Lin S.D. Water and Wastewater Calculations Manual

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Factors for Conversion 915

U. S. Customary units Multiply by SI or US Customary units

Flowrate

cubic feet per second (ft

/s, cfs) 0.646 million gallons daily (MGD)

448.8 gallons per minutes (gpm)

28.32 liter per second (L/s)

0.02832 m

million gallons daily (MGD) 3.785 m

/d, (CMD)

0.04381 m

157.7 m

694 gallons per minute

1.547 cubic feet per second (ft

/s)

gallons per minute (gpm) 3.785 liters per minute (L/min)

0.06308 liters per second (L/s)

0.0000631 m

0.227 m

8.021 cubic feet per hour (ft

/h)

0.002228 cubic feet per second (cfs, ft

/s)

gallons per day 3.785 liters (or kilograms) per day

MGD per acre-ft 0.4302 gpm per cubic yard

0.9354 m

⭈ d

acre-feet per day 0.01427 m

Application or loading rate

cubic feet (ft

) per gallon 7.4805 m

per million gallons 0.00748 m

/1000 m

per 1000 ft

per minute 0.001 m

⭈ min

per ft

per hour 180 gal/ft

⭈ d

per minute per foot 0.00748 m

/min ⭈ m

gallons per foot per day 0.0124 m

/m ⭈ d

gallons per square feet per 40.7458 L/m

⭈ min

minute 0.04075 m

⭈ min

2.445 m

⭈ h

58.6740 m

⭈ d

gallons per acre 0.00935 m

/ha

MGD per acre-feet 0.430 gpm/yd

square root of qpm per

square foot (gal/min) 0.5/ft

2.70 (L/s) 0.5/m

pound per acre (lb/a) 1.121 kilograms per hectare (kg/ha)

pound per pound per day 1 kg/kg ⭈ d

pound per day 0.4536 kg/d

lb/ft

⭈ h 4.8827 kg/m

⭈ h

lb/1000 ft

⭈ d 0.0049 kg/m

⭈ d

pound per acre per day 1.1209 kg/ha ⭈ d

lb/ft

⭈ h 16.0185 kg/m

⭈ h

lb/1000 ft

⭈ d 0.0160 kg/m

⭈ d

pound per 1000 gallons 120.48 kg/1000 m

pound per million 0.12 mg/L

gallon

pounds per foot per 1.4882 kg/m ⭈ h

hour(lb/ft ⭈ h)

pounds per horse power 0.608 kg/kw ⭈ h

per hour (lb/hp ⭈ h)

U. S. Customary units Multiply by SI or US Customary units

Force

pounds 0.4536 kilograms force (kgf)

453.6 grams

4.448 newtons (N)

Pressure

pounds per square inch 2.309 feet head of water

(lb/in

, psi)

2.036 inches head of mercury

51.71 mmHg

6895 newtons per square meter

(N/m

)

= pascal (Pa)

703.1 kgf/m

0.0703 kgf/cm

0.0690 bars

pounds per square foot (lb/ft

) 4.882 kgf/m

47.88 N/m

(Pa)

pounds per cubic inch 0.01602 gmf/cm

16.017 gmf/L

tons per square inch 1.5479 kg/mm

millibars (mb) 100 N/m

inches of mercury 345.34 kg/m

0.0345 kg/cm

0.0334 bar

0.491 psi (lb/in

)

inches of water 248.84 pascals (Pa)

atmosphere 101,325 Pa

1013 millibars (1 mb = 100 Pa)

14.696 psi (lb/in

)

29.92 inches of mercury

33.90 feet of water

pascal (SI) 1.0 N/m

1.0 ⫻ 10

⫺5

bar

1.0200 ⫻ 10

⫺5

kg/m

9.8692 ⫻ 10

⫺6

atmospheres (atm)

1.40504 ⫻ 10

⫺4

psi (lb/in

)

