the author of several articles, and
is co-author of

Food Processing Operations and Scale-Up.

Dr. Valentas received the “Food, Pharmaceutical, and Bioengineering Division Award”
from AIChE in 1990 for outstanding contributions to research and development in the food
processing industry and exemplary leadership in the application of chemical engineering
principles to food processing.
His current research interests include the application of biorefining principles to food
processing wastes and production of amino acids via fermentation from thermal tolerant
methlyotrophs.


Copyright © 1997 CRC Press, LLC

Contributors

Ed Boehmer

StarchTech, Inc.
Golden Valley, Minnesota

David Bresnahan

Kraft Foods, Inc.
Tarrytown, New York

Chin Shu Chen

Citrus Research and Education Center
University of Florida
Lake Alfred, Florida

Julius Chu

The Pillsbury Company
Minneapolis, Minnesota

J. Peter Clark

Fluor Daniel, Inc.
Chicago, Illinois


Donald J. Cleland

Centre for Postharvest
and Refrigeration Research
Massey University
Palmerston North, New Zealand

Guillermo H. Crapiste

PLAPIQUI
Universidad Nacional del Sur–CONICET
Bahia Blanca, Argentina

Brian E. Farkas

Department of Food Science
North Carolina State University
Raleigh, North Carolina

Daniel F. Farkas

Department of Food Science
and Technology
Oregon State University
Corvallis, Oregon

Ernesto Hernandez

Food Protein Research

and Development Center
Texas A & M University
College Station, Texas

Ruben J. Hernandez

School of Packaging
Michigan State University
East Lansing, Michigan

Theodore P. Labuza

Department of Food Science and Nutrition
University of Minnesota
St. Paul, Minnesota

Leon Levine

Leon Levine & Associates, Inc.
Plymouth, Minnesota

Jorge E. Lozano

PLAPIQUI
Universidad Nacional del Sur–CONICET
Bahia Blanca, Argentina

Jatal D. Mannapperuma

California Institute of Food and

Agricultural Research
Department of Food Science and Technology
University of California, Davis
Davis, California

Martha Muehlenkamp

Department of Food Science and Nutrition
University of Minnesota
St. Paul, Minnesota

Hosahilli S. Ramaswamy

Department of Food Science
and Agricultural Chemistry
MacDonald Campus of McGill University
Ste. Anne de Bellevue, Quebec
Canada

Copyright © 1997 CRC Press, LLC

Enrique Rotstein

The Pillsbury Company
Minneapolis, Minnesota

I. Sam Saguy

Department of Biochemistry, Food Science,
and Nutrition

Faculty of Agriculture
The Hebrew University of Jerusalem
Rehovot, Israel

Dale A. Seiberling

Seiberling Associates, Inc.
Roscoe, Illinois

R. Paul Singh

Department of Biological
and Agricultural Engineering and
Department of Food Science and Technology
University of California, Davis
Davis, California

James F. Steffe

Department of Agricultural Engineering
and Department of Food Science
and Human Nutrition
Michigan State University
East Lansing, Michigan

Petros S. Taoukis

Department of Chemical Engineering
Laboratory of Food Chemistry
and Technology

National Technical University of Athens
Athens, Greece

Martin J. Urbicain

PLAPIQUI
Universidad Nacional del Sur–CONICET
Bahia Blanca, Argentina

Kenneth J. Valentas

University of Minnesota
St. Paul, Minnesota

Joseph J. Warthesen

Department of Food Science
and Nutrition
University of Minnesota
St. Paul, Minnesota

John Henry Wells

Department of Biological
and Agricultural Engineering
Louisiana State University Agricultural
Center
Baton Rouge, Louisiana

Copyright © 1997 CRC Press, LLC


Preface

The food engineering discipline has been gaining increasing recognition in the food industry
over the last three decades. Although food engineers formally graduated as such are relatively
few, food engineering practitioners are an essential part of the food industry’s workforce.
The significant contribution of food engineers to the industry is documented in the constant
stream of new food products and their manufacturing processes, the capital projects to
implement these processes, and the growing number of patents and publications that span
this emerging profession.
While a number of important food engineering books have been published over the years,
the

