Applied Math FOR WASTEWATER PLANT OPERATORS JOANNE KIRKPATRICK PRICE Training Cons CRC PRESS Boca Raton London NewYork Washington, DC. Library of Congress Cataloging-in-Pubiicstion Data Main entry under tie Applied Math for Wastewater Plant Operators I Full Catalog m r di s available from the Library of Congrass I This book contains information obtained fbm authentic and highly regarded sources. Reprinted material is quoted with permission, and sotmx are indicated. A wide variety of refmnces are listed. Reasonable efforts have been made to publish eliabie data and infonnaton, but the authors and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or mnsmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for gend distribution, for promotion, for creating new works, or for resale. Specific pennission must be obtained in writing ftom CRC Press U Cf or such copying. k tall i nquiries to CRC Press UC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. 'hdemark Notice: Product or corporate names may be trademarks or registered trademarks, and am used only for identification and explanation, without intent to infringe. Visit the CRC Press Web site at www.crcpress.com Q 1991 by CRC Press U C Originally Published by Tcchnomic Publishing No claim to original U.S. Government works htemational Standard Book Number 87762-809-2 Library of Congress Card Number 90-7188 1 Printed in the United States of America 3 4 5 6 7 8 9 0 Printed on acid-free paper Dedication This book is dedicated to my family: To my husband Benton C. Price who was patient and supportive during the two years it took to write these texts, and who not only had to carry extra responsibilities at home during this time, but also, as a sanitary engineer, provided frequent technical critique and suggestions. To our children Lisa, Derek, Kimberly, and Corinne, who so many times had to pitch in while I was busy writing, and who frequently had to wait for my attention. To my mother who has always been so encouraging and who helped in so many ways throughout the writing process. To my father, who passed away since the writing of the fmt edition, but who, I know, would have had just as instrumental a role in these books. To the other members of my family, who have had to put up with this and many other projects, but who maintain a sense of humor about it. Thank you for your love in allowing me to do something that was important to me. J.K.P. Contents .................................... Dedication iii .................... Preface To The Second Edition ix .............................. Acknowledgments xi ........................ HOWT OU se These Books niii . ..................... 1 Applied Volume Calculations 1 ..................... Tank volume calculations 4 .......... Channel or pipeline volume calculations 6 ..................... Other volume calculations 8 . .................... 2 Flow and Velocity Calculations 11 ....................... Instantaneous flow rates 16 .......................... Velocity calculations 26 ........................... Average flow rates 30 ............................ Flow conversions 32 . ... 3 Milligrams per Liter to Pounds per Day Calculations 35 .................. Chemical dosage calculations 36 ....... Loading calculations--BOD. COD. and SS 42 ........................ BODandSSremoval 44 ............... Pounds of solids under aeration 46 ................ WAS pumping rate calculations 48 . ....................... 4 Loading Rate Calculations 51 ........................ Hydraulic loading rate 56 ......................... Surface overflow rate 60 ............................... Filtration rate 62 .............................. Backwash rate 64 ......................... Unit filter run volume 66 ........................... Weir overflow rate 68 .......................... Organic loading rate 70 ..................... Food/microorganism ratio 72 ........................... Solids loading rate 74 ......................... Digester loading rate 76 ................. Digester volatile solids loading 78 ..... Population loading and population equivalent 80 . ......... 5 Detention and Retention Times Calculations 83 .............................. Detentiontime 86 ................................. Sludge age 90 ......... Solids retention time (also called MCRT) 94 . ............... 6 Efficiency and Other Percent Calculations 99 ............................ Unit process efficiency 104 ............... Percent solids and sludge pumping rate 106 ............... Mixing different percent solids sludges 108 ............................. Percent volatile solids 110 ............................... Percent seed sludge 112 ....................... Percent strength 0f.a solution 114 ............ Mixing different percent strength solutions 116 .............. Pump and motor efficiency calculations 118 . ................................ 7 Pumping Calculations 121 ........................ Density and specific gravity 130 ................................ hssure and force 134 ............................... Head and head loss 142 ..................................... Horsepower 150 ................................... Pump capacity 156 . ......... 8 Wastewater Collection and Preliminary Treatment 163 ................................ Wet well capacity 166 ............................ Wet well pumping rate 168 .............................. Screenings removed 170 ............................ Screenings pit capacity 172 .............................. Grit channel velocity 174 .................................... Grit removal 176 ............................... Flow measurement 178 . ..................................... 9 Sedimentation 187 .................................. Detention time 190 ............................... Weir overflow rate 192 ............................. Sllrface overflow rate 194 ............................... Solids loading rate 196 ................. BOD and suspended solids removed 198 ............................ Unit process efficiency 200 . .................................... 10 Trickling Filters 203 ............................ Hydraulic loading rate 206 .............................. Organic loading rate 208 ............................. BOD and SS removed 210 ................... Unit process or overall efficiency 212 ............................... Rccirculation ratio 214 vii . .......................... 