Formula / Conversion Tables

INDIANA DEPARTMENT OF ENVIRONMENTAL MANAGEMENT Conversion Table / Formula Sheet for Water Treatment and Distribution Exams

Part 1: Abbreviations and Conversions

Abbreviations Abbreviations continued ac acre(s) TDH total dynamic head bhp brake horsepower TTHM total trihalomethanes cfs cubic feet per second TOC Total organic carbon DO dissolved oxygen TSS Total suspended solids EDTA ethylenediaminetetraacetic acid ug/L Micrograms per liter (ug/L ≈ ppb) ft or ’ foot (feet) VS Volatile solids fps feet per second g gram(s) Conversion Factors gal gallon(s) 1 acre 43,560 square ft gpcd gallons per capita per day 1 acre foot 326,000 gallons gpd gallons per day 1 cubic foot (ft3) 7.48 gallons gpg grains per gallon 1 cubic foot (ft3) 62.4 pounds (water) gpm gallons per minute 1 cubic foot per second 0.646 MGD hp horsepower 1 day 1,440 minutes hr hour(s) 1 foot 0.305 meters HTH high test hypochlorite 1 foot of water 0.433 psi in or ” inch(es) 1 gallon 8.34 pounds (water) kW kilowatt 1 gallon 3.79 liters kWh Kilowatt hour 1 grain per gallon 17.1 mg/L L liter(s) 1 horsepower 0.746 kW lb(s) pound(s) 1 horsepower 746 watts mg milligram(s) 1 horsepower 33,000 ft lbs/min mg/L milligrams per liter 1 mile 5,280 feet MGD million gallons per day 1 million gallons per day 694 gpm mhp motor horsepower 1 million gallons per day 1.55 cfs mil gal million gallons 1 pound 0.454 kilograms mL milliliter 1 pound per square inch 2.31 feet of water min minute(s) 1 ton 2,000 pounds ppb parts per billion (ppb ug/L) 1% 10,000 mg/L ppd pounds per day π (pi) 3.14159 ≈ ppm parts per million (ppm mg/L) psf pounds per square foot Miscellaneous psi pounds per square inch≈ Decimal percent = Percentage, expressed as a Q Flow decimal, e.g. 65% = 0.65 sec second(s) sq ft square foot (feet) SS settleable solids

Formula Sheet Page 1 of 6 • IDEM Water Operator Certification Examination Formulas • www.idem.IN.gov

Part 2: Formulas in Alphabetical Order

Alternative Formula Formula / Notes l (Titrant Volume, mL) (Acid Normality)(50,000) l Alkalinity, as mg CaCO /L 3 Sample Volume, mL l Volts l Amps Ohms l (Flow, Ft3) l Area, ft2 (Velocity, Ft/Sec) Area of a Circle (0.785) (Diameter2) (π)(Radius2) Area of a Cone

(lateral area) ( )(Radius) Radius + Height Area of a Cone 2 2 ( )(Radiusπ )(Radius�) + Radius + Height (total surface area) Area of a Cylinder [Surface area of end #1] + [Surface area2 of end #2]2 + π � (total exterior surface area) [( )(Diameter) (Height or Depth)]

Area of a Rectangle π (Length) (Width)

Area of a Right Triangle (0.5) (Base) (Height) Average l Sum of all terms l

(arithmetic mean) Number of terms Average The nth root of the [(X )(X )(X )…(X )]1/n (geometric mean) 1 2 3 n product of n numbers Chemical dry feeder l (Dry chemical collected, grams) (1440 min/day) l

calibration, lbs/day (454 grams/lb) (Time, min) Chemical feed pump l Desired flow x 100% l

setting, % stroke Maximum flow Chemical feed pump (Flow, MGD) (Dose, mg/L) (3.785 L/gal) (1,000,000 gal/MG)

setting, mL/min (Liquid, mg/mL) (1440 min/day) Circumference of Circle (π)(Diameter) (2π)(Radius) Composite sample single l (Instantaneous flow) (Total sample volume) l

portion (Number of portions) (Average flow) CT Calculation (Disinfectant residual concentration, mg/L) (Time, min) (°F – 32) Degrees Celsius (°F – 32) (5/9) 1.8 (°C) (1.8) + 32 Degrees Fahrenheit (°C) (9/5) + 32

l Volume l Detention time Flow

Formula Sheet Page 2 of 6 • IDEM Water Operator Certification Examination Formulas • www.idem.IN.gov

Alternative Formula Formula / Notes Electromotive Force (Current, amps) (Resistance, ohms) E = IR (EMF), volts l (Dosage, mg/L) (Capacity, MGD) (8.34 lbs/gal) l Feed rate, lbs/day Purity, decimal percent Feed rate, gal/min l (Plant capacity, gpm) (Dosage, mg/L) l

(Fluoride Saturator) 18,000 mg/L Feed rate, lbs/day l (Dosage, mg/L) (Capacity, MGD) (8.34 lbs/gal) l

(Fluoride) (Available Fluoride ion, decimal percent) (Purity, decimal percent) Filter backwash rise rate, l (Backwash rate, gpm/ft2) (12 in/ft) l

in/min 7.48 gal/ft3 Filter drop test velocity, l Water drop, ft l

ft/min Time of drop, min Filter flow rate or l Flow, gpm l

backwash rate, gpm/ft2 Filter area, ft2 l (Solids loading, lbs/day) (Recovery, decimal percent) l Filter yield, lbs/hr/ft2 (Filter operation, hr/day) (Area, ft2) Flow rate (Area) (Velocity)