Handbook of Food Engineering Practice

will stand alone for its emphasis on practical
professional application. This handbook is written for the food engineer and food manufac-
turer. The very fact that this is a book for industrial application will make it a useful source
for academic teaching and research.
A major segment of this handbook is devoted to some of the most common unit operations
employed in the food industry. Each chapter is intended to provide terse, to-the-point descrip-
tions of fundamentals, applications, example calculations, and, when appropriate, a review
of economics.
• The introductory chapter addresses one of the key needs in any food industry
namely the design of pumping systems. This chapter provides mathematical pro-
cedures appropriate to liquid foods with Newtonian and non-Newtonian flow char-
acteristics. Following the ubiquitous topic of pumping, several food preservation
operations are considered. The ability to mathematically determine a food steril-
ization process has been the foundation of the food canning industry. During the
last two decades, several new approaches have appeared in the literature that provide

improved calculation procedures for determining food sterilization processes.
• Chapter 2 provides an in-depth description of several recently developed methods
with solved examples.
• Chapter 3 is a comprehensive treatment of food freezing operations. This chapter
examines the phase change problem with appropriate mathematical procedures that
have proven to be most successful in predicting freezing times in food. The drying
process has been used for millennia to preserve foods, yet a quantitative description
of the drying process remains a challenging exercise.
• Chapter 4 presents a detailed background on fundamentals that provide insight into
some of the mechanisms involved in typical drying processes. Simplified mathe-
matical approaches to designing food dryers are discussed. In the food industry,
concentration of foods is most commonly carried out either with membranes or
evaporator systems. During the last two decades, numerous developments have
taken place in designing new types of membranes.
• Chapter 5 provides an overview of the most recent advances and key information
useful in designing membrane systems for separation and concentration purposes.
• The design of evaporator systems is the subject of Chapter 6. The procedures given
in this chapter are also useful in analyzing the performance of existing evaporators.
• One of the most common computations necessary in designing any evaporator is
calculating the material and energy balance. Several illustrative approaches on how
to conduct material and energy balances in food processing systems are presented
in Chapter 7.

Copyright © 1997 CRC Press, LLC

• After processing, foods must be packaged to minimize any deleterious changes in
quality. A thorough understanding of the barrier properties of food packaging
materials is essential for the proper selection and use of these materials in the
design of packaging systems. A comprehensive review of commonly available
packaging materials and their important properties is presented in Chapter 8.

• Packaged foods may remain for considerable time in transport and in wholesale and
retail storage. Accelerated storage studies can be a useful tool in predicting the shelf
life of a given food; procedures to design such studies are presented in Chapter 9.
• Among various environmental factors, temperature plays a major role in influencing
the shelf life of foods. The temperature tolerance of foods during distribution must
be known to minimize changes in quality deterioration. To address this issue,
approaches to determine temperature effects on the shelf life of foods are given in
Chapter 10.
• In designing and evaluating food processing operations, a food engineer relies on
the knowledge of physical and rheological properties of foods. The published
literature contains numerous studies that provide experimental data on food prop-
erties. In Chapter 11, a comprehensive resource is provided on predictive methods
to estimate physical and rheological properties.
• The importance of physical and rheological properties in designing a food system
is further illustrated in Chapter 12 for a dough processing system. Dough rheology
is a complex subject; an engineer must rely on experimental, predictive, and
mathematical approaches to design processing systems for manufacturing dough,
as delineated in this chapter.
The last five chapters in this handbook provide supportive material that is applicable to
any of the unit operations presented in the preceding chapters.
• For example, estimation of cost and profitability one of the key calculations that
must be carried out in designing new processing systems. Chapter 13 provides
useful methods for conducting cost/profit analyses along with illustrative examples.
• As computers have become more common in the workplace, use of simulations
and optimization procedures are gaining considerable attention in the food industry.
Procedures useful in simulation and optimization are presented in Chapter 14.
• In food processing, it is imperative that any design of a system adheres to a variety
of sanitary guidelines. Chapter 15 includes a broad description of issues that must
be considered to satisfy these important guidelines.
• The use of process controllers in food processing is becoming more prevalent as

improved sensors appear in the market. Approaches to the design and implementation
of process controllers in food processing applications are discussed in Chapter 16.
• Food engineers must rely on a number of basic sciences in dealing with problems
at hand. An in-depth knowledge of food chemistry is generally regarded as one of
the most critical. In Chapter 17, an overview of food chemistry with specific
reference to the needs of engineers is provided.
It should be evident that this handbook assimilates many of the key food processing
operations. Topics not covered in the current edition, such as food extrusion, microwave
processing, and other emerging technologies, are left for future consideration. While we
realize that this book covers new ground, we hope to hear from our readers, to benefit from
their experience in future editions.