11 Rotating Biological Contactors 217 .............................. Hydraulic loading rate 220 ..................................... Soluble BOD 222 ............................... Organic loading rate 224 . ..................................... 12 Activated Sludge 227 .................................... Tankvolumes 238 .............................. BOD or COD loading 240 ................... Solids inventory in the aeration tank 242 .......................... F~croorganismra tio 244 ................................ Sludge age (Gould) 246 .............. Solids retention time (also called MCRT) 250 ................................. Return sludge rate 254 ...................................... Wastingrate 260 ................................ WAS pumping rate 266 ........................ Oxidation ditch detention time 268 ..................................... BOD loading 274 ............................... Organic loading rate 276 ............................ BOD removal efficiency 278 .............................. HydrauKc loading rate 280 ........... Population loading and population equivalent 282 .................................... Detention time 284 . ..................................... 14 Chemical Dosage 287 ............ Chemical feed rate-Eull-strength chemicals 292 ................... Chlorine dose. demand, and residual 294 ..... Chemical feed rate-less than full-strength chemicals 296 ......................... Percent strength of solutions 298 .................. Mixing solutions of different strength 302 .................. Solution chemical feeder setting.@ 306 ............ Chemical feed pumppercent stroke setting 308 ............... Solution chemical feeder setting. Wmin 310 ........................ Dry chemical feed calibration 312 ............ Solution feed calibration. given mdJmin flow 314 ........ Solution feed calibration. given drop in tank level 316 ............................ Average use calculations 318 . ........................ 1 5 Sludge Production and Thickening 321 ......... Primary and secondary clarifier solids production 332 ..................... Percent solids and sludge pumping 334 ............ Sludge thickening and sludge volume changes 336 ........................ Gravity thickening calculations 338 ............ Dissolved air flotation thickening calculations 348 ..................... Centrifuge thickening calculations 354 . ...................................... 16 Sludge Digestion 361 .................. Mixing different percent solids sludges 370 .............................. Sludge volume pumped 372 .......................... Sludge pump operating time 374 .......................... Volatile solids to the digester 376 .................. Seed sludge based on digester capacii y 378 .............. Seed sludge based on volatile solids loading 380 ............. Digester loading rate. lbs VS addedldaylcu ft 382 .................... Digester sludge to remain in storage 384 ......................... Volatile aciddalkalinity ratio 386 ....................... Lime required for neutralization 388 ........................ Percent volatile solids reduction 390 ............................. Volatile solids destroyed 392 .............................. Digester gas production 394 ...................................... Solids balance 396 ..................................... Digestion time 398 .................... Air requirements and oxygen uptake 400 .......................... pH adjustment using jar tests 402 . .......................... 17 Sludge Dewatering and Disposal 405 ..................... Filter press dewatering calculations 412 .................. Belt filter press dewatering calculations 414 .............. Vacuum filter press dewatering calculations 420 ......................... Sand drying beds calculations 424 ............................. Cornposting calculations 428 . ................................. 18 Laboratory Calculations 439 .......................... Biochemical oxygen demand 444 .................................. Molarity and moles 448 ............................ Normality and equivalents 452 ....................................... Settleability 456 .................................. Settleability solids 458 ........................ Sludge total and volatile solids 460 ........... Suspended solids and volatile suspended solids 464 ............ Sludge volume index and sludge density index 466 ....................................... Temperature 470 Preface to the Second Edition The first edition of these texts was written at the conclusion of three and a half years of instruction at Orange Coast College, Costa Mesa, California, for two different water and wastewater technology courses. The fundamental philosophy that governed the writing of these texts was that those who have difficulty in math often do not lack the ability for mathematical calculation, they merely have not learned, or have not been taught, the "language of math." The books, therefore, represent an attempt to bridge the gap between the reasoning processes and the language of math that exists for students who have difficulty in mathematics. In the years since the first edition, I have continued to consider ways in which the texts could be improved. In this regard, I researched several topics including how people learn (learning styles, etc.), how the brain functions in storing and retrieving infornation, and the fundamentals of memory systems. Many of the changes incorporated in this second edition are a result of this research. Two features of this second edition are of particular importance: the skills check section provided at the beginning of every basic math chapter a grouping of similar types of calculations in the applied math texts The skills check feature of the basic math text enables the student to pinpoint the areas of rnath weakness, and thereby customizes the instruction to the needs of the individual student. The first six chapters of each applie math text include calculations grouped by type of problem. These chapters have been included so that students could see the common thread in a variety of seemingly different calculations. The changes incorporated in this second edition were field-tested during a three-year period in which I taught a water and was tewater mathematics course for Palomar Community College, San Marcos, California. Written comments or suggestions regarding the improvement of any section of these texts or workbooks will be greatly appreciated by the author. Joanne Kirkpatrick Price