ࡱ>  6bjbj! ! @CfCfE%+$$$D$$$b%l%d$ޞ2'2'(Z'Z'Z'!######$ȠzTGQ$!GZ'Z'^PZ'$Z'!!."pZ'{p 0ޞΣ[RΣΣ$PGGޞΣ :    3/15/2005 Formulas, Conversions, and Common Scientific Units  ABC Formulas, Conversions & Abbreviations  DEP Dry and Liquid Chemical Feed Diagrams Unit Cancellation Steps  Units of Weight, Volume, Time, Density, Concentration & Flow Formulas & Conversions Formulas The symbol " = Pie = 3.14 Alkalinity = (mL of Titrant) (Acid Normality) (50,000) mL of Sample Area of Circle = (.785) (Diameter2) or (") (Radius2) Area of Cylinder Surface = [(.785) (Diameter2)] + [(") (Diameter) (Height)] Curved Surface Area of a Cylinder = 2 (() (Radius) (Height) End Surface areas of a Cylinder (both ends) = 2 (() (Radius2) Volume of a Cylinder = (() (Radius2) (Height) Area of Rectangle = (Length) (Width) Area of Triangle = (Base) (Height) 2 Circumference of Circle = (") (Diameter) or (2) (") (Radius) Chlorine Demand (lbs/day) = lbs of Chlorine Fed/day  [(Chlorine Residual, mg/l) (Flow, MGD) (8.34)] Detention Time (minutes) = Volume of Tank (gallons) Influent Flow (gpm) Discharge = Volume Time Dosage, lbs/day = (mg/L) (8.34) (MGD) Efficiency, % = (Mass In Mass Out) (100%) May substitute weight for mass Mass In Feed Rate, lbs/day = (Plant Capacity, MGD) (Dosage, mg/L) (8.34 lbs/gal) Filter Backwash rate = Flow (gpm) Filter surface area (ft2) Food/Microorganism Ratio = Influent BOD, lbs/day Aeration System MLVSS, lbs Gallons/Capita/Day = Gallons Per Day Population Hardness = (mL of Titrant) (1,000) (for 0.2 N EDTA) mL of Sample Horsepower (hp): theoretical hp = (Flow, gpm) (Total Water Head, ft) 3960 brake hp = theoretical hp pump efficiency Hydraulic Surface Loading Rate (gpd/ft2) = Flow Rate (gpd) Surface Area (ft2) Loading rate (lbs/day) = (Concentration, mg/l) (Flow, MGD) (8.34) Mean Cell Residence Time (MCRT): (lbs of Suspended Solids in Aeration System) (lbs of Suspended Solids Wasted/Day + lbs of Suspended Solids Lost in Effluent/Day Organic Loading Rate = Organic Load, lbs BOD/day Volume in 1000 ft3 Oxygen Uptake = Oxygen Usage (mg/L) Time (min) Population Equivalent = (Flow, MGD) (BOD, mg/L) (8.34 lbs/gal) 0.18 lbs BOD/day/person Reduction in Flow, % = (Original Flow - Reduced Flow) (100%) Original Flow Slope = Drop or Rise Distance Sludge Volume Index = (Settleable Solids, %) (10,000) MLSS, mg/L Solids Applied (liquid), lbs/day = (Flow, MGD) (Concentration, mg/l) (8.34 lbs/gal) Solids Loading, lbs/day/sq ft = Solids Applied, lbs/day Surface Area, sq ft Solids, mg/L = (Dry Solids, grams) (1,000,000) mL of Sample Surface Loading Rate (GPD/ft2) Flow Rate, GPD Surface Area, ft2 Velocity = Flow or Distance Area Time Volatile Solids, % = (Dry Solids Ash Solids) (100%) Dry Solids Volume of Rectangular Tank (ft3) = (Length) (Width) (Height) Volume of Cone (ft3) = (1/3) (.785) (Diameter2) (Height) Volume of Cylinder (ft3) = (.785) (Diameter2) (Height) or (() (Radius2 ) (Height) Waste Milliequivalents = (mL) (Normality) Waste Normality = (Titrant Volume) (Titrant Normality) Note: Volumes are in same units Sample Volume Weir Overflow Rate = Flow (gpm) Weir Length, (ft) Conversion Factors: 1 acre = 43,560 square feet 1 cubic foot = 7.47 Gallons 1 foot = 0.305 meters 1 gallon = 3.79 liters 1 gallon = 8.34 pounds 1 grain per gallon = 17.1mg/L 1 mg/l = 1 ppm1 horsepower = 0.746 kilowatts 1 million gallons per day = 694 gallons per minute 1 pound = 0.454 kilograms 