Enrique Rotstein
R. Paul Singh
Kenneth Valentas

Copyright © 1997 CRC Press, LLC

Table of Contents

Chapter 1

Pipeline Design Calculations for Newtonian and Non-Newtonian Fluids

James F. Steffe and R. Paul Singh

Chapter 2

Sterilization Process Engineering


Hosahalli S. Ramaswamy, and R. Paul Singh

Chapter 3

Prediction of Freezing Time and Design of Food Freezers

Donald J. Cleland and Kenneth J. Valentas

Chapter 4

Design and Performance Evaluation of Dryers

Guillermo H. Crapiste and Enrique Rotstein

Chapter 5

Design and Performance Evaluation of Membrane Systems

Jatal D. Mannapperuma

Chapter 6

Design and Performance Evaluation of Evaporation

Chin Shu Chen and Ernesto Hernandez

Chapter 7

Material and Energy Balances


Brian E. Farkas and Daniel F. Farkas

Chapter 8

Food Packaging Materials, Barrier Properties, and Selection

Ruben J. Hernandez

Chapter 9

Kinetics of Food Deterioration and Shelf-Life Prediction

Petros S. Taoukis, Theodore P. Labuza, and I. Sam Saguy

Chapter 10

Temperature Tolerance of Foods during Distribution

John Henry Wells and R. Paul Singh

Copyright © 1997 CRC Press, LLC

Chapter 11

Definition, Measurement, and Prediction of Thermophysical and
Rheological Properties

Martin J. Urbicain and Jorge E. Lozano

Chapter 12


Dough Processing Systems

Leon Levine and Ed Boehmer

Chapter 13

Cost and Profitability Estimation

J. Peter Clark

Chapter 14

Simulation and Optimization

Enrique Rotstein, Julius Chu, and I. Sam Saguy

Chapter 15

CIP Sanitary Process Design

Dale A. Seiberling

Chapter 16

Process Control

David Bresnahan

Chapter 17


Food Chemistry for Engineers

Joseph J. Warthesen and Martha R. Meuhlenkamp


Copyright © 1997 CRC Press, LLC

1

Pipeline Design Calculations
for Newtonian
and Non-Newtonian Fluids

James F. Steffe and R. Paul Singh

CONTENTS

1.1 Introduction
1.2 Mechanical Energy Balance
1.2.1 Fanning Friction Factor
1.2.1.1 Newtonian Fluids
1.2.1.2 Power Law Fluids
1.2.1.3 Bingham Plastic Fluids
1.2.1.4 Herschel-Bulkley Fluids
1.2.1.5 Generalized Approach to Determine Pressure Drop in a Pipe
1.2.2 Kinetic Energy Evaluation
1.2.3 Friction Losses: Contractions, Expansions, Valves, and Fittings
1.3 Example Calculations
1.3.1 Case 1: Newtonian Fluid in Laminar Flow

1.3.2 Case 2: Newtonian Fluid in Turbulent Flow
1.3.3 Case 3: Power Law Fluid in Laminar Flow
1.3.4 Case 4: Power Law Fluid in Turbulent Flow
1.3.5 Case 5: Bingham Plastic Fluid in Laminar Flow
1.3.6 Case 6: Herschel-Bulkley Fluid in Laminar Flow
1.4 Velocity Profiles in Tube Flow
1.4.1 Laminar Flow
1.4.2 Turbulent Flow
1.4.2.1 Newtonian Fluids
1.4.2.2 Power Law Fluids
1.5 Selection of Optimum Economic Pipe Diameter
Nomenclature
References

Copyright © 1997 CRC Press, LLC

1.1 INTRODUCTION

The purpose of this chapter is to provide the practical information necessary to predict
pressure drop for non-time-dependent, homogeneous, non-Newtonian fluids in tube flow. The
intended application of this material is pipeline design and pump selection. More information
regarding pipe flow of time-dependent, viscoelastic, or multi-phase materials may be found
in Grovier and Aziz (1972), and Brown and Heywood (1991). A complete discussion of
pipeline design information for Newtonian fluids is available in Sakiadis (1984). Methods
for evaluating the rheological properties of fluid foods are given in Steffe (1992) and typical
values are provided in Tables 1.1, 1.2, and 1.3. Consult Rao and Steffe (1992) for additional
information on advanced rheological techniques.

1.2 MECHANICAL ENERGY BALANCE


A rigorous derivation of the mechanical energy balance is lengthy and beyond the scope of this
work but may be found in Bird et al. (1960). The equation is a very practical form of the
conservation of energy equation (it can also be derived from the principle of conservation of
momentum (Denn, 1980)) commonly called the “engineering Bernouli equation” (Denn, 1980;
Brodkey and Hershey, 1988). Numerous assumptions are made in developing the equation:
constant fluid density; the absence of thermal energy effects; single phase, uniform material
properties; uniform equivalent pressure (

ρ

g h term over the cross-section of the pipe is negligible).
The mechanical energy balance for an incompressible fluid in a pipe may be written as
(1.1)
where

Σ

F, the summation of all friction losses is
(1.2)
and subscripts 1 and 2 refer to two specific locations in the system. The friction losses include
those from pipes of different diameters and a contribution from each individual valve, fitting,
etc. Pressure losses in other types of in-line equipment, such as strainers, should also be
included in

Σ

F.