4.0148 ⫻ 10

⫺3

in. head of water

7.5001 ⫻ 10

⫺4

cm head of mercury

Mass and density

slug 14.594 kg

32.174 lb (mass)

pound 0.4536 kg

slug per foot

515.4 kg/m

density (g) of water 62.4 lb/ft

at 50⬚F

980.2 N/m

at 10⬚C

specific wt (r) of water 1.94 slugs/ft

1000 kg/m

1 kg/L

1 gram per milliliter (g/mL)

Viscosity

pound-second per foot

or 47.88 newton second per square

slug per foot second meter (N s/m

)

square feet per second (ft

/s) 0.0929 m

916 Appendix E

Factors for Conversion 917

U. S. Customary units Multiply by SI or US Customary units

Work

British thermal units (Btu) 1.0551 kilo joules (kj)

778 ft lb

0.293 watt-h

1 heat required to change 1 lb of

water by 1⬚F

Work

Btu per pound 2.3241 kJ per kg

Btu/ft

⭈⬚F ⭈ h 5.6735 W/m

⭈⬚C ⭈ h

hp-h 2545 Btu

0.746 kW-h

kw-h 3413 Btu

1.34 hp-h

hp per 1000 gallons 0.1970 kW per m

Power

horsepower (hp) 550 ft lb per sec

746 watt

2545 Btu per h

kilowatts (kW) 3413 Btu per h

Btu per hour 0.293 watt

12.96 ft lb per min

0.00039 hp

Temperature

degree Fahrenheit (⬚F) (⬚F ⫺ 32) ⫻ (5/9) degree Celsius (⬚C)

(⬚C) (⬚C ⫻ (9/5) ⫹ 32 (⬚F)

⬚C ⫹ 273.15 Kelvin (K)

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Index

/O process, 766–772

Absolute viscosity, 231–232

Accumulation of sludge deposits, 52–54

Achromobacter, 727, 791

Activated carbon adsorption isotherm

equations, 440–444

Activated sludge, 618, 797

Activated-sludge process, 621–696

aeration and mixing systems, 681–683

aerated lagoon, 690–696

diffused air aeration, 683–688

mechanically aerated systems,

688–690

oxygen transfer and utilization,

681–683

aeration periods and BOD loadings,

622–623

biochemical reactions, 626

conventional process, 664–666

food-to-microorganism (F/M) ratio,

623–626

mathematical modeling of, 627–649

complete mix with recycle, 629–631,

635

MLSS settling curve, 642–648

oxygen requirements in process,

634–635

plug-flow with recycle, 648–649

process design and control

relationships, 631–633

sludge production, 633

modified processes, 663–681

biological nitrification, 681

complete-mix process, 668–669

contact stabilization, 671–672

deep shaft reactor, 679–680

extended aeration, 669–670

Hatfield process, 673

high rate aeration, 671

high-purity oxygen system, 674–677

Kraus process, 673–674

oxidation ditch, 677–679

sequencing batch reactor, 674

short-term aeration, 671

Activated-sludge process, modified

processes (Cont.):

step aeration, 667–668

tapered aeration, 666–667

operation and control of, 649–663

aeration tank mass balance, 654–656

return activated sludge, 650–654

secondary clarifier mass balance, 657

sludge age, 657–662

sludge bulking, 662–663

sludge density index, 650

sludge volume index, 649–651

waste activated sludge, 657

process design concepts, 626–627

Adsorbate, 440–441

Adsorbent, 440–441

Advanced treatment process, 578–579,

772–773

Advanced treatment system, 578–579

Advanced wastewater treatment (AWT),

578–579, 752–796

defined, 578

nitrogen control, 772–796

advanced processes for, 772–796

biological nitrification, 773–775

combined carbon oxidation-

nitrification in attached growth

reactors, 786–791

conventional processes for, 772–796

denitrification, 791–793

denitrification with RBC process,

794–796

environmental effects of nitrogen

compounds, 772

kinetics of denitrification, 793–794

kinetics of nitrification, 775–786

nitrifying biofilm properties, 775

phosphorus removal, 753–770, 772

by biological processes, 766–772

by chemical precipitation, 754–766

suspended solids removal, 752

Advection (groundwater contamination),

212

Aerated lagoon, 690–696

919

Aeration:

