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Technical calculations for

malting and brewery technologists

Technological calculations, benchmarks and correlations to

optimize the process

Prof. Dr. sc. techn. Gerolf Annemüller

Dr. sc. techn. Hans-J. Manger

Published by VLB Berlin

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Bibliographic information from the German National Library: The

German National Library lists this publication in the German National Bibliography; detailed bibliographic
data are available online at dnb.ddb.de.

Contact address of the authors: Prof.

Dr. sc. techn. Gerolf Annemüller Buschiner Str.
34 A 12683 Berlin E-Mail:
g.annemueller@t-
online.de

1st edition 2015

ISBN 978-3-921690-78-9

© VLB Berlin, Seestraße 13, D-13353 Berlin, www.vlb-berlin.org All

rights reserved, especially the right to translation into other languages.
No part of this book may be reproduced in any form without the written permission of the publisher.

All rights reserved (including those of translation into other languages).

No part of this book may be reproduced in any form.

Production: VLB Berlin, PR and Publishing Department

Cover photo: © Gina Sanders, fotolia.com
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Technical calculations for malting and brewery technologists

Technological calculations, benchmarks and correlations to optimize the

Procedure

Table of contents

Calculation examples as an overview 11

Abbreviations and symbols 18

Foreword 19

1. Some notes on the rule of three, percentage and interest calculations and simple
statistics 20
1.1 Notes on basic arithmetic 20
1.2 Rule of three calculation with direct proportionality of the basic and partial amounts 1.3 20
Rule of three calculation with inverse proportionality of the basic and partial amounts21
1.4 Percentage calculation 22
1.5 The interest 23
calculation 1.6 The mixture calculation and its extended application 23
1.7 The application of statistical methods in the evaluation of
Study results (a short summary for beginners) 30

2. Tank geometries – Calculation of areas, volumes and filling quantities in malt

houses and breweries 2.1 Calculation of the surface 55
areas of the most important standard areas 55
2.1.1 The rectangle and the square 2.1.2 The 55
parallelogram 2.1.3 The trapezoid 55
2.1.4 The triangle 55
56
2.1.5 The circle 56
2.1.6 The circular ring 56
2.1.7 The ellipse 57
2.2 Some example calculations using area equations 2.3 Calculation of the volume V of 57
the most important bodies used for the
Malting and brewing are important 2.3.1 The 58
cuboid 2.3.2 The 58
cone and the truncated cone 2.3.3 The 59
pyramid and the truncated pyramid 2.3.4 The sphere 60
and the spherical segment 2.3.5 The cylinder 60
61

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2.4 Some example calculations for malting and brewing using volume equations
62

3. Grain storage, grain care and grain transport 69

3.1 Calculating possible storage losses for freshly harvested grain 69
3.1.1 Technological significance and guideline values 3.1.2 69

Balance equations for the metabolism of stored barley 3.1.3 Calculation of 70

substance loss, oxygen demand, CO2 and water formation during barley storage 3.1.4
Calculation of the heating of stored barley 3.2 Pre-storage 70

of freshly harvested grain without preservation and without aeration 71

of the grain 3.3 Aeration of the grain in the pre-storage phase with atmospheric
76

Air and cooled air 76

3.4 Grain drying 3.5 Grain 79

ventilation and cooling 3.5.1 Required air volume 3.5.2 81

Pressure losses in the hopper 3.6 81

Internal transport of grain 82

84
3.6.1 Belt conveyor 84
3.6.2 Bucket elevators 84
3.6.3 Screw conveyor 85

3.6.4 Pneumatic conveying 87

3.7 Conversion of a grain batch to a base moisture value 3.8 Cleaning and sorting 88

of a barley batch 89

3.8.1 Technological objectives of the malthouse: 3.9 89

Storage space requirements for grain 90

4. Malt production 92
4.1 Calculation of the degree of soaking 92

4.2 Calculation of the required soaking space 4.3 Water 93

requirement during soaking 93

4.4 Temperature regulation, CO2 extraction and water absorption

when switching 95

4.5 Germination box occupancy 96

4.6 Germination air requirement, cooling, humidification of the germination air and energy
consumption, design of kiln fans and electrical energy consumption, pressure
loss calculations in pipe ducts for gases and vapors 97