1 pound per square inch = 2.31 feet of water Degrees Celsius = (Degrees Fahrenheit 32) (5/9) Degrees Farenheit = (Degrees Celsius) * 1.8 + 32 1 Ft of water column = 0.43 psi Abbreviations: BOD Biochemical Oxygen Demand ft feet gpd gallons per day gpg grains per gallon gpm gallons per minute lbs pounds mg/L milligrams per Liter MGD million gallons per day mL milliliter MLSS mixed liquor suspended solids MLVSS mixed liquor volatile suspended solids ppm parts per million                                  Unit Cancellation Steps Step 1: List unknown data as a question mark (?) including units, followed by an equals sign (=). Sept 2: Place data with same numerator unit to the right of the equal sign followed by a multiplication sign. Step 3: To cancel unwanted denominator unit, next place data with same numerator unit. Step 4: Continue to place data into equation to systematically cancel all unwanted units until only the unknown units remain. Step 5: Do the math (multiply all numerator values, multiply all denominator values; then divide numerator by the denominator.)  Example: ? lbs = 1 x 1 g x 3785 mL = 8.34 lbs gal 454 g mL 1 gal Helpful Hints: Numerator Denominator Vertical format: 5 gal = 5 gal 1 1 g = 1000 mg is written: 1 g OR 1000 mg 1000 mg 1 g per means divided by: Example: 5 gpm = 5 gal min Inverting: 5 gal = 1 min min 5 gal UNITS OF WEIGHTEnglishMetric pound - lb gram - g milligram - mg kilogram - kgCONVERSIONSMetric/MetricMetric/English1000 mg = 1 g or 1000 mg/g 1000 gm = 1 kg or 1000 g/kg 1 lb = 454 g or 454 g/lb 1 kg = 2.2 lbs or 2.2 lbs/kg UNITS OF VOLUMEEnglishMetric gallon - gal million gallon - Mgal cubic feet - cu ft liter - L milliliter - mLCONVERSIONS Metric/MetricMetric/EnglishEnglish/English 11000 mL = 1 liter or 1000 mL/L 1 gal = 3.785 L or 3.785 L/gal 1 gal = 3785 mL or 3785 mL/gal7.48 gal = 1 cu ft or 7.48 gal/cu ft UNITS OF TIMEday - day hour - hrminute - min second - sec CONVERSIONS1 day = 24 hr or 24 hr/day 1 hr = 60 min or 60 min/hr1 min = 60 sec or 60 sec/min 1 day = 1440 min or 1440 min/day UNITS OF DENSITYEnglishMetric lbs/gal lbs/cu ftkg/L g/mL THE DENSITY OF WATER EnglishMetric/Metric 8.34 lbs/gal 62.4 lbs/cu ft1 kg/L 1 g/mL UNITS OF CONCENTRATIONEnglishMetriclbs/galmg/LCONVERSION1 lb/gal = 120,000 mg/L UNITS OF FLOW English Metric gallons per minute - gal/min - GPM gallons per day - gal/day - GPD million gallons per day - Mgal/day - MGD cubic feet per second - cu ft/sec - CFS milliliters per minute - mL/minCONVERSIONS English/EnglishEnglish/Metric 1 MGD = 694 GPM or 694 GPM/MGD 1 MGD = 1.55 CFS or 1.55 CFS/MGD1 gal/day = 2.63 mL/min     A- PAGE 3 A- PAGE 1 Commonwealth of Pennsylvania Bureau of Water Supply and Wastewater Management Chemical Product Product Feed (lbs/day) C o n v e r s i o n s Plant Flow (gal/min) (x) 3.785 (() Plant Flow (L/min) Dry Chemical Dosage (lbs/gal) Dry Chemical Dosage (mg/L) (x) 315 (() Chemical Product Product Feed (mg/min) (x) 120,000 (() gal (Plant) min lbs (Dry) gal (Plant) L (Plant) min mg (Dry) L (Plant) mg (Dry) min lbs (Dry) day ( ( ( ( ( ( ( ( ( ( ( ( CHEMICAL FEED CALCULATION DIAGRAM DRY FEED Procedure: Fill in known data; put a question mark (?) for the value of the unknown data; convert all data to the units on the side where the (?) was placed and fill in the values; use unit cancellation to solve for the unknown. 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