1.2.1 F


ANNING

F

RICTION

F

ACTOR

In this section, friction factors for time-independent fluids in laminar and turbulent flow are
discussed and criteria for determining the flow regime, laminar or turbulent, are presented.
It is important to note that it is impossible to accurately predict transition from laminar to
turbulent flow in actual processing systems and the equations given are guidelines to be used
in conjunction with good judgment. Friction factor equations are only presented for smooth
pipes, the rule for sanitary piping systems. Also, the discussion related to the turbulent flow
of high yield stress materials has been limited for a number of reasons: (a) Friction factor
equations and turbulence criteria have limited experimental verification for these materials;
(b) It is very difficult (and economically impractical) to get fluids with a significant yield
stress to flow under turbulent conditions; and (c) Rheological data for foods that have a high
yield stress are very limited. Yield stress measurement in food materials remains a difficult
task for rheologists and the problem is often complicated by the presence of time-dependent
behavior (Steffe, 1992).
uu
gz z
PP
FW
2
2
2

1
2
1
21
21
0
()
−
()






+−
()
+
−
++=
αα ρ
Σ
ΣΣ ΣF
fu L
D
ku
f
=
()
+

()
2
2
1
2
2

Copyright © 1997 CRC Press, LLC

The Fanning friction factor (ƒ) is proportional to the ratio of the wall shear stress in a
pipe to the kinetic energy per unit volume:
(1.3)

TABLE 1.1
Rheological Properties of Dairy, Fish, and Meat Products

Product
T
(°C)
n
(–)
K
(Pa·s

n

)

σσ
σσ


o


(Pa)

·

γγ
γγ


(s

–1

)

Cream, 10% fat 40 1.0 .00148 — —
60 1.0 .00107 — —
80 1.0 .00083 — —
Cream, 20% fat 40 1.0 .00238 — —
60 1.0 .00171 — —
80 1.0 .00129 — —
Cream, 30% fat 40 1.0 .00395 — —
60 1.0 .00289 — —
80 1.0 .00220 — —
Cream, 40% fat 40 1.0 .00690 — —
60 1.0 .00510 — —
80 1.0 .00395 — —

Minced fish paste 3–6 .91 8.55 1600.0 67–238
Raw, meat batters
15

a

13

b

68.8

c

15 .156 639.3 1.53 300–500
18.7 12.9 65.9 15 .104 858.0 .28 300–500
22.5 12.1 63.2 15 .209 429.5 0 300–500
30.0 10.4 57.5 15 .341 160.2 27.8 300–500
33.8 9.5 54.5 15 .390 103.3 17.9 300–500
45.0 6.9 45.9 15 .723 14.0 2.3 300–500
45.0 6.9 45.9 15 .685 17.9 27.6 300–500
67.3 28.9 1.8 15 .205 306.8 0 300–500
Milk, homogenized 20 1.0 .002000 — —
30 1.0 .001500 — —
40 1.0 .001100 — —
50 1.0 .000950 — —
60 1.0 .000775 — —
70 1.0 .00070 — —
80 1.0 .00060 — —
Milk, raw 0 1.0 .00344 — —

5 1.0 .00305 — —
10 1.0 .00264 — —
20 1.0 .00199 — —
25 1.0 .00170 — —
30 1.0 .00149 — —
35 1.0 .00134 — —
40 1.0 .00123 — —

a

%Fat

b

%Protein

c

%Moisture Content
From Steffe, J. F. 1992.

Rheological Methods in Food Process Engineering

.
Freeman Press, East Lansing, MI. With permission.
f
u
w
=
()

2
2
σ
ρ

Copyright © 1997 CRC Press, LLC

ƒ can be considered in terms of pressure drop by substituting the definition of the shear stress
at the wall:
(1.4)

TABLE 1.2
Rheological Properties of Oils and Miscellaneous Products

Product % Total solids
T
(°C)
n
(–)
K
(Pa·s

n

)

σσ
σσ

o


(Pa)

·

γγ
γγ

(s

–1

)

Chocolate, melted 46.1 .574 .57 1.16
Honey
Buckwheat 18.6 24.8 1.0 3.86
Golden Rod 19.4 24.3 1.0 2.93
Sage 18.6 25.9 1.0 8.88
Sweet Clover 17.0 24.7 1.0 7.20
White Clover 18.2 25.2 1.0 4.80
Mayonnaise 25 .55 6.4 30–1300
25 .60 4.2 40–1100
Mustard 25 .39 18.5 30–1300
25 .34 27.0 40–1100
Oils
Castor 10 1.0 2.42
30 1.0 .451
40 1.0 .231
100 1.0 .0169

