Milli- Kilo- Cu Cu Inches metres Miles metres Feet Metres. Cu Cu Sq Sq Yards Metres Feet Metres Feet Metres. Pints Litres Gallons Litres Yards Metres
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1 CONVERSIONS AND CALCULATIONS The figures in the central columns can be read as either the metric or the Canadian measure. Thus 1 inch = 25.4 millimetres; or 1 millimetre = inches. Milli- Kilo- Cu Cu Inches metres Miles metres Feet Metres l Cu Cu Sq Sq Yards Metres Feet Metres Feet Metres Pints Litres Gallons Litres Yards Metres Sq Sq Kilo Yards Metres Ounces Grams Pounds grams Circumference of a Circle = d Area: Volume: Rectangle = L x W Rectangle = L x W x D Triangle = 1/2 B x H Prism = 1/2 B x H x D Circle = r 2 or d 2 or.785(d 2 ) Cylinder = r 2 x D or d 2 x D or 4 4 Sphere = d 2 or 4 r 2 or 4x.785(d 2 ) Cylinder = (0.785) (d 2 ) (h) Cone = r 2 x h 3 Sphere = (d) 3 or 2/3 (0.785) (d 3 ) 6 1 U.S. Gallon = 8.33 lb 1 U.S. Gallon = 3.785L 7.48 U.S. gallon/ft 3 1 U.S. Gallon =.833 ig 1 L = U.S. Gallon 1 ig = 1.2 U.S. Gallon Velocity = flow rate divided by cross sectional area Detention time = volume/flow 1 ig = 10 lb 1 m 3 = 1000 kg 1 psi pressure = 2.31 ft head (water) 1 ft (water) = psi ft water/in. of mercury 1 metre head = 9.8 kpa 1 ft 3 = 6.24 ig 1440 min/day 5280 ft/mile 1760 yd/mile 43,560 sq. ft/acre 10,000 sqm/hectare
2 Horsepower Power (kw)= Flow (L/sec) x Head (m) x 9.8 l hp = kw 1000 = 33,000 ft lb/min Water hp = lb of H 2 O raised per min. x head in ft 33,000 Brake hp = Whp divided by efficiency l Bhp = 746 watts Density (Water) 8.34 lb/u.s. gallon 10 lb/ig 62.4 lb/ft 3 MISC CONVERSIONS temperature: C = 5/9 ( F - 32 F) F = 9/5 ( C) + 32 F mass: 1 grain = gram mass: 1 gram = grains 1 grain/u.s gallon = 17.1 mg/l 1 grain/imperial gallon = mg/l L = 1 kg at + 4 degrees Celsius power: 1 Newton metre (N. m) = ft lb Volume: 1m 3 = ig pressure: 1 kilopascal (Kpa) = psi area: 1 hectare (ha) = 2.47 acres force: 45 Newtons = 1 lb force energy: 1 kilojoule (kj) = BTU flow: 1 igpd x = m 3 /day electricity: Watts = I (amps) x V (volts) V (volts) = I (current) x R (ohms resistance) Backwash rate normally 24 in rise per minute requires 12.5 IGPM/sq. ft or 15 U.S.GPM/sq ft Water Softening Equations Carbonate hardness 1. Ca(HCO 3 ) 2 + Ca(OH) 2 = 2CaCO 3 + 2H 2 O (Lime) 2. Mg(HCO ) + Ca(OH) 2 = CaCO 3 + Mg CO 3 + 2H 2 O 3 2 (Lime) Non Carbonate hardness 3. CaSO 4 + Na 2 CO 3 = CaCO 3 + Na 2 SO 4 (soda ash) 4. MgSO + Ca(OH) 2 + Na 2 CO 3 = CaCO 3 + Mg(OH) 2 + Na 2 SO 4 4 (Lime) CO 2 reaction 5. CO 2 + Ca(OH) 2 = CaCO 3 + H 2 O WATER TREATMENT CALCULATIONS