4.7 h,x-diagram in the malthouse 4.7.1 97

General information 4.7.2 97

Thermodynamic principles 4.7.3 The h,x-diagram for 97

humid air 4.7.4 Important changes of state 100

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4.8 Assessment of the malting process and malt quality 4.8.1 Assessment of 110
leaf germ length 4.8.2 Malt yield, malting 110
waste and malting factor 4.9 Malt germs produced 111
112

5. Crushing the malt (grinding) 113

5.1 Guide values for malt grist 113
5.2 Assessment of lauter tun grist 5.3 Wetting of 114
grain before milling or grinding 115
5.4 Shot volume 116

6. Calculations for brewing water and alkaline cleaning agents118

6.1 Reference values and technological significance of brewing water 6.2 118
Conversions in water chemistry 6.3 Notes on 120
the analysis of water salts and their calculation 6.4 Calculations of the 120
residual alkalinity RA of brewing water 6.5 Decarbonization of 122
brewing water with lime water 123
6.5.1 Chemical reactions 123
6.5.2 Determination of the concentration of the lime water 123
6.5.3 Determination of the concentration of the dissolved CO2 content of the
raw water 124
6.5.4 Calculation of the required amount of lime water to reduce the carbonate
hardness in the raw water 124
6.5.5 Total amount of lime water required 6.6 Estimates 124
of the mash pH value depending on the malt quality and the residual alkalinity
of the brewing water 6.7 Reducing the residual alkalinity of 125
the mashing water by adding
Ca ions 125
6.8 Determination of the cleaning active component in alkaline
Cleaning solutions 126

7. Wort production 7.1 Pouring 130

process and brewhouse yield 7.1.1 Required main 130
pouring quantity depending on the desired first wort concentration
130
7.1.2 Calculation of the total mash volume and the required mash tank volume
131
7.1.3 Calculating the required amount of water for the sparging 7.1.4 Volume of 132
first wort and pan full wort per brew 7.1.5 Calculating the brewhouse 133
yield 7.1.6 Calculating the expected amount of 134
hot cast wort 134
7.1.7 Required total evaporation, based on pan full wort 135

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7.1.8 Estimation of spent grains per brew 7.1.9 Amount 136

of water required for wort production 136

7.2 Adjusting the pH value in mash and wort 137

7.2.1 Technological significance 7.2.2 137

Guide values for acidification with lactic acid 7.3 Calculation 137

of the boiling mash content 7.4 Mash vessel heating 139

139

7.4.1 Heat transfer 7.4.2 140

Calculating heat quantities and heating surfaces 7.4.3 Designing heat 140

transfer surfaces on brewing vessels 7.4.4 Temperature increase through mixed 144

condensation 7.5 Wort clarification 146

150

7.5.1 Technological relationships 7.5.2 Some 150

guideline values for the lautering process 7.5.3 Attempt to 151

determine the influence of the spent grain height and the influence of the substance
to demonstrate the influence of lauter wort on lautering speed
151

7.5.4 Influence of lautering technology during sweetening of spent grains on the porosity
of the spent grain cake in the lauter tun 153

7.5.5 Calculation of the required mash capacity of a mash filter

154
7.5.6 Required size of the spent grain silo 155

7.5.7 Extract content of the wort 7.6 Boiling 155

the wort 156

7.6.1 Technological objectives and guideline values of the wort boiling process 7.6.2 156

The water evaporation during wort boiling and the

required energy expenditure 7.7 157

Bitter substance administration and bitter substance yield (BA) 158

7.7.1 Guide values for bittering substance yields (BA) in the wort and for bittering substance
losses from the initial wort to the finished beer for different technological processes
7.7.2 Calculation of the required hop quantity and bittering 158

substance balance 7.7.3 Simplified calculation of the available hops in the operation 160

Bitter substance yield and for correcting the ÿ-acid addition per
hectoliter of pan full wort (cold) 162

7.7.4 Simplified calculation of bitter substance yield BA related

on the finished beer 163

7.8 Calculations for the change in the bulk composition 164

7.8.1 Calculating the desired malt color for a malt blend 7.8.2 A simple method for 164

converting the extract input by

Malt surrogates for extract balancing using brewhouse yield 165

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7.9 Extract yield and yield balance 166

