Math for Wastewater Treatment Operators Grades 1 & 2: Practice Problems to Prepare for Wastewater Treatment Operator Certification Exams

381 Pages·2009·6.66 MB·English

by  John Giorgi

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A Guide to Preparing for Wastewater Treatment

Operator Certifi cation Exams
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AWWA is the authoritative resource for knowledge, information, and advocacy to improve the quality
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The Authoritative Resource on Safe Water ®
1P-1.5M-20628-03/07-EB
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MATH FOR WASTEWATER
TREATMENT OPERATORS
GRADES 1 AND 2
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20662 Math for Wastewater 1-2.indb 2 1/13/2009 3:27:20 PM
MATH FOR WASTEWATER
TREATMENT OPERATORS
GRADES 1 AND 2
A Guide to Preparing for Wastewater Treatment
Operator Certification Exams
John Giorgi
First Edition
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This work is dedicated to my wife, Flora Zhou Giorgi; my children, Sara, Stephanie,
and Steve; my mother, Thelma Giorgi; and my father, Albert Peter Giorgi.
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Math for Wastewater Treatment Operators Grades 1 and 2
Copyright © 2009 American Water Works Association

AWWA Publications Manager: Gay Porter De Nileon
Technical Editor/Project Manager: Martha Ripley Gray
Production: Hop-To-It Design Works & SquareOne Publishing

All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means,
electronic or mechanical, including photocopy, recording, or any information or retrieval system, except in the form
of brief excerpts or quotations for review purposes, without the written permission of the publisher.

Disclaimer
The authors, contributors, editors, and publisher do not assume responsibility for the validity of the content or any
consequences of their use. In no event will AWWA be liable for direct, indirect, special, incidental, or consequential
damages arising out of the use of information presented in this book. In particular, AWWA will not be responsible
for any costs, including, but not limited to, those incurred as a result of lost revenue. In no event shall AWWA’s
liability exceed the amount paid for the purchase of this book.
Although this study guide has been extensively reviewed for accuracy, there may be an occasion to dispute an
answer, either factually or in the interpretation of the question. Both AWWA and the author have made every effort
to correct or eliminate any questions that may be confusing or ambiguous. If you do find a question that you feel is
confusing or incorrect, please contact the AWWA Publishing Group.
Additionally, it is important to understand the purpose of this study guide. It does not guarantee certification. It is
intended to provide the operator with an understanding of the types of math questions he or she will be presented
with on a certification exam and the areas of knowledge that will be covered. AWWA highly recommends that you
make use of the additional resources listed at the end of this study guide and any other resources recommended by
your state certification board in preparing for your exam.
Library of Congress Cataloging-in-Publication Data

Giorgi, John.
Math for wastewater treatment operators grades 1 and 2 : practice problems to prepare for wastewater treatment
operator certification exams / John Giorgi and prepared by the editors of American Water Works Association. -- 1st ed.
p. cm.
Includes bibliographical references.
ISBN 978-1-58321-587-6
1. Sewage--Purification--Mathematics. 2. Sewage--Purification--Problems, exercises, etc. 3. Sewage disposal
plants--Employees--Certification. 4. Water--Purification--Mathematics. 5. Water--Purification--Problems, exercises,
etc. 6. Water treatment plants--Employees--Certification. 7. Engineering mathematics--Formulae. I. Title. II. Title:
Math for wastewater treatment operators grades one and two.

