Operator Reference

Formulas

Every formula from the wastewater treatment, collection, industrial waste and laboratory exam tables. US and metric forms are shown together so you never have to guess which one you were handed. 12 of them also have a pie wheel.

General & Everyday Math

Averages, percent removal, temperature and detention time.

Average (arithmetic mean)

AverageSum of All TermsNumber of Terms

Average (geometric mean)

Average[(X₁)(X₂)(X₃)(X₄)(Xₙ)]^(1/n)

The nth root of the product of n numbers.

Degrees Celsius

°C°F − 321.8

Degrees Fahrenheit

°F°C1.8+ 32

Removal, %

Removal, %In − OutIn× 100%

Slope, %

Slope, %Drop or RiseDistance× 100%

Water Use

Water Use, gpcdVolume of Water Produced, gpdPopulation

Metric

Water Use, LpcdVolume of Water Produced, LpdPopulation

Area & Volume

Tank and channel geometry — the starting point for most volume math.

Area of Circle

Pie wheel

From diameter

Area of Circle0.785Diameter²

From radius

Area of Circle3.14Radius²

Area of Cone (lateral area)

Lateral Area of Cone3.14Radius√(Radius² + Height²)

Area of Cone (total surface area)

Total Surface Area of Cone3.14RadiusRadius + √(Radius² + Height²)

Area of Cylinder (total exterior surface area)

Total Exterior Surface Area[End #1 SA] + [End #2 SA] + [(3.14)(Diameter)(Height or Depth)]

Where SA = surface area.

Area of Rectangle

Pie wheel

Area of RectangleLengthWidth

Area of Right Triangle

Pie wheel

Area of Right TriangleBaseHeight2

Circumference of Circle

Circumference3.14Diameter

Volume of Cone

Pie wheel

Volume of Cone1/30.785Diameter²Height

Volume of Cylinder

Pie wheel

Volume of Cylinder0.785Diameter²Height

Volume of Rectangular Tank

Pie wheel

Volume of Rectangular TankLengthWidthHeight

Flow & Hydraulics

Velocity, flow rate, force and pump cycle timing.

Detention Time

Detention TimeVolumeFlow

Units must be compatible.

Cycle Time

Cycle Time, minStorage Volume, gal(Pump Capacity, gpm) − (Wet Well Inflow, gpm)

Metric

Cycle Time, minStorage Volume, m³(Pump Capacity, m³/min) − (Wet Well Inflow, m³/min)

Flow Rate

Pie wheel

Flow Rate, ft³/secArea, ft²Velocity, ft/sec

Metric

Flow Rate, m³/secArea, m²Velocity, m/sec

Force

Pie wheel

Force, lbPressure, psiArea, in²

Metric

Force, newtonsPressure, pascalsArea, m²

Velocity

US · from flow

Velocity, ft/secFlow Rate, ft³/secArea, ft²

US · from distance

Velocity, ft/secDistance, ftTime, sec

Metric · from flow

Velocity, m/secFlow Rate, m³/secArea, m²

Metric · from distance

Velocity, m/secDistance, mTime, sec

Process Control

Loading rates, sludge age, SVI, return rates and filter performance.

Filter Backwash Rate

Filter Backwash Rate, gpm/ft²Flow, gpmFilter Area, ft²

Metric

Filter Backwash Rate, L/sec/m²Flow, L/secFilter Area, m²

Filter Backwash Rise Rate

Filter Backwash Rise Rate, in/minBackwash Rate, gpm/ft²12 in/ft7.48 gal/ft³

Metric

Filter Backwash Rise Rate, cm/minWater Rise, cmTime, min

Filter Yield

Filter Yield, lb/hr/ft²Solids Loading, lb/dayRecovery, % expressed as a decimalFilter Operation, hr/dayArea, ft²

Metric

Filter Yield, kg/hr/m²Solids Concentration, % expressed as a decimalSludge Feed Rate, L/hr10Surface Area of Filter, m²

