Canadian ABC Formula/Conversion Table for Water Treatment, Distribution and Laboratory Exams

(Titrant Volume, mL) (Acid Normality) (50,000) Alkalinity, as mg CaCO3/L = Sample Volume, mL

Volts Amps = Ohms

Area of Circle = (0.785) (Diameter2) or (Π) (Radius2)

Area of Cone (lateral area) = (Π) (Radius) Radius 2 + Height 2

Area of Cone (total surface area) = (Π) (Radius) (Radius + Radius 2 + Height 2 )

Area of Cylinder (total outside surface area) = [Surface Area of End #1] + [Surface Area of End #2] + [(Π) (Diameter) (Height or Depth)]

Area of Rectangle = (Length) (Width)

(Base) (Height) Area of a Right Triangle = 2

Sum of All Terms Average (arithmetic mean) = Number of Terms

1/n Average (geometric mean) = [(X1) (X2) (X3) (X4) (Xn)] The nth root of the product of n numbers (Desired Flow) (100%) Chemical Feed Pump Setting, % Stroke = Maximum Flow

(Flow, m 3/day) (Dose, mg/L) Chemical Feed Pump Setting, mL/min = (Chemical Feed Density, g/cm 3 ) (Active Chemical, %)(1,440)

Circumference of Circle = (Π) (Diameter)

(Instantaneous Flow) (Total Sample Volume) Composite Sample Single Portion = (Number of Portions) (Average Flow)

( o F − 32) Degrees Celsius = [(Degrees Fahrenheit - 32) (5/9)] or 1.8

Degrees Fahrenheit = [(Degrees Celsius) (9/5) + 32] or [(Degrees Celsius) (1.8) + 32]

Volume Detention Time = Note: Units must be compatible. Flow Electromotive Force (E.M.F), volts = (Current, amps) (Resistance, ohms) or E =IR (Dosage, mg/L) (Flow Rate, m3/day) Feed Rate, kg/day = (Purity, Decimal Percentage ) 1,000

(Plant capacity, litre/min) (Dosage, mg/L) Feed Rate, litre/min (Fluoride Saturator) = (18,000 mg/L ) Effective January 12, 2009 Water Rise, cm Filter Backwash Rise Rate, cm/min = Time, minute

Water Drop, m Filter Drop Test Velocity, meter/min = Time of Drop, minute

2 Flow, L/sec Filter Flow Rate or Backwash Rate, L/m sec = 2 Filter Area, m (Solids Concentration, %)(Sludge Feed Rate, L/hr)(10) Filter Yield, kg/m2 hr = (Surface Area of Filter, m 2 )

Flow Rate, m3/sec = (Area, m2) (Velocity, m/sec) or Q = AV where: Q = flow rate, A = area, V= velocity Force, Newton = (Pressure, pascals) (Area, m2)

Volume of Water Produced, L/day Litres/Capita/Day = Population

(Titrant Volume, mL) (1,000) Hardness, as mg CaCO3/L = Only when the titration factor is 1.00 of EDTA Sample Volume, mL

(Flow, gpm) (Head, ft) Horsepower, Brake (bhp) = (3,960) (Decimal Pump Efficiency)

(Flow, gpm) (Head, ft) Horsepower, Motor (mhp) = (3,960) (Decimal Pump Efficiency) (Decimal Motor Efficiency)

(Flow, gpm) (Head, ft) Horsepower, Water (whp) = 3,960

Total Flow Applied, m 3 /day Hydraulic Loading Rate, m3/m2 day = Area, m 2

(Chlorine Required, Kg) (100) Hypochlorite Strength, % = (Hypochlorite Solution Needed, Kg)

Volume, L Leakage, Lpd = Time, days

(Volume, m 3 )(Concentration, mg/L) Mass, kg = 1,000

(Volume, m 3 / day)(Concentration, mg/L) Mass Flux, kg/day = 1,000

Milliequivalent = (mL) (Normality)

Moles of Solute Molarity = Litres of Solution

Effective January 12, 2009 Number of Equivalent Weights of Solute Normality = Litres of Solution

Total Weight Number of Equivalent Weights = Equivalent Weight

Total Weight Number of Moles = Molecular Weight (Flow, L/sec) (Head, m)(9.8) Power, kW = 1,000

(Original Flow - Reduced Flow) (100%) Reduction in Flow, % = Original Flow

(In − Out) (100) Removal, % = In

Drop or Rise Slope, % = x 100 Distance

(Dry Solids, grams) (1,000,000) Solids, mg/L = Sample Volume, mL

Weight, mg Solids Concentration, mg/L = Volume, L

Specific Weight of Substance, kg/L Specific Gravity = Specific Weight of Water, kg/L

Flow, Lpd Surface Loading Rate, Lpd/m2 = Area, m 2

Three Normal Equation = (N1 x V1) + (N2 x V2) = (N3 x V3), where V1 + V2 = V3

Two Normal Equation = N1 x V1 = N2 x V2, where N = concentration (normality), V = volume or flow

Flow Rate, m3 / sec Distance, m Velocity, m/second = or Area, m 2 Time, second

Volume of Cone = (1/3) (0.785) (Diameter2) (Height) Volume of Cylinder = (0.785) (Diameter2) (Height) Volume of Rectangular Tank = (Length) (Width) (Height) Watts (DC circuit) = (Volts) (Amps)

Watts (AC circuit) = (Volts) (Amps) (Power Factor) Flow, Lpd Weir Overflow Rate, Lpd/m = Weir Length, m

Effective January 12, 2009 Water Horsepower, HP Wire-to-Water Efficiency, % = x 100 Power Input, HP or Motor HP

(Flow, gpm) (Total Dynamic Head, ft) (0.746 kw/hp) (100) Wire-to-Water Efficiency, % = (3,960) (Electrical Demand, kilowatts)

Alkalinity Relationships:

Alkalinity, mg/L as CaCO3 Result of Hydroxide Carbonate Bicarbonate Titration Alkalinity Alkalinity Concentration

as CaCO3 as CaCO3 as CaCO3 P = 0 0 0 T P < ½T 0 2P T – 2P P = ½T 0 2P 0 P > ½T 2P – T 2(T – P) 0 P = T T 0 0 *Key: P – phenolphthalein alkalinity; T – total alkalinity

Conversion Factors: 1 acre = 4046.9 square metres 1 cubic metre = 1,000 kilograms 1 cubic metre = 1,000 litres 1 cubic metre = 219.97 Imperial gallons 1 cubic metre per second = 19.01 MIGD 1 foot = 0.305 metre 1 gallon = 3.79 litres 1 hectare = 10,000 square metres 1 horsepower = 0.746 kW or 33,000 foot-pounds/min 1 metre head = 9.8 kPa 1 pound = 0.454 kilograms 1 pound per square inch = 6.89 kPa 1 square metre = 1.19 square yards 1% = 10,000 mg/L Π or pi = 3.14159

Abbreviations: cm centimetres mL millilitre DO dissolved oxygen MLD million litres per day g grams ppb parts per billion kPa kilopascals ppm parts per million kg kilograms psi pounds per square inch kW kilowatt Q flow L litres SS settleable solids Lpd litres per day TTHM Total trihalomethanes Lpm litres per minute TOC total organic carbon m metres TSS total suspended solids mg/L milligrams per litre VS volatile solids MIGD million Imperial gallons per day

Effective January 12, 2009