7.9.1 Guidelines for the evaluation of extract yields 7.9.2 Calculation of 166

the classic brewhouse yield (SHA) 7.9.3 Assessment of extract 167

recovery using the “Overall Brewhouse Yield” (OBY) method

168

7.9.4 Required specifications of the extract additions and removals due to the use of
clear water and trub 7.9.5 Example of an extract balance 169

in conjunction with the corresponding spent grain analysis 7.10 Cooling the cast wort to
pitching 171

temperature and variants for utilizing the liquid heat 7.10.1 Comparison of wort
cooling variants using model calculations 7.10.2 Results 171

of a model calculation and conclusions 172

176

8. Fermentation and maturation of beer 8.1 178

Calculations for brewery yeast 178

8.1.1 Physical parameters of the yeast cell and their influence on the
effective mass transfer surface of the yeast 178
8.1.2 The density of the yeast cell and its sedimentation behavior 179

8.1.3 The yeast content of the different yeast products and their influence on the yeast
addition during pitching 180
8.1.4 The size of yeast cells and its influence on clarification behavior 182

8.1.5 The proliferation kinetics of yeast and their influence on the design
the yeast propagation systems 185

8.1.6 Calculation of the required oxygen and air input during

Yeast propagation in beer wort 192

8.2 Fermentation, degree of fermentation, original wort, rate of fermentation 197

8.2.1 Material turnover in the process of fermentation and original wort of beer 197
8.2.2 Fermentation and degrees of fermentation 199

8.2.3 The amount of water obtained from 1000 g of wort 8.2.4 203

Volume conversion of wort and beer 8.2.5 Assessment of a 204

young beer during bunging 8.2.6 Alcohol and extract calculations 204

according to Tabarié 8.3 The fermentable residual extract at the 205

right time for bunging

and the maximum possible CO2 formation 206

8.4 The rate of fermentation 8.4.1 Average 208

decrease in the apparent extract in the
and main fermentation phase 24 h each 208

8.4.2 Average fermentation per unit volume 8.4.3 Technological factors 208

influencing average fermentation 210

8.4.4 Specific extract degradation per yeast cell 212
8.4.5 Fermentation rate according to Schröderheim 212

8.5 Calculation of the bunging pressure 212

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9. Clarification and stabilization of beer 9.1 Objectives and process 214

steps 9.2 Calculations for diatomaceous earth 214
dosage 9.2.1 Precoating 9.2.2 Filtration time and 214
ongoing dosage 9.2.3 Differential 214
pressure increase and filtration time 9.3 Filter aid 215
preparation 9.4 Crossflow membrane filtration 216
217
219
9.5 Preparation of the mixture when using the protein stabilizing agent silica gel 220

10. Thermal preservation of beer (pasteurization) 222

10.1 Objectives, definitions and guide 222
values 10.2 Pasteurization by short-time 222
heating 10.3 Bottle pasteurization in the tunnel 225
pasteurizer 10.4 The D-value and the z-value as determined guide values for the killing
a special microorganism 226

11. The energy content of beer and the ethanol degradation during
People 11.1 232
Energy equivalents of beer ingredients 11.2 Beer 232
consumption and blood alcohol content 233

12. Bottling 237

12.1 Gas diffusion 237
12.2 Storage capacity of a bottle buffer belt 12.3 240
Carryover of caustic solution in a bottle washer 12.4 Vapour extraction 242
of a bottle washer (FRM) 246
12.5 Forklifts 12.6 249
Acceptance of filling systems, warranties 12.6.1 250
General information 12.5.2 250
Results of acceptance and determination of consumption values 12.6.3 251
International acceptance and determination of consumption values 12.6.4 253
Important terms for the assessment of filling systems 12.6.5 255
Time concepts 12.7 255
Compliance with the nominal filling 256
quantity 12.8 Space requirements for the storage of empty and full bottles 260
12.9 Space and room requirements for filling systems 261