Food/Microorganism Ratio

F/M RatioBOD₅, lb/dayMLVSS, lb

Metric

F/M RatioBOD₅, kg/dayMLVSS, kg

Hydraulic Loading Rate

Hydraulic Loading Rate, gpd/ft²Total Flow Applied, gpdArea, ft²

Metric

Hydraulic Loading Rate, m³/day/m²Total Flow Applied, m³/dayArea, m²

Loading Rate

Pie wheel

Loading Rate, lb/dayFlow, MGDConcentration, mg/L8.34 lb/gal

Metric

Loading Rate, kg/dayFlow, m³/dayConcentration, mg/L1,000

Mass

Pie wheel

Mass, lbVolume, MGConcentration, mg/L8.34 lb/gal

Metric

Mass, kgVolume, m³Concentration, mg/L1,000

Mean Cell Residence Time / Solids Retention Time

MCRT or SRT, days(Aeration Tank TSS, lb) + (Clarifier TSS, lb)(TSS Wasted, lb/day) + (Effluent TSS, lb/day)

Metric

MCRT or SRT, days(Aeration Tank TSS, kg) + (Clarifier TSS, kg)(TSS Wasted, kg/day) + (Effluent TSS, kg/day)

Organic Loading Rate — RBC

Organic Loading Rate, lb SBOD₅/day/1,000 ft²Organic Load, lb SBOD₅/daySurface Area of Media, 1,000 ft²

Metric

Organic Loading Rate, kg SBOD₅/m²·dayOrganic Load, kg SBOD₅/daySurface Area of Media, m²

Organic Loading Rate — Trickling Filter

Organic Loading Rate, lb BOD₅/day/1,000 ft³Organic Load, lb BOD₅/dayVolume, 1,000 ft³

Metric

Organic Loading Rate, kg/m³·dayOrganic Load, kg BOD₅/dayVolume, m³

Population Equivalent, Organic

Population EquivalentFlow, MGDBOD, mg/L8.34 lb/gal0.17 lb BOD/day/person

Metric

Population EquivalentFlow, m³/dayBOD, mg/L1,0000.077 kg BOD/day/person

Recirculation Ratio — Trickling Filter

Recirculation RatioRecirculated FlowPrimary Effluent Flow

Return Rate, %

Return Rate, %Return Flow RateInfluent Flow Rate× 100%

Return Sludge Rate — Solids Balance

Return Sludge Rate, MGDMLSS, mg/LFlow Rate, MGD(RAS Suspended Solids, mg/L) − (MLSS, mg/L)

Sludge Density Index

SDI100SVI

Sludge Volume Index

SVI, mL/gSSV₃₀, mL/L1,000 mg/gMLSS, mg/L

Solids Loading Rate

Solids Loading Rate, lb/day/ft²Solids Applied, lb/daySurface Area, ft²

Metric

Solids Loading Rate, kg/day/m²Solids Applied, kg/daySurface Area, m²

Surface Loading Rate / Surface Overflow Rate

Surface Overflow Rate, gpd/ft²Flow, gpdArea, ft²

Metric

Surface Overflow Rate, Lpd/m²Flow, LpdArea, m²

Weir Overflow Rate

Weir Overflow Rate, gpd/ftFlow, gpdWeir Length, ft

Metric

Weir Overflow Rate, Lpd/mFlow, LpdWeir Length, m

Lab & Chemistry

Titrations, solids, BOD, normality and molarity.

Alkalinity

Alkalinity, mg/L as CaCO₃Titrant Volume, mLAcid Normality50,000Sample Volume, mL

Biochemical Oxygen Demand (seeded)

BOD, mg/L(Initial DO, mg/L) − (Final DO, mg/L) − (Seed Correction, mg/L)300 mLSample Volume, mL

Biochemical Oxygen Demand (unseeded)

BOD, mg/L(Initial DO, mg/L) − (Final DO, mg/L)300 mLSample Volume, mL

Blending or Three Normal Equation

Blending(C₁ × V₁) + (C₂ × V₂) = (C₃ × V₃)

Where V₁ + V₂ = V₃; C = concentration, V = volume or flow. Concentration units must match and volume units must match.

# CFU/100 mL

# CFU/100 mL# of Colonies on Plate100Sample Volume, mL

Composite Sample Single Portion

Single PortionInstantaneous FlowTotal Sample VolumeNumber of PortionsAverage Flow

Dilution or Two Normal Equation

Dilution(C₁ × V₁) = (C₂ × V₂)

Where C = concentration, V = volume or flow. Concentration units must match and volume units must match.

Hardness

Hardness, as mg CaCO₃/LTitrant Volume, mL1,000Sample Volume, mL

Only when the titration factor is 1.00 of EDTA.