TD745.G56 2008
628.301’51--dc22
2008016635
6666 West Quincy Avenue
Denver, Colorado 80235-3098
800.926.7337
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CONTENTS
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xv
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
CHAPTER 1 WASTEWATER TREATMENT GRADE 1  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Significant Figures ........................................................ 7
Common Miscellaneous Conversion Problems .................................. 8
Temperature Conversion Problems .......................................... 12
Ratio Calculations ....................................................... 13
Percent and ppm Conversion Problems ...................................... 14
Percent Calculations ..................................................... 15
Percent Strength by Weight Solution Problems ................................ 16
Percent Solids By Weight Calculations ....................................... 18
Percent Volatile Solids Reduction ........................................... 19
Percent Moisture Reduction Problems ....................................... 20
Volatile Solids Pumping Calculations ........................................ 22
Calculations for Arithmetic Mean, Median, Range, Mode, and Geometric Mean ...... 23
Area Problems .......................................................... 27
Circumference Problems .................................................. 28
Volume Problems ........................................................ 29
Density Calculations ..................................................... 33
Specific Gravity of Liquids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Specific Gravity of Solids .................................................. 36
Pressure Problems ....................................................... 37
Hydraulic Press Calculations .............................................. 38
Screening Material Removal Calculations .................................... 40
Screening Pit Capacity Calculations ......................................... 41
vii
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MATH FOR WASTEWATER TREATMENT OPERATORS GRADES 1 AND 2
Grit Removal Calculations ................................................ 42
Recirculation Ratio Problems .............................................. 43
Detention Time Calculations ............................................... 44
Weir Overflow Rate Problems .............................................. 45
Surface Overflow Rate Calculations ......................................... 47
Flow and Velocity Problems ................................................ 48
Pump Discharge Problems ................................................ 50
Solids and Hydraulic Loading Rate Calculations .............................. 52
Sludge Pumping Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Biosolids Pumping and Production Problems ................................. 55
Waste Activated Sludge Pumping Rate Calculations ............................ 57
Total Dynamic Head Calculations ........................................... 58
Pumping Horsepower and Efficiency Calculations ............................. 59
Calculations of Chlorine Dose, Demand, and Residual .......................... 63
Dosage Problems ........................................................ 64
Chemical Feed Solution Settings ........................................... 67
Dry Chemical Feed Settings ............................................... 69
Sludge Production Calculations ............................................ 70
Sludge-Age (Gould) Calculations ........................................... 72
Sludge Volume Index and Sludge Volume Density Calculations ................... 73
Organic Loading Rate Calculations ......................................... 74
Suspended Solids Loading Calculations ...................................... 75
Biochemical Oxygen Demand Loading Calculations ............................ 76
Soluble and Particulate Biochemical Oxygen Demand Calculations ............... 78
Chemical Oxygen Demand Loading Calculations .............................. 81
Hydraulic Digestion Time Calculations ...................................... 82
Digester Loading Rate Calculations ......................................... 83
Mean Cell Residence Time (Solids Retention Time) Calculations. . . . . . . . . . . . . . . . . . 84
Digester Volatile Solids Loading Ratio Calculations ............................ 85
Digester Gas Production Problems .......................................... 87
Volatile Acids–to–Alkalinity Ratio Problems .................................. 88
Lime Neutralization Problems ............................................. 89
Poulation Loading Calculations ............................................ 91
Poulation Equivalent Calculations .......................................... 92
Solids under Aeration .................................................... 93
Suspended Solids Removal ................................................ 94
Biochemical Oxygen Demand Removal Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Food-to-Microorganism Ratio Calculations ................................... 97
Seed Sludge Problems .................................................... 98
viii
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CONTENTS
Gravity Thickener Solid Loading Problems ................................... 99
Dissolved Air Flotation: Thickener Solids Loading Problems .................... 101
Dissolved Air Flotation: Air-to-Solids Ratio Calculations ....................... 102
Dissolved Air Flotation: Air Rate Flow Calculations ........................... 103
Centrifuge Thickening Problems ........................................... 104
Sand Drying Bed Problems ............................................... 105
Deatering Calculations .................................................. 106
Vacuum Filter Yield and Operating Time Calculations ......................... 108
Biosolids Volume Index and Biosolids Density Index Calculations ............... 110
Settleable Solids Calculations ............................................. 111
Chemistry and Laboratory Problems ....................................... 112
Basic Electricity Problems ................................................ 114
WASTEWATER TREATMENT—GRADE 1 TEST . . . . . . . . . . . . . . . . . . . . . . . . . .115
WASTEWATER TREATMENT—GRADE 1 TEST SOLUTIONS . . . . . . . . . . . . . .119
CHAPTER 2 WASTEWATER TREATMENT GRADE 2  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Common Miscellaneous Conversion Problems ................................ 135
Temperature Conversion Problems ......................................... 137
Ratio Calculations ...................................................... 138
Percent and ppm Conversion Problems ..................................... 140
Percent Calculations .................................................... 141
Percent Strength by Weight Solution Problems ............................... 142
Percent Solids by Weight Calculations ...................................... 143
Percent Volatile Solids Reduction .......................................... 144
Percent Moisture Reduction Problems ...................................... 146
Volatile Solids Pumping Calculations ....................................... 147
Solution Mixture Calculations ............................................ 149
Calculations for Arithmetic Mean, Median, Range, Mode, and Geometric Mean ..... 150
Area Problems ......................................................... 153
Circumference Problems ................................................. 155
Volume Problems ....................................................... 156
Density Calculations .................................................... 159
Specific Gravity of Liquids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Specific Gravity of Solids ................................................. 161
Pressure Problems ...................................................... 162
Hydraulic Press Calculations ............................................. 162
Screening Material Removal Calculations ................................... 164
Screening Pit Capacity Calculations ........................................ 165
ix
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