13. Example calculations for the preparation of non-alcoholic soft drinks 13.1 Overview and some
requirements 13.2 Preparation 263
calculation for a lemonade 13.3 The sugar-acid ratio 263
264
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13.4 Reduced-calorie non-alcoholic soft drinks 13.5 Carbonation of non- 268

alcoholic soft drinks 13.5.1 CO2 solution, guideline values and definitions 270

13.5.2 Calculations for adjusting the CO2 concentration in 270

water and lemonades

272

14. Product pipelines in the brewery 274

14.1 Important aspects for the design of pipelines in the beverage industry
274

14.1.1 The flow velocity 14.1.2 The 274

pressure loss when flowing through a pipe or

fitting 275

14.1.3 Pressure loss estimation using a nomogram for liquids 14.1.3 The Reynolds 278

number 14.1.4 The boundary 282

layer thickness 283

14.2 The flow velocity during product conveyance 14.3 Instructions 288

for the design of pipelines 14.3.1 General instructions 14.3.2 290

Thermally induced length changes 290

14.3.3 Venting of the pipelines, oxygen removal 291

292

15. Pumps 297

15.1 Geodetic head 297

15.2 Efficiency of the drive motors 15.3 Cavitation 300

300

15.4 Power requirements of a centrifugal pump 302

15.5 Notes on pump selection 15.5.1 306

Characteristic curves and ways of influencing them 15.5.2 Starting 306

conditions: 308

16. Compressor 312

16.1 General information 16.2 312

Energy requirements of compressors 16.3 313

Notes on the use of compressors 315

16.3.1 Possibilities for improving efficiency 16.3.2 Notes on 315

compressors in the beverage industry 315

16.3.3 General information on compressors 316

17. Heat exchanger 17.1 Heat 317

flow 317

17.2 Thermal transmittance coefficient 17.3 317

General information on the calculation of heat transfer 317

coefficients 17.4 Thermal dimensioning 319

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17.5 Mean logarithmic temperature difference 321

18. Key figures for plant planning 323

18.1 Raw materials 323
18.2 Balance equations for respiration and fermentation 323
18.3 Specific heat capacity 18.4 Specific 324
consumption values for breweries 18.5 Specific 324
parameters for malting plants 18.5.1 325
Consumption values 325
18.5.2 Specific loading/occupancy in the malthouse 18.5.3 Malting 325
waste 18.5.4 Energy 325
consumption values 18.5.5 Electrical 325
energy: See Table 120: 18.5.6 Water consumption/ 326
waste water 327
18.6 Specific consumption values for bottle cleaning 18.7 Specific 327
volumes for brewing vessels, brewhouse parameters 18.8 ZKT for fermentation/ 327
maturation/storage 18.9 Filtration systems for 328
beer 18.10 Extract and volume 329
loss 329
18.11 Selected characteristics for steam and water 330
18.12 Characteristics of selected packaging materials: 331

19. Physical-technical units in the brewing and malting industry 336

index 345
Source reference 355

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The calculation examples as an overview

Chapter 1: Basic arithmetic Example

1.1: Beer pump Example 20
1.2: Barley storage room Example 20
1.3: Rule of three 21
Example 1.4: Original wort calculation 21
Example 1.5: Malt calculation 22
Example 1.6: Interest 23
amount Example 1.7: Setting the water temperature using the mixing cross
and mixing 25
calculation Example 1.8: Mixing calculation with multiple water
quantities and water 25
temperatures Example 1.9: Calculating a center of 26
gravity coordinate Example 1.10: Specific 27
heat capacity Example 1.11: 27
Water mixture Example 1.12: Grade point 28
average of a class Example 1.13: Temperature of malt grist 29

Statistical Calculations Example

1.14: Standard Deviation Example 1.15: Outlier 39
Test 1 Example 1.16: Outlier Test 2 42
Example 1.17: Outlier Test 3 Example 43
1.18: Comparison of Means Example 44
1.19: Interpretation of a Correlation and 46
Regression Analysis Example 1.20: Partial Coefficient of Determination 50
53

Chapter 2: Container Geometries

Example 2.1: Grain transport on a conveyor belt 57
Example 2.2: Lautering tray load 58
Example 2.3: Calculation of a barley steeping 62
tank Example 2.4: Volume of a cylindroconical shot keg 63
Example 2.5: Volume calculation of a mash tun Example 64
2.6: Volume calculation of a horizontal storage tank Example 64
2.7: Volume calculation of a storage or classic wooden transport
barrel Example 2.8: 65
Calculation of a cylindroconical tank (ZKT) 67

Chapter 3: Grain storage, grain care and grain transport Example 3.1: Calculation
of the material turnover and storage losses during
Barley storage 70
Example 3.2: Calculation of the amount of heat generated Example 3.3: 71
Calculation of the specific heat capacity cP of grain Example 3.4: Theoretical barley heating Example 72
3.5: Calculation of the specific heat capacity cP 72
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Example 3.6: Rapid determination of the specific heat development using