3 Wastewater Calculations Loading = Flow (m 3 /day) x conc. (mg/l) = kg/day 1000 BOD 5 = DO 1 - DO 2 x 300 ml ml of sample Sludge Volume index = ml settled sludge x 1000 mg/l MLSS Wastewater Treatment Calculations F:M ratio = kg/day BOD: kg/day MLVSS in aeration tank Sludge Age Aeration tank plus Clarifier (days) = MCRT (mean cell residence time) Sludge Age = Suspended Solids in Aerator, lbs Suspended Solids in Primary Effluent, lb/day MLSS mg/l x Aerator Vol,. M.G. x 8.34 lb/u.s. gal Prim.Eff. SS,. mg/l x Flow MGD x 8.34 lb/u.s. gal or MLSS mg/l x Aerator Vol, m 3 Prim.Eff, SS, mg/l x Flow m 3 /day = Days Sludge Age MCRT = (Va)(x)+(Vc)(x) (Qw)(Xu)+(Qe)(xe) Va = Volume of aeration tanks (gal) x = average solids conc. in aeration tanks (mg/l) Vc = volume of final settling tank (gal) Qw = flow rate per day of sludge wasted (gpd) x u = average activated sludge conc. in final settling tank (mg/l) Qe = final effluent flow rate (gpd) xe = final effluent average solids conc.(mg/l) SS Wasting Rate (lb/day): = solids conc. of aeration (lb) - Solids conc. in effluent (lb/day) MCRT (days) SS Wasting Rate (gal/day): = SS wasted (lb.day) x 1,000,000 mg/l RAS SS (mg/l) x 10 lb/gal Activated Sludge SOLVING WASTEWATER TREATMENT PLANT PROBLEMS 1. MLSS, lbs = (Aer Vol, MG)(MLSS, mg/l)(8.34 lbs/u.s. gal) 2a. Settleable Solids % = (Settleable Solids, ml)(100%) 2b. Return Sludge Rate, MGD = (Total Flow, MGD)(Settling volume ml/l, x 100%) 1000 ml/l (settling volume, ml/l) 3a. Solids in Aerator, lbs = (Aerator Vol, MG)(MLSS, mg/l)(8.34 lbs/u.s. gal) 3b. Solids Added, lbs/day = (Flow, MGD)(PE SS, mg/l)(8.34 lbs/u.s. gal) 3c. Sludge Age, days = Suspended Solids in Aerators, lbs Solids added by PE, lbs/day 4a. Desired MLSS, lbs = (Sludge Age, days)(solids Added, lbs/day)
4 4b. Desired MLSS, mg/l = Desired MLSS, lbs (Aerator Vol, MG)(8.34 lb/u.s. gal) 5a. Change in WAS Pumping, MGD = (Actual MLSS, lbs - Desired MLSS, lbs)/day (Waste Sludge Conc, mg/l)(8.34 lbs/u.s. gal) 5b New WAS Pumping GPM = Current WAS + Change in WAS Pumping, GPM Pumping, GPM 6a. Aerator Loading, lbs COD/day = (Flow, MGD) (PE COD, mg/l) (8.34 lbs/u.s. gal) 6b. MLVSS, lbs = Aerator Loading, lbs COD/day Loading Factor, lbs COD/day/lb MLVSS 6c. MLVSS, mg/l = MLVSS, lbs (Aerator Vol, MG)(8.34 lbs/u.s. gal) 6d. Food/Microorganisms = Aerator Loading, lbs COD/day (Aerator Vol, MG) (MLVSS, mg/l) (8.34 lbs/u.s. gal) 7. MCRT, days = Suspended Solids in Aeration System, lbs SS Wasted, lbs/day, + SS Lost, lbs/day 8a. WAS, lbs/day = SS in Aeration System, lbs - SS Lost, lbs/day MCRT, days 8b. WAS Pumping, MGD = WAS, lbs/day (WAS SS, mg/l)(8.34 lbs/u.s. gal) SLUDGE DIGESTION 9. Seed Sludge, gal = Digester Volume, gal) (Seed Sludge, %) 100% 10a.Volatile Solids Pumped lbs/day = (Raw Sludge, GPD) (Raw SI