Corn 38 1.0 .0317
25 1.0 .0565
Cottonseed 20 1.0 .0704
38 1.0 .0306
Linseed 50 1.0 .0176
90 1.0 .0071
Olive 10 1.0 .1380
40 1.0 .0363
70 1.0 .0124
Peanut 25.5 1.0 .0656
38.0 1.0 .0251
21.1 1.0 .0647 .32–64
37.8 1.0 .0387 .32–64
54.4 1.0 .0268 .32–64
Rapeseed 0.0 1.0 2.530
20.0 1.0 .163
30.0 1.0 .096
Safflower 38.0 1.0 .0286
25.0 1.0 .0522
Sesame 38.0 1.0 .0324
Soybean 30.0 1.0 .0406
50.0 1.0 .0206
90.0 1.0 .0078
Sunflower 38.0 1.0 .0311
From Steffe, J. F. 1992.

Rheological Methods in Food Process Engineering

. Freeman Press,
East Lansing, MI. With permission.

f
PR
Lu
PD
Lu
=
()
=
()
δ
ρ
δ
ρ
22
2

Copyright © 1997 CRC Press, LLC

TABLE 1.3
Rheological Properties of Fruit and Vegetable Products

Product
Total solids
(%)
T
(°C)
n
(–)
K
(Pa·s


n

)

·

γγ
γγ


(s

–1

)

Apple
Pulp — 25.0 .084 65.03 —
Sauce 11.6 27 .28 12.7 160–340
11.0 30 .30 11.6 5–50
11.0 82.2 .30 9.0 5–50
10.5 26 .45 7.32 .78–1260
9.6 26 .45 5.63 .78–1260
8.5 26 .44 4.18 .78–1260
Apricots
Puree 17.7 26.6 .29 5.4 —
23.4 26.6 .35 11.2 —
41.4 26.6 .35 54.0 —
44.3 26.6 .37 56.0 .5–80

51.4 26.6 .36 108.0 .5–80
55.2 26.6 .34 152.0 .5–80
59.3 26.6 .32 300.0 .5–80
Reliable, conc.
Green 27.0 4.4 .25 170.0 3.3–137
27.0 25 .22 141.0 3.3–137
Ripe 24.1 4.4 .25 67.0 3.3–137
24.1 25 .22 54.0 3.3–137
Ripened 25.6 4.4 .24 85.0 3.3–137
25.6 25 .26 71.0 3.3–137
Overripe 26.0 4.4 .27 90.0 3.3–137
26.0 25 .30 67.0 3.3–137
Banana
Puree A — 23.8 .458 6.5 —
Puree B — 23.8 .333 10.7 —
Puree (17.7 Brix) — 22 .283 107.3 28–200
Blueberry, pie filling — 20 .426 6.08 3.3–530
Carrot, Puree — 25 .228 24.16 —
Green Bean, Puree — 25 .246 16.91 —
Guava, Puree (10.3 Brix) — 23.4 .494 39.98 15–400
Mango, Puree (9.3 Brix) — 24.2 .334 20.58 15–1000
Orange Juice
Concentrate
Hamlin, early — 25 .585 4.121 0–500
42.5 Brix — 15 .602 5.973 0–500
— 0 .676 9.157 0–500
— –10 .705 14.255 0–500
Hamlin, late — 25 .725 1.930 0–500
41.1 Brix — 15 .560 8.118 0–500
— 0 .620 1.754 0–500

— –10 .708 13.875 0–500
Pineapple, early — 25 .643 2.613 0–500
40.3 Brix — 15 .587 5.887 0–500
— 0 .681 8.938 0–500
— –10 .713 12.184 0–500

Copyright © 1997 CRC Press, LLC

Pineapple, late — 25 .532 8.564 0–500
41.8 Brix — 15 .538 13.432 0–500
— 0 .636 18.584 0–500
— –10 .629 36.414 0–500
Valencia, early — 25 .583 5.059 0–500
43.0 Brix — 15 .609 6.714 0–500
— –10 .619 27.16 0–500
Valencia, late — 25 .538 8.417 0–500
41.9 Brix — 15 .568 11.802 0–500
— 0 .644 18.751 0–500
— –10 .628 41.412 0–500
Naval
65.1 Brix — –18.5 .71 29.2 —
— –14.1 .76 14.6 —
— –9.3 .74 10.8 —
— –5.0 .72 7.9 —
— –0.7 .71 5.9 —
— 10.1 .73 2.7 —
— 29.9 .72 1.6 —
— 29.5 .74 .9 —
Papaya, puree (7.3 Brix) — 26.0 .528 9.09 20–450
Peach