Force, lbs (Pressure, psi) (Area, in2) l Volume of water produced, gpd l Gallons/capita/day Population l (Titrant volume, mL) (1,000) l Note: only when the Hardness, as mg CaCO3/L titration factor is 1.00 of Sample volume, mL EDTA l (Flow, gpm) (Head, ft) l Horsepower, brake (bhp) (3,960) (Pump efficiency, decimal percent) l (Flow, gpm) (Head, ft) l Horsepower, motor (mhp) (3,960) (Pump efficiency, decimal percent) (Motor efficiency, decimal percent) l (Flow, gpm) (Head, ft) l Horsepower, water (whp) 3,960 Hydraulic loading rate, l Total flow applied, gpd l

gpd/ft2 Area, ft2 l Chlorine required, lbs x 100% l Hypochlorite strength, % (Hypochlorite solution needed, gal) (8.34 lbs/gal)

Langelier Index pH – pHS l Volume, gallons l Leakage, gpd Time, days Mass, lbs (Volume, MG) (Concentration, mg/L) (8.34 lbs/gal)

Formula Sheet Page 3 of 6 • IDEM Water Operator Certification Examination Formulas • www.idem.IN.gov

Alternative Formula Formula / Notes Mass flux, lbs/day (Flow, MGD) (Concentration, mg/L) (8.34 lbs/gal)

Milliequivalent (mL) (Normality) l Moles of solute l Molarity Liters of solution 1 Number of equivalent weights of solute 1 Normality Liters of solution Number of equivalent l Total weight l

weights Equivalent weight l Total weight l Number of moles Molecular weight 1 (Original flow – Reduced flow) x100% 1 Reduction in flow, % Original flow 1 (In – Out) x 100% 1 Removal, % In Reservoir Surface Area, 1 (Surface area, ft2) 1

acres 43,560 ft2/ac 1 Drop or Rise x 100% 1 Slope, % Distance 1 (Dry solids, grams) (1,000,000) 1 Solids, mg/L Sample volume, mL l Weight, mg l Solids Concentration, mg/L Volume, L 1 Specific weight of substance, lbs/gal 1 Specific Gravity Specific weight of water, lbs/gal Surface loading (overflow) l Flow, gpd l

rate, gpd/ft2 Area, ft2 Where Three Normal Equation (N1 x V1) + (N2 x V2) = (N3 x V3) V1 + V2 = V3 N = normality Two Normal Equation N x V = N x V 1 1 2 2 V = volume or flow 1 Flow rate, ft3/sec 1 Distance, ft Velocity, ft/sec 2 Area, ft Time, sec 2 2 (1/3) [(π) (Radius ) Volume of Cone (1/3) (0.785) (Diameter ) (Height) (Height)] 2 2 (π) (Radius ) Volume of Cylinder (0.785) (Diameter ) (Height) (Height) Volume of Sphere (4/3)(π)(Radius3) Volume of Rectangular (Length) (Width) (Height) Tank

Formula Sheet Page 4 of 6 • IDEM Water Operator Certification Examination Formulas • www.idem.IN.gov

Alternative Formula Formula / Notes Watts (Volts) (Amps) (Power Factor) (AC circuit) Watts (Volts) (Amps) (DC circuit) l Flow, gpd l Weir Overflow Rate, gpd/ft Weir length, ft Wire-to-Water Efficiency, 1 Water horsepower, hp x 100% 1

% Power input, hp or Motor hp Wire-to-Water Efficiency, (Flow, gpm) (Total dynamic head, ft) (0.746 kW/hp) x 100%

% (3,960) (Electrical demand, kW)

Formula Sheet Page 5 of 6 • IDEM Water Operator Certification Examination Formulas • www.idem.IN.gov Area of Circle *Pie wheels

Area - To find the quantity above the horizontal line, multiply the pie wedges below the line together. Circle - To solve for one of the pie wedges below the horizontal line, cover that pie wedge, then divide the remaining pie 2 0.785 D wedge(s) into the quantity above the horizontal line.

Given units must match the units shown in the pie wheel.

Area of Rectangle Area of Right Triangle Electromotive Force (EMF), volts

Area Area Volts Rectangle Right Triangle EMF

Amps Ohms Height 1 Length Width 2 Current Resistance Base

Feed Rate, lbs/day Flow Rate, cfs Force, lbs lbs/day cfs Pounds Chemical Feed Flow Rate Force 100% Purity

MGD 8.34 2 2 ft ft/sec psi in Flow lbs/gal mg/L Area Velocity Pressure Area Dose

Horsepower, Water (whp) Mass, lbs Mass Flux, lbs/day

whp lbs lbs/day Horsepower Mass Mass Flux

gpm 1 l mil gal 8.34 MGD 8.34 Flow 3,960 Vol. lbs/gal Flow lbs/gal feet mg/L mg/L Head Conc. Conc.

Volume of Cone Volume of Cylinder Volume of Rectangular Tank

Volume Volume Volume Cone Cylinder Rectangle

1 0.785 0.785 Height Length Height 3 2 D H D2 Width

Formula Sheet Page 6 of 6 • IDEM Operator Certification Examination Formulas • www.idem.IN.gov