activated-sludge process, 681–683

aerated lagoon, 690–696

aeration periods and BOD loadings,

622–623

diffused air aeration, 683–688

extended aeration, 669–670

high rate aeration, 671

mechanically aerated systems,

688–690

oxygen transfer and utilization,

681–683

short-term aeration, 671

step aeration, 667–668

tapered aeration, 666–667

contaminants removed by, 521

public water supply, 343–368

diffused aeration, 355–357

gas transfer models, 347–356

nozzles, 365–368

packed towers, 357–365

two-film gas transfer model, 347–355

Aerobacter aerogen, 714

Aerobic sludge digestion, 820–826

Aerobic stabilization ponds, 734–735

Agronomic rate (biosolids), 845–846

Air piping, 684

Air requirement, 635

in activated sludge process, 681

of aerobic digestion, 821–822

diffused, 822, 825

Air stripping, 343 (See also Aeration)

Alcaligenes, 621, 727

Algae, 6, 107–108, 151–153

ALI (See Aquatic life impairment index)

Alkalinity, nitrification and, 779–780

ALMP (See Ambient lake monitoring

program)

ALR (See Areal loading rate)

Alum, 827

coagulation with, 368, 372–374, 389

in phosphorus removal, 755–760

in sludge, 458

Ambient lake monitoring program

(ALMP), 139–140

Ammonia concentration on nitrification,

775

Ammonia nitrogen:

chlorination for removal of, 469–471

groundwater contamination by, 847

influent concentrations of, 787

in nitrification process, 774, 775, 780

in raw wastewater, 537

Ammonia nitrogen (Cont.):

RBC removal of, 711, 716–717

in sludge, 828

standards for, 579

in wastewater effluent, 79

Ammonia oxidation, 773–786

Anaerobic sludge digestion,

812–815

Anaerobic stabilization ponds, 735

Animal feed lots, 496

Anions, 427, 430–432

Anisotropic aquifers, 197–198

Anisotropy, 197

Annual biosolids application rate, 847

Annual pollutant loading rate for

biosolids, 846

Annual whole sludge application rate

(ASAR), 846, 847

A/O process (phosphorus removal),

766–772

Apportionment of stream users,

79–86

Aquatic life, 158–168

Aquatic life impairment index (ALI),

158–161

Aquifers, 180–181

anisotropic aquifers, 197–198

confined, 180–181, 899–904

defined, 180–181

isotropic, 197

porosity, 184–185

steady flows in, 195–196

storativity, 185

transmissivity, 185–186

unconfined, 180, 181

Archromobacter, 791

Areal loading rate (ALR):

free water surface wetlands, 868

stabilization ponds, 728–731

Arithmetic method (population

estimates), 312

Arrhenius model, 474

Arsenic (in drinking water), 323

ASAR (See Annual whole sludge

application rate)

Asbestos, 324, 445

Assimilatory (synthesis) denitrification,

791–793

Atrazine, 326, 341–342

Attached-growth biological treatment

effluent, 736–739, 786

AWT (See Advanced wastewater

treatment)

920 Index

Bacteria, 621, 727 (See also Indicator

bacteria)

Baffling, 478–479

Belt filter press (BFP), 830–833

Benzene, 326

Bernoulli equation, 240

BFP (See Belt filter press)