Pie Filling — 20.0 .46 20.22 1–140
Puree 10.9 26.6 .44 .94 —
17.0 26.6 .55 1.38 —
21.9 26.6 .55 2.11 —
26.0 26.6 .40 13.4 80–1000
29.6 26.6 .40 18.0 80–1000
37.5 26.6 .38 44.0 —
40.1 26.6 .35 58.5 2–300
49.8 26.6 .34 85.5 2–300
58.4 26.6 .34 440.0 —
11.7 30.0 .28 7.2 5–50
11.7 82.2 .27 5.8 5–50
10.0 27.0 .34 4.5 160–3200
Pear
Puree 15.2 26.6 .35 4.25 —
24.3 26.6 .39 5.75 —
33.4 26.6 .38 38.5 80–1000
37.6 26.6 .38 49.7 —
39.5 26.6 .38 64.8 2–300
47.6 26.6 .33 120.0 .5–1000
49.3 26.6 .34 170.0 —
51.3 26.6 .34 205.0 —
45.8 32.2 .479 35.5 —
45.8 48.8 .477 26.0 —
45.8 65.5 .484 20.0 —
45.8 82.2 .481 16.0 —
14.0 30.0 .35 5.6 5–50
14.0 82.2 .35 4.6 5–50

TABLE 1.3 (continued)

Rheological Properties of Fruit and Vegetable Products

Product
Total solids
(%)
T
(°C)
n
(–)
K
(Pa·s

n

)

·

γγ
γγ


(s

–1

)

Copyright © 1997 CRC Press, LLC


Simplification yields the energy loss per unit mass required in the mechanical energy balance:
(1.5)
There are many mathematical models available to describe the behavior of fluid foods
(Ofoli et al., 1987); only those most useful in pressure drop calculations have been included
in the current work. The simplest model, which adequately describes the behavior of the food
should be used; however, oversimplification can cause significant calculation errors (Steffe,
1984).

1.2.1.1 Newtonian Fluids

The volumetric average velocity for a Newtonian fluid (

σ

=

µγ

·

in laminar, tube flow is
(1.6)

Plum
Puree 14.0 30.0 .34 2.2 5–50
14.0 82.2 .34 2.0 5–50
Squash
Puree A — 25 .149 20.65 —
Puree B — 25 .281 11.42 —
Tomato

Juice conc. 5.8 32.2 .59 .22 500–800
5.8 38.8 .54 .27 500–800
5.8 65.5 .47 .37 500–800
12.8 32.2 .43 2.0 500–800
12.8 48.8 .43 2.28 500–800
12.8 65.5 .34 2.28 500–800
12.8 82.2 .35 2.12 500–800
16.0 32.2 .45 3.16 500–800
16.0 48.8 .45 2.77 500–800
16.0 65.5 .40 3.18 500–800
16.0 82.2 .38 3.27 500–800
25.0 32.2 .41 12.9 500–800
25.0 48.8 .42 10.5 500–800
25.0 65.5 .43 8.0 500–800
25.0 82.2 .43 6.1 500–800
30.0 32.2 .40 18.7 500–800
30.0 48.8 .42 15.1 500–800
30.0 65.5 .43 11.7 500–800
30.0 82.2 .45 7.9 500–800
From Steffe, J. F. 1992.

Rheological Methods in Food Process Engineering.

Freeman Press,
East Lansing, MI. With permission.

TABLE 1.3 (continued)
Rheological Properties of Fruit and Vegetable Products

Product

Total solids
(%)
T
(°C)
n
(–)
K
(Pa·s

n

)

·

γγ
γγ


(s

–1

)
δ
ρ
P
fLu
D
()

=
2
2
u
Q
RR
PR
L
PD
L
==
()
µ






=
()
µππ
πδ δ
22
42
1
832

Copyright © 1997 CRC Press, LLC


Solving Equation 1.6 for the pressure drop per unit length gives
(1.7)
Inserting Equation 1.7 into the definition of the Fanning friction factor, Equation 1.4, yields
(1.8)
which can be used to predict friction factors in the laminar flow regime, N

Re

< 2100 where
N

Re

=

ρ

D u/

µ

. In turbulent flow, N

Re

> 4000, the von Karman correlation is recommended
(Brodkey and Hershey, 1988):
(1.9)
The friction factor in the transition range, approximately 2100 < N


Re

< 4000, cannot be
predicted but the laminar and turbulent flow equations can be used to establish appropriate
limits.