Nomogram according to Jouin 74
Example 3.7: Determining the permissible storage period for grain Example 3.8: 77
Calculating the required heat quantity for drying Example 3.9: Setting the temperature difference 79
between dry air and dry material Example 3.10: Air quantity for ventilation/cooling of grain Example
3.11: Pressure 81
loss of a layer of barley Example 3.12: Belt conveyor Example 3.13: Drive power 81
of a bucket elevator Example 3.14: Conveyor volume and 83
connected load of a screw conveyor 84
Example 3.15: Pneumatic conveyor system Example 3.16: 85
Calculating the contractually agreed, exact delivery quantity Example 3.17: Composition of a batch of 86
barley Example 3.18: Calculating a barley storage facility 88
88
89
90

Chapter 4: Malt Production Example 4.1:

Calculating the Soaking Degree (Variant 1) 92
Example 4.2: Calculation of the softening degree (variant 2) 92
Example 4.3: Calculating the required amount of soft water Example 4.4: Influence of 94
the soft water temperature on the soaking time Example 4.5: Calculating the amount of 94
heat to be removed from a germination box Example 4.6: Temperature of the germination
material in the 95
event of a cooling failure Example 4.7: What amount of CO2 would have to be 95
removed? 96
Example 4.8: Calculating a germination area Example 96
4.9: Mixing two air volumes Example 4.10: Mixing two 104
moist air volumes Example 4.11: Air humidification Example 4.12: 105
Humidifying and cooling air Example 105
4.13: Dryer, unheated Example 4.14: Dryer, heated Example 106
4.15: Malt drying Example 4.16: Determining the 107
degree of leaf germ development Example 108
4.17: Calculating the malt yield 109
Example 4.18: Malting waste Example 4.19: Calculating the amount of crude 110
protein in malt germs 111
111
112

Chapter 5: Crushing the malt (grinding)

Example 5.1: Assessment of dry grist Example 5.2: Assessment 114
of conditioned grist Example 5.3: Calculation of the water quantity during 114
conditioning Example 5.4: Water balance of grist Example 5.5: Dimensioning of grist 115
container 115
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Chapter 6: Calculations for brewing water and alkaline cleaning agents

Example 6.1:
Assessment of treated brewing water Example 6.2: Addition 122
of lime water to reduce carbonate hardness Example 6.3: Influence 124
of residual alkalinity on the pH value of the mash Example 6.4: 125
Calculation of the Ca ion addition to brewing water Example 6.5: 125
Testing and concentration of a cleaning solution 127

Chapter 7: Wort Production

Example 7.1: Calculating the specific main mash volume 131
Example 7.2: Required gross volume of the mash vessel 132
Example 7.3: Calculating the required second mash volume 133
Example 7.4: Calculating the pan full wort volume 133
Example 7.5: Calculating the brewhouse yield within the scope of the mash 134
management Example 7.6: Calculating the anticipated hot cast-out wort volume 134
Example 7.7: Calculating the required evaporation Example 135
7.8: Calculating the spent grain volume Example 136
7.9: Required water quantity for wort production Example 7.10: 136
Calculating the required boiling mash volume Example 7.11: 138
Calculating the required boiling mash volume Example 7.12: 139
Calculating the heat quantity for heating Example 7.13: 142
Calculating the required heating surface Example 144
7.14: Calculating a heat transfer coefficient Example 145
7.15: Mash heating by mixed condensation Example 7.16: 147
Mash heating by Mixed condensation Example 7.17: Wort 148
heating by mixed condensation Example 7.18: Calculation 149
of variables during lautering Example 7.19: Estimation 152
of the influence of changing the spent grain height on
the specific refining speed 153
Example 7.20: Estimation of the influence of changes in material properties
on the specific lautering speed Example 7.21: Spent 153
grain buoyancy depending on the lautering technology in the lauter tun
154
Example 7.22: Calculation of the required number of filter frames of a mash filter and their
specific capacity 154
Example 7.23: Calculation of the required spent grain silo volume Example 7.24: 155
Extract content of a clear water Example 7.25: Influence 155
of the evaporation coefficient on the energy consumption during
Wort boiling 158
Example 7.26: Calculation of bittering agent addition and bittering agent balance 160
Example 7.27: Calculation: Bittering agent addition according to ÿ-acid per brew 161
Example 7.28: Calculation: Average hop boiling time Example 7.29: Calculation 162
of the simplified bittering agent yield BA in the cold
Pitching wort and correction of the specific ÿ-acid addition Example 163
7.30: Calculation of the simplified bitter substance yield, based on
the finished beer 164
Example 7.31: Calculating the desired malt color for a malt mixture in the mash
164