Biochemical oxygen demand (BOD):

analysis, 10–13

deoxygenation rate and ultimate BOD,

18–32

determination of k

, 62–63

first-order reaction, 15–18

models and K

computation, 14–41

reaeration rate constant K

, 43–45

second-order reaction, 37–41

temperature effect on K

, 32–37

ultimate (total), 18–32

for wastewater, 10–13, 538–540

Biodegradation (groundwater), 213, 522

Biofilms, 504–505, 775

Biologic floc, 618

Biological nitrification:

activated sludge, 681

advanced wastewater treatment,

773–775

Biological slime, 696

Biological treatment systems

(wastewater), 578, 617–621

basin sizing, 736–739

cell growth, 619–621

Biosolids (sewage sludge), 840–841

Class A, 843–844

Class B, 844–845

defined, 841

land application of, 845–861

and agronomic rate, 845–846

annual biosolids application rate on

agricultural land, 847

annual whole sludge application rate,

846–847

nitrogen-based calculation, 847–851

phosphorus-based calculation, 851

pollutant limitation-based

calculation, 852–853

site evaluation and selection, 847

supplemental potassium (K)

fertilizer, 853–861

pathogen reduction, 842–844

regulatory requirements for, 841–842

use/disposal of, 842

Blue-green algae, 151–153, 155

BOD (See Biochemical oxygen demand)

BOD slide rule, 32

Boiling water, 520–522

Bottled water, 520, 521

Bottom slope of lake, 128–129

Bouwer and Rice slug test, 208–211

Boyle-Mariotte law, 234–235

Boyle’s law, 234–235

Brackish water, 452–454

Breakpoint chlorination, 469–474

Bromate, 492, 494, 498

Brownian movement, 372

Buried sewers, 572–574

Cadmium, 324, 846, 853

Calcium bicarbonate, 404, 406–407

Calcium carbonate:

hardness, 407–411

lime precipitation as, 760–762

mass of, 765

pellet softening, 411–415, 417

solubility constant for, 905

solubility equilibrium for, 369

and water quality, 427

Calcium hardness, 407–410, 423–424

Calcium hydroxide, 755, 905

Calcium oxide, lime, 754–755

Calculations:

of annual biosolids application rate on

agricultural land, 847

of bacterial density, 109–120

based on nitrogen, 847–851

based on phosphorus, 851

based on pollutant limitations, 852–853

Canada, 549–550

Carbon dioxide, 14–15

in activated sludge process, 622, 675

in advanced wastewater treatment,

753, 760–762, 773

from aeration, 343, 345

in aerobic digestion, 820

in anaerobic digestion, 812–818

in anaerobic ponds, 735

biodegradation to, 213

in composting, 826–827

in facultative ponds, 727

gas constant and density for, 235–236

lime removal of, 404

nozzles for removal of, 365–366

in photosynthesis, 54, 151

and sewage sludge disposal, 842

with trickling filters, 696

in wastewater, 537

Carbon usage rate (CUR), 441, 443

Index 921

Carbonaceous BOD (CBOD), 538–540

Carcinogens (in drinking water):

disinfectants as, 492, 493

dose-response model for, 515, 517

EPA classifications of, 333–334

federal standards for, 321, 323,

327–330

multistage model for, 517–519

one-hit model for, 517

reference dose, 332–335, 523

risks of, 517–519, 523, 524

Carlson’s index, 156–157

Carmen-Kozeny equation, 396

Cation exchangers, 418, 423–424

Cation resins, 419, 425

Cations, 420

Caustic soda (in pellet softening),

411–417

CBOD (See Carbonaceous BOD)

CCL (See National Drinking Water

Contaminant Candidate List), 332

Cell maintenance, 626

Cell residence time, 649

Centrifugal pumps, 265

Centrifugation (sludge dewatering), 836

Centrifuge sludge thickening, 807–811

CFR (See Code of Federal Registration)