1.2.1.2 Power Law Fluids

The power law fluid model (

σ

= K (

γ

·

)

n

) is one of the most useful in pipeline design work for
non-Newtonian fluids. It has been studied extensively and accurately expresses the behavior of
many fluid foods which commonly exhibit shear-thinning (0 < n < 1) behavior. The volumetric
flow rate of a power law fluid in a tube may be calculated in terms of the average velocity:
(1.10)
meaning
(1.11)
which, when inserted into Equation 1.4, gives an expression analogous to Equation 1.8:

(1.12)
where the power law Reynolds number is defined as
(1.13)
δP
L
u
D
()
=
µ32
2
f
P
L
D
u
u
D
D
uN
=
()













=
µ












=
δ
ρρ2
32
2
16
222
Re
1
40 04
10
f

Nf=
()
−.log .
Re
u
Q
R
P
LK
n
n
R
R
n
nn
=
()






+





















+
()
π
π
δ
π
2
1
31
2
231
1
δP
L
uK
D

n
n
n
n
n
()
=
+




+
426
1
f
P
L
D
u
uK
D
n
n
D
Lu N
n
n
n
PL

=












=






+















=
+
δ
ρ2
426
2
16
21 2
Re,
N
Du
K
n
n
Du
K
n
n
PL
n
n
n
n
n
n

n
Re,
=
()






+




=
()






+




−−
−

8
26 8
4
31
22
1
ρρ

Copyright © 1997 CRC Press, LLC

Experimental data (Table 1.4) indicate that Equation 1.12 will tend to slightly overpredict
the friction factor for many power law food materials. This may be due to wall slip or time-
dependent changes in rheological properties which can develop in suspension and emulsion
type food products.
Equation 1.12 is appropriate for laminar flow which occurs when the following inequality
is satisfied (Grovier and Aziz, 1972):
(1.14)
The critical Reynolds number varies significantly with n (Figure 1.1) and reaches a maximum
value around n = 0.4.
When Equation 1.14 is not satisfied, ƒ can be predicted for turbulent flow conditions
using the equation proposed by Dodge and Metzner (1959):
(1.15)
This equation is simple and gives good results in comparison to other prediction equations
(Garcia and Steffe, 1987). The graphical solution (Figure 1.2) to Equation 1.15 illustrates the
strong influence of the flow-behavior index on the friction factor.

1.2.1.3 Bingham Plastic Fluids

Taking an approach similar to that used for pseudoplastic fluids, the pressure drop per unit
length of a Bingham plastic fluid (


σ

=

µ

pl

γ

·

=

σ

o

) can be calculated from the volumetric flow
rate equation:
(1.16)

TABLE 1.4
Fanning Friction Factor Correlations for the Laminar Flow of Power-Law Food
Products Using the Following Equation: ƒ = a (N

Re,PL

)


b

Product(s) a* b* Source

Ideal power law 16.0 –1.00 Theoretical prediction
Pineapple pulp 13.6 –1.00 Rozema and Beverloo (1974)
Apricot puree 12.4 –1.00 Rozema and Beverloo (1974)
Orange concentrate 14.2 –1.00 Rozema and Beverloo (1974)
Applesauce 11.7 –1.00 Rozema and Beverloo (1974)
Mustard 12.3 –1.00 Rozema and Beverloo (1974)
Mayonnaise 15.4 –1.00 Rozema and Beverloo (1974)
Applejuice concentrate 18.4 –1.00 Rozema and Beverloo (1974)
Combined data of tomato concentrate and apple puree 29.1 –.992 Lewicki and Skierkowski (1988)
Applesauce 14.14 –1.05 Steffe et al. (1984)
* a and b are dimensionless numbers.
N
n
nn
N
PL
nn
PLRe, Re,
<
+
()
+
()
()
=

()
+
()
+
()
6464
13 12
2
21
critical
14 04
075
10
12
12
fn
Nf
n
PL
n
=




()
[]
−





−
()
()
.
Re,
.
log
.
δ
π
P
L
Q
Rcc
pl
()
=
µ






−+







8
1
143 3
44

Copyright © 1997 CRC Press, LLC

Written in terms of the average velocity, Equation 1.16 becomes
(1.17)
which, when substituted into Equation 1.4, yields
(1.18)
where c is an implicit function of the friction factor
(1.19)
The friction factor may also be written in terms of a Bingham Reynolds number (N

Re,B

)
and the Hedstrom Number (N

He

), (Grovier and Aziz, 1972):

FIGURE 1.1

Critical value of the power-law Reynolds number (N


Re,PL

) for different values of the
flow-behavior index (n).
δP
L
u
Dcc
pl
()
=
µ






−+






32
1
143 3
24

f
P
L
D
u
u
Dcc
D
u
Du c c
pl pl
=
()






()






=
µ







−+












()






=
µ
−+







δ
ρρ
ρ
2
32
1
143 3
2
16
1
143 3
2
24
2
4
–
c
L
DP
fu
o
w
oo
== =
()
σ
σ

σ
δ
σ
ρ
42
2

Copyright © 1997 CRC Press, LLC

(1.20)
where
(1.21)
and
(1.22)
Equations 1.18 or 1.20 may be used for estimating ƒ in steady-state laminar flow which
occurs when the following inequality is satisfied (Hanks, 1963):
(1.23)
where c

c

is the critical value of c defined as
(1.24)