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Example 7.32: Calculation of the bulk proportions when using malt substitutes 165 Example
7.33: Calculation of the classic brewhouse yield and evaluation 168 Example 7.34: Simple
calculation of the Overall Brewhouse Yield (OBY) 168 Example 7.35: Extract corrections through trub and liquor
management 169 Example 7.36: Yield balancing taking into account the

Grain residue extract 171

Example 7.37: Cooling the wort to pitching temperature 173

Chapter 8: Fermentation and maturation of beer Example 8.1:

Calculation of the effective mass transfer area after pitching the wort Example 8.2: What
influence does the density 179
of the yeast cell have on its
Sedimentation behavior Example 180
8.3: Liquid yeast addition per 1 hL of wort Example 8.4: Yeast 181
addition using dry yeast Example 8.5: Sedimentation rate of different yeast cell 181
sizes Example 8.6: Influence of the agglomerate size of a broken yeast on its settling rate and 183
clarification time Example 8.7: Permissible discharge volume Example 8.8: Calculating
the required process time for propagation 184
Example 8.9: Required tank volume for a yeast 189
propagation system Example 8.10: Calculating the required tank volume for a yeast propagation 189
system in batch operation 190

191
Example 8.11: Calculation of the total oxygen and air requirement Example 8.12: 194
Calculation of the required oxygen input in the starting
and in the final phase of yeast propagation Example 195
8.13: Estimation of the required aeration time for a
Yeast propagation in brewery wort Example 196
8.14: Original gravity calculation of a shipping beer Example 8.15: Final 198
fermentation degrees, the fermented extracts and their
Residual extracts in three types of beer 201
Example 8.16: Calculation of the alcohol content A, the remaining
unfermented extract Ew, the amount of yeast formed HTS and the amount of CO2
formed in the final fermented beer from 1000 g
Seasoning for the three types of beer 202
Example 8.17: Calculation of the alcohol content and the actual residual extract
content Example 8.18: 203
The amount of water in the final fermented beer from 1000 g of wort
203
Example 8.19: Wort and beer volume V from 1000g pitching wort Example 8.20: 204
Calculation of the fermentation cellar fermentation degrees and the remaining
existing fermentable residual extracts for the three beer types from Example 8.15
(sampling at the end of the main fermentation) 205 Example 8.21: Calculations according to
Tabarié 206 Example 8.22: The required fermentable residual extract for CO2 formation 206 Example 8.23: A
quick approximate solution for the time of bunging 207 Example 8.24: Calculation of the average fermentation
Gd 209

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Example 8.25: Use of a statistically verified,

technological context for the concrete calculation of the influence of
individual influencing factors 210
Example 8.26: Use of the determined technological relationship for the calculation of the
required fermentation time depending on the available fermentable sugar
quantity Example 8.27: Fermentation rate Gw according 211
to Schröderheim Example 8.28: Calculation of the bunging pressure 212
213

Chapter 9: Clarification and Stabilization of Beer Example 9.1: Calculation of the

1st Precoat 214 Example 9.2: Calculation of the 2nd Precoat 215 Example 9.3: Calculation of the Free Truss
Space and its Potential Utilization 216 Example 9.4: Differential Pressure Rise, Filtration Time, and Filtrate
Amount 216 Example 9.5: Comparison of the Calculations with the Reference Values from the Literature 217
Example 9.6: Calculation of the FHM Batch 217 Example 9.7: Dilution of the Beer by Continuous Diatomaceous
Earth Dosing 218 Example 9.8: Capacity Calculation of a Crossflow Membrane Filter System 219 Example 9.9:
Diatomaceous Earth Batch Preparation Using Silica Gel 220

Chapter 10: Thermal preservation of beer (pasteurization)