Sol, %) (Volatile, %) (8.34 UG gal) (100%) (100%) 10b. Seed Sludge, lbs Volatile Solids = Volatile Solids Pumped, lbs VS/day Loading Factor, lbs VS/day/lb VS in Digester 10c. Seed Sludge, gallons = Volatile Solids Pumped, lbs VS/day (Seed Sludge, lbs/gal)(solids, %)( VS, %) 100% 100% 11. Lime Req'd lbs = (Sludge volume MG)(Volatile Acids, mg/l)(8.34 lbs/u.s. gal) 12. Piston Pump Vol., gal/stroke = (0.785)(Diameter, ft) 2 (Distance, ft/stroke)(7.5 U.S. gal/cu ft) 13a. Dry Solids, lbs = (Raw Sludge, gal) (Raw Sludge %) (8.34 lbs/u.s. gal) 100% 13b. Volatile Solids, lbs = (Dry Solids, lbs) (Raw Sludge, % VS) 100% 14. Reduction of Volatile Solids, % = (In - Out)(100%) In - (In x Out) 15. Digester Loading, lbs VS/day/cu ft = Volatile Solids Added, lbs/day
5 Digester Volume, cu ft 16. Digested Sludge in Storage, lbs = (VS Added, lbs/day) x (Loading, lbs Dig. SI) lbs VS/day 17. VS Destroyed, lbs/day/cu ft = (VS Added, lbs/day) (VS Reduction, %) (Digester Volume, cu ft) (100%) 18. Gas Production, cu ft/lb VS = Gas Produced, cu ft/day VS Destroyed, lbs/day 19. Solids Balance Water Change, lbs = EFFLUENT DISPOSAL (Water In, lbs) - (Water Out, lbs) - ( Supernatant Out, lbs) 20. BOD Load, lbs BOD/day = (Flow, MGD)(BOD, mg/l)(8.34 lbs/u.s. gal) 21. Average BOD, mg/l = Sum of Measurements, mg/l Number of Measurements MAINTENANCE 22. Pump Capacity, GPM = Volume Pumped Pumping Time, minutes 23a. Velocity, ft/sec = Distance, ft Time, sec. 23b. Flow, cu ft/sec = (Area, sq ft)(velocity, ft/sec) LABORATORY 24. Temperature, o F = (Temperature, o C)(1.8) + 32 o 25. Sludge pumped, GPD = (Sludge Removed, ml/l)(1000 mg/ml)(flow, MGD) 26a. Total Susp. Sol, mg/l = (Dry Weight, mg)(1000 ml/l) 26b. Volatile Susp. Sol, mg/l = (Volatile Weight, mg)(1000 mg/l) 26c. Volatile SS, % = (Volatile SS, mg/l)(100%) Total SS, mg/l 26d. Fixed Susp Solids, mg/l = (Ash Weight, mg)(1000 ml/l) 26e. Fixed SS, % = (Fixed SS, mg/l)(100%) Total SS, mg/l 27. Removal, % = (In - Out)(100%) In 28. Suspended Solids Removed, lbs/day = 29. SVI = (Set Sol, %)(10,000) (Flow MGD)(SS Removed, mg/l)(8.34 lbs/u.s. gal)
6 MLSS, mg/l 30. CO 2,% = (Total Volume, ml - Gas Remaining, ml)(100%) Total Volume ml 31. DO Saturation, % = (DO of Sample, mg/l)(100%) DO at Saturation, mg/l 32. BOD Sample Size, ml = 1200 Estimated BOD, mg/l 33. BOD5, mg/l = [Initial DO of Diluted Sample, mg/l - DO of Sample After 5 days, mg/l] [BOD Bottle Vol, ml Sample Vol, ml DATA ANALYSIS 34a. Mean = Sum of All Measurements Number of Measurements 34b. Median = Middle measurement 34c. Mode = Measurement that occurs most frequently 34d. Range = Largest Measurement - Smallest Measurement
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