FIGURE 1.2

Fanning friction factor (ƒ) for power-law fluids from the relationship of Dodge and
Metzner (1959). (From Garcia, E. J. and Steffe, J. F. 1986, Special Report, Department of Agricultural
Engineering, Michigan State University, East Lansing, MI.)
1

16
63
2
4
3
8
N
f
N
N
N
fN
B
He
B
He
B
Re,
Re, Re,
=−
()
+
()
()
N
D
He
o
pl
=

µ
()
2
2
σρ
N
Du
B
pl
Re,
=
µ
ρ
N
N
c
cc N
B
He
c
cc BRe, Re,
≤−+




=
()
8
1

4
3
1
3
4
critical
c
c
N
c
c
He
1
16 800
3
−
()
=
,

Copyright © 1997 CRC Press, LLC

c

c

varies (Figure 1.3) from 0 to 1 and the critical value of the Bingham Reynolds number
increases with increasing values of the Hedstrom number (Figure 1.4).
The friction factor for the turbulent flow of a Bingham plastic fluid can be considered a
special case of the Herschel-Bulkley fluid using the relationship presented by Torrance (1963):


FIGURE 1.3.

Variation of c

c

with the Hedstrom number (N

He

) for the laminar flow of Bingham plastic
fluids. (From Steffe, J. F. 1992, Rheological Methods in Food Process Engineering, Freeman Press,
East Lansing, MI. With permission.)
FIGURE 1.4. Variation of the critical Bingham Reynolds number (N
Re,B
) with the Hedstrom number
(N
He
). (From Steffe, J. F. 1992, Rheological Methods in Food Process Engineering, Freeman Press, East
Lansing, MI. With permission.)
Copyright © 1997 CRC Press, LLC
(1.25)
Increasing values of the yield stress will significantly increase the friction factor (Figure 1.5).
In turbulent flow with very high pressure drops, c may be small simplifying Equation 1.25 to
(1.26)
1.2.1.4 Herschel-Bulkley Fluids
The Fanning friction factor for the laminar flow of a Herschel-Bulkley fluid (σ = K (γ
·
n

+
σ
o
) can be calculated from the equations provided by Hanks (1978) and summarized by
Garcia and Steffe (1987):
(1.27)
where
(1.28)
c can be expressed as an implicit function of N
Re,PL
and a modified form of the Hedstrom
number (N
He,M
):
FIGURE 1.5 Fanning friction factor (ƒ) for Bingham plastic fluids (N
Re,PL
) from the relationship of
Torrance (1963). (From Garcia, E. J. and Steffe, J. F. 1986, Special Report, Department of Agricultural
Engineering, Michigan State University, East Lansing, MI.)
1
453 1 453 23
10 10
f
cNf
B
=−
()
+
()
()

−.log .log .
Re,
1
453 23
10
f
Nf
B
=
()
−.log .
Re,
f
N
PL
=
16
Ψ
Re,
Ψ= +
()
−
()
−
()
+
()
+
−
()

+
()
+
+
()






+
13 1
1
13
21
12 1
1
2
2
nc
c
n
cc
n
c
n
nn
n
Copyright © 1997 CRC Press, LLC

(1.29)
where
(1.30)
To find ƒ for Herschel-Bulkley fluids, c is determined through an iteration of Equation 1.29
using Equation 1.28, then the friction factor may be directly computed from Equation 1.27.
Graphical solutions (Figures 1.6 to 1.15) are useful to ease the computational problems
associated with Herschel-Bulkley fluids. These figures indicate the value of the critical
Reynolds number at different values of N
He,M
for a particular value of n. The critical Reynolds
number is based on theoretical principles and has little experimental verification. Figure 1.6
(for n = 1) is also the solution for the special case of a Bingham plastic fluid and compares
favorably with the Torrance (1963) solution presented in Figure 1.5.
1.2.1.5 Generalized Approach to Determine Pressure Drop in a Pipe
Metzner (1956) discusses a generalized approach to relate flow rate and pressure drop for
time-independent fluids in laminar flow. The overall equation is written as
(1.31)
FIGURE 1.6 Fanning friction factor (ƒ) for a Herschel-Bulkley fluid with n = 1.0, based on the
relationship of Hanks (1978). (From Garcia, E. J. and Steffe, J. F. 1986, Special Report, Department
of Agricultural Engineering, Michigan State University, East Lansing, MI.)
NN
n
nc
PL He M
n
n
Re, ,
=
+









−
2
13
2
2
Ψ
N
D
KK
M
o
n
n
Re,
=




−
2
2
ρ

σ
δ
π
PR
L
K
Q
R
n
()
=
′




′
2
4
3
Copyright © 1997 CRC Press, LLC