Milliequivalent

MilliequivalentmLNormality

Molarity

MolarityMoles of SoluteLiters of Solution

Normality

NormalityNumber of Equivalent Weights of SoluteLiters of Solution

Number of Equivalent Weights

Number of Equivalent WeightsTotal WeightEquivalent Weight

Number of Moles

Number of MolesTotal WeightMolecular Weight

Oxygen Uptake Rate / Oxygen Consumption Rate

OUR, mg/L/minOxygen Usage, mg/LTime, min

Specific Oxygen Uptake Rate / Respiration Rate

SOUR, (mg/g)/hrOUR, mg/L/min60 minMLVSS, g/L1 hr

Reduction of Volatile Solids, %

Reduction of VS, %VS in − VS outVS in − (VS in × VS out)× 100%

All information (in and out) must be in decimal form.

Solids Capture, % (Centrifuges)

Solids Capture, %[ Cake TS, % ÷ Feed Sludge TS, % ] × [ ((Feed Sludge TS, %) − (Centrate TSS, %)) ÷ ((Cake TS, %) − (Centrate TSS, %)) ] × 100%

Solids, mg/L

Solids, mg/LDry Solids, g1,000,000Sample Volume, mL

Solids Concentration, mg/L

Solids Concentration, mg/LWeight, mgVolume, L

Specific Gravity

Specific GravitySpecific Weight of Substance, lb/gal8.34 lb/gal

Metric

Specific GravitySpecific Weight of Substance, kg/L1.0 kg/L

Total Solids, %

Total Solids, %(Dried Weight, g) − (Tare Weight, g)(Wet Weight, g) − (Tare Weight, g)× 100%

Volatile Solids, %

Volatile Solids, %(Dry Solids, g) − (Fixed Solids, g)Dry Solids, g× 100%

Chemical Feed

Feed rate and chemical feed pump settings.

Chemical Feed Pump Setting, % Stroke

Pump Setting, % StrokeDesired FlowMaximum Flow× 100%

Chemical Feed Pump Setting, mL/min

Pump Setting, mL/minFlow, MGDDose, mg/L3.785 L/gal1,000,000 gal/MGFeed Chemical Density, mg/mLActive Chemical, % expressed as a decimal1,440 min/day

Metric

Pump Setting, mL/minFlow, m³/dayDose, mg/LFeed Chemical Density, g/cm³Active Chemical, % expressed as a decimal1,440 min/day

Feed Rate

Pie wheel

Feed Rate, lb/dayDosage, mg/LFlow, MGD8.34 lb/galPurity, % expressed as a decimal

Metric

Feed Rate, kg/dayDosage, mg/LFlow Rate, m³/dayPurity, % expressed as a decimal1,000

Pumps & Electrical

Horsepower, efficiency, watts and amps.

Amps

AmpsVoltsOhms

Electromotive Force (EMF)

Pie wheel

EMF, voltsCurrent, ampsResistance, ohms

Horsepower, Brake

Brake Horsepower, hpFlow, gpmHead, ft3,960Pump Efficiency, % expressed as a decimal

Metric

Brake Power, kW9.8Flow, m³/secHead, mPump Efficiency, % expressed as a decimal

Horsepower, Motor

Motor Horsepower, hpFlow, gpmHead, ft3,960Pump Efficiency, % expressed as a decimalMotor Efficiency, % expressed as a decimal

Metric

Motor Power, kW9.8Flow, m³/secHead, mPump Efficiency, % expressed as a decimalMotor Efficiency, % expressed as a decimal

Horsepower, Water

Water Horsepower, hpFlow, gpmHead, ft3,960

Metric

Water Power, kW9.8Flow, m³/secHead, m

Motor Efficiency, %

Motor Efficiency, %Brake hpMotor hp× 100%

Power, kW

Power, kWFlow, L/secHead, m9.81,000

Watts

AC circuit

WattsVoltsAmpsPower Factor

DC circuit

WattsVoltsAmps

Wire-to-Water Efficiency, %

From horsepower

Wire-to-Water Efficiency, %Water hpMotor hp× 100%

From electrical demand

Wire-to-Water Efficiency, %Flow, gpmTotal Dynamic Head, ft0.746 kW/hp100%3,960Electrical Demand, kW