Channel dam reaeration, 93–94, 96–97

Characteristics:

of wastewater, 533–542

of water, 55, 108–109, 141, 148

Charles-Gay-Lussac law, 234

Chemical conditioning of sludge, 827

Chemical constituents of wastewater,

537–541

Chemical oxygen demand (COD), 10, 535,

538–541, 557

Cheng-Ching Lake Advanced Water

Purification Plant (Taiwan), 411

Che’zy equation for uniform flow, 272–273

Chick’s law, 118–119, 474–475

Chick-Watson model, 474–475

Chloramine, 468–471

in dechlorination, 742–743, 746

as a disinfectant, 491, 492, 494, 497,

505

drinking water standards for, 323

and inactivation of Giardia lamblia,

481, 489, 490

and inactivation of viruses, 481

and pH of water, 323

Chloramine inactivation, 489

Chlorination, 464–473, 742–752

Chlorine:

available chlorine, 468–469

and disinfection, 491, 492, 494, 505

dosage of, 743–746

drinking water standards for, 323

free available, 464–468

free residual, 468

Chlorine dioxide (ClO

), 491, 492, 494,

497–498, 505

Chloroform, 345, 492, 911

Chlorophyll, in lakes and reservoirs,

155–156

Churchill equation, 46

Churchill-Buckingham method, 59–62

Circular basin design, 614–617

Cladothrix, 714

Clarifiers (See Sedimentation tanks)

Class A biosolids, 843–844

Class B biosolids, 844–845

Clean Lakes Program (CLP),

137–176

diagnostic/feasibility study (phase 1),

140–142

eligibility for financial assistance,

138

implementation (phase 2), 145

in-lake monitoring, 146–156

lake budgets, 168–173

lake use support analysis, 158–168

objectives of, 138

post-restoration monitoring (phase 3),

145–146

soil loss rate, 173–176

state lake classification survey,

139–140

trophic state index, 156–159

types of funds, 138

watershed protection approach, 146

Clean Water Act (CWA), 137, 161

CLP (See Clean Lakes Program)

Coagulation (water supply), 371–380,

499–500, 505

COD (See Chemical oxygen demand)

Code of Federal Registration (CFR),

826–828, 841–842

Coefficients:

of contraction, 255

of diffusion, 88, 213–214

of dilution, 474

of discharge, 255, 293, 296, 297, 585

of drag, 380–381, 396

of endogenous decay, 630

of entrance, 255

922 Index

Coefficients (Cont.):

of internal friction of backfill, 573

of oxygen saturation, 682

of permeability, 188–190, 192–195

of retention capacity of soil, 215

of roughness, 246, 282

of runoff, 671

of storage of aquifers, 198–199

of surface roughness, 563

of transmissibility, 199

of variance, 557

Coldwell-Lawrence diagrams, 405

Coliform density, 108–117

Coliforms, 322

Collins-Selleck model, 749–752

Colloidal fouling, potential, 457

Combined available chlorine, 468–469

Combined carbon oxidation, 774, 778,

780, 786–791

Combined kinetic expression for

nitrification, 780–781

Combined nitrification in attached

growth reactors, 786–791

Combined sewers, 543–544

Comminutors, 586

Complete mix (activated sludge),

629–631, 635–643, 669–670

Complete mixing, 89, 97, 377–378, 657

Compliance standards:

for drinking water, 321–331, 340–341

for wastewater effluent, 79, 580–581

(See also Regulations)

Composting (sludge stabilization),

826–827

Compression settling, 606–607

Concentration factor, 802–803, 807

Cone of depression, 181–184, 199,

218–219

Confined aquifers, 180, 181, 899–904

“Conservation Authorities” (Ontario),

549

Constant percentage growth rate,

312–313

Constructed wetlands, 863–884

denitrification in, 865

environmental/health considerations,

864–866

free water surface wetlands,

866–876

vegetated submerged bed systems,

876–884

Contact stabilization (activated sludge),

671–672

Contact time:

in CT value, 475–480, 489–490

and DO concentration, 353–354

in effluent disinfection, 742–743,

747–752

in flocculation, 380

of GAC and water, 442

in with RBCs, 717

in recarbonation basin, 762

and retention time, 549

Contaminant transport (pathway),

212–214

Contaminants (in drinking water),

321–342

compliance with standards, 340–341

federal standards for (tables), 322–332

leaking storage tank, 521

maximum contaminant level goal,

332–335

maximum contamination level, 335

treatment strategies for, 521–525

updated rules for, 2006, 335–339

Contamination of groundwater, 211–214

(See also Pollutants)