Example 10.1: Calculation of the required holding temperature Example 10.2: 223
Calculation of the PE with constant holding time and depending on the holding
temperature above 60 °C 224
Example 10.3: Determination of PE units for the tunnel pasteurizer, variant 1 Example 225
10.4: Determination of PE units for the tunnel pasteurizer, variant 2 Example 10.5: 226
Calculation of the required holding time for non-alcoholic beer
taking into account wild yeast spores 230
Example 10.6: Influence of increasing the holding temperature on the holding
time for the heterofermentative Lactobacillus strain G Example 10.7: 230
Required holding temperature and holding time for a wort infection with the mesophilic bacterium
Clostridium sporogenes
231

Chapter 11: The energy content of beer and ethanol metabolism in humans

Example 11.1: Energy content of a full-bodied beer 232

Example 11.2: Simple approximate calculation to estimate the alcohol content
in the blood 234
Example 11.3: Calculating the time required for alcohol degradation in the blood 234 Example 11.4: Converting
alcohol concentrations from vol.% to grams/liter
235

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Chapter 12: Filling Example 12.1:

What amount of oxygen diffuses into a PET bottle in 30 days and what amount of CO2 is released
into the environment at about 23 °C during this time
237
Example 12.2: What amount of oxygen will diffuse into a PET bottle in 60 days?
239
Example 12.3: What amount of oxygen is released through the seal of a
Crown caps diffuse into a bottle in 3 months? 240
Example 12.4: How many bottles can be stored on a buffer area AP of 3 m2
stand? 241
Example 12.5: Calculation of the alkali concentrations in a bottle washing
machine 243
Example 12.6: Determination of the concentrations in the spray zones Example 12.7: 244
Determination of the amount of dirt introduced, the volume of liquid discharged and
the alkali concentration at time t Example 12.8: What amount of
heat is removed from a FRM 245
when the
Machine is operated at 80 °C and the fan delivers 3500 m3 /h at 0 °C Example
12.9: What amount of 247
H2 must be discharged? 247
Example 12.10: Calculating the required forklift mass mS Example 12.11: 249
Determining parameters according to DIN 8782 Example 12.12: Determining 252
line efficiency Example 12.13: Determining the OEE 253
Example 12.14: Checking the filling quantity of 253
beer bottles Example 12.15: Checking the filling quantity of beer bottles 259
Example 12.16: Specific space requirement of a filling system for 259
250,000 hL VB/a Example 12.17: Space requirement of a filling system variant 1 Example 12.18: 260
Space requirement of a filling system variant 2 262
262

Chapter 13: Example calculations for the preparation of non-alcoholic soft drinks Example
13.1: Calculating the beverage preparation for a lemonade
Example 13.2: Calculating the ratio of the beverage according to Example 13.1 Example 13.3: 265
Compare the calorie content of a normal lemonade with a lemonade with a calorific value 268
reduced to approximately 15% Example 13.4: Possible CO2 concentration in water Example 13.5:
Carbonation of a lemonade at 20 °C Example 13.6: Carbonation of a lemonade 269
at 10 °C 272
273
273

Chapter 14: Product Pipelines in the Brewery Example 14.1: Calculating the
Flow Velocity Example 14.2: Estimating the Pressure Drop in a Pipeline 275
Example 14.3: Nomogram Application Example 14.4: Calculating an Re Number 277
Example 14.5: Calculating the Mean Flow Velocity 280
Example 14.6: Calculating the Boundary Layer 282
Thickness Example 14.7: Flow Velocity at the Boundary Layer Surface 16 286
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Example 14.8: Expansion of a pipeline due to temperature increase Example 14.9: 292
Determination of compressive stress when expansion is prevented Example 14.10: 292
Removal of gas from a pipeline Example 14.11: Removal of oxygen 293
from a pipeline 294

Chapter 15: Pumps Example

15.1: Determination of the pressure difference during pumping 298
Example 15.2: Determination of the drive power of a pump motor Example 298
15.3: Power requirement of a centrifugal pump Example 304
15.4: Filter pump 309

Chapter 16: Compressors

Example 16.1: Design of a kiln fan 314

Chapter 17: Heat exchangers Example

17.1: Calculation of heat recovery Example 17.2: Mean 320
logarithmic temperature difference Example 17.3: Wort cooler 322
322

17