Conventional process:

for activated-sludge, 664–666

for nitrogen control, 772

Conversion factors (table), 913–917

Cooper-Jacob method (unsteady flows),

201–204

Copper, 906

coefficient of roughness for, 246, 248

in drinking water, 324

in runoff, 557

in sewage biosolids, 846, 853

Copper sulfate, 151–153

Cornfield, 855–860

Correction factor:

for altitude, 695

in channel dam reaeration, 93–94

and CT value determination, 477,

486–487

for DO saturation concentrations, 8–9

elevation, 49

in gas transfer models, 353

in Hardy-Cross method, 264

for larger flumes, 303

for nitrogenous KN in wastewater

effluent, 73–74

for oxygen transfer, 688–689

pH, 781

for resin, 427, 431

for salinity surface tension, 688

Index 923

Correction factor (Cont.):

for surface area in wastewater

treatment, 722

temperature, 345, 781

water quality, 96–97

Cost of pumping (CP), 270–272

Cost-benefit analysis for water quality

standards, 335

Critical depth (water flow), 285–287

Critical point of oxygen sag curve, 64–76

Critical time (t

), 64

Critical value for DO deficiency, 64, 682

Critical velocity, 285–286, 399

Cryptosporidium, 322, 336–339, 445, 476,

492, 496, 499, 500

CT (concentration × contact time) values,

477–491

CUR (See Carbon usage rate)

CWA (See Clean Water Act)

Cyanide (in drinking water), 324

DAF sludge thickening (See Dissolved air

flotation sludge thickening)

Daily difference method, 19

Dalton’s law, 343–344

Dams, 92–95

Darcy’s law, 186–191, 212

Darcy-Weisback equation, 241–242, 249

DBPR rule, Stage 2 (See Stage 2

Disinfectants and Disinfection

By-products Rule)

DBPs (See Disinfection by-products)

Dechlorination (wastewater), 746–747

Declining growth method (estimation),

313

Deep shaft reactor (activated sludge),

679–680

Demineralization, 448

Denitrification, 791–796

in constructed wetlands, 865

with RBC, 794–796

(See also Nitrogen control)

Density (r):

algal, 107

of backfill, 573

bacterial, 109–118, 147–148, 162, 542,

619–620, 737, 743, 745, 749, 751,

842–844

of fluid in pipes, 237

of GAC, 441

of grit, 586

mass, 233, 381

microbial, 474, 716

Density (r) (Cont.):

of organic loading, 747

of perfect gas, 234–235

population, 544, 554

of sand, 400

for screening, 586

of sediment particles, 384–385,

389, 592

silt density index, 458

sludge, 461–462, 649–651

of soil, 213–214

and specific weight, 228–229

water, 233, 346, 385–386, 396

of water plant residuals, 461–462

Deoxygenation coefficient (K

), 13, 43, 59

Deoxygenation rate, 18–32

in field, 55

in laboratory, 55–56

logarithmic formula, 30–32

moment method, 23–29

rapid method, 32

slope method, 19–23

streams and rivers, 18–32, 44–45

temperature effect on, 32–37

Depressed sewers (inverted siphons),

565–568

Desalination, 447, 448

Design:

of packed towers, 357–365

of storm drainage systems, 551

Design average flow (wastewater), 548

Design peak flow (wastewater), 548

Design wastewater flow rates, 547–548

Detention time multiplier, 610–611

Determination:

of CT values, 477–491

of deoxygenation rate k

, 57

and BOD, 14–41

of k

, 62–63

of lateral radius of influence,

219–222

direct measurement method, 221

Theis equation method, 221–222

volumetric flow equation, 222–223

of reaeration rate constant K

, 41–49

of ultimate BOD, 18–32

logarithmic formula, 30–32

moment method, 23–29

rapid methods, 32

slope method, 19–23

Diagnostic study, 141–142

Diagrams for flow measurement through

Parshall flumes, 303–304

924 Index