FORMULAS - MANITOBA CERTIFICATION EXAMINATIONS (Revised January 2006) AREAS CIRCUMFERENCE VOLUMES

Transcription

1 FORMULS - MNITOB CERTIFICTION EXMINTIONS (Revised January 006) RES Triangle rea (m ) ½ B x H B length of base (m) H height of triangle (m) Circle πd.14xdxd rea (m ) π R 4 4 Rectangle rea (m ) L x W L length of rectangle (m) W width of rectangle (m) R radius (m) D diameter (m) Circle Circumference (m) πr or πd or C.14 x D Rectangular tank Volume (m ) area of base x H or V L x W x H CIRCUMFERENCE VOLUMES R radius (m) C circumference(m) D diameter (m) L W H length of rectangle (m) width of rectangle (m) height of rectangle (m) Cylindrical tank Volume (m ) area of base x H πd or V x H or V πr x H 4 D diameter of base (m) H height of cylinder (m) R radius of base (m) Cone Volume (m ) 1/ area of base x H or V 1/π R x H D 1 or V 1/ π x H π D x H 4 1 R radius of base(m) D diameter of base (m) H height of cone from base to apex (m) Prism Volume (m ) area of base of prism x H or V x H Sphere (ball) 4πR Volume (m ) 4 D 1 or V π π D 8 6 area of base of prism (m ) H height or depth of prism (m) R radius of sphere (m) D diameter of sphere (m) Lagoon Volume (m WxL + (W SH)x(L SH) ) x H W width of lagoon (m) L length of lagoon (m) S slope (ratio of horizontal to vertical distances on the interior sides of lagoon). Example: :1, slope is taken as. H height of liquid or depth of liquid in lagoon. (m)

2 Em Ep Hp kpa mg g kg sq TIME 1 day 4 hrs [or] 1440 minutes [or] 86,400 seconds TEMPERTURE 9 Fahrenheit 5 ( C ) + F Celsius ( F F) 5 9 motor inefficiency pump efficiency horsepower kilopascal milligram grams kilogram square Metric Units 10 millimetres (mm) 1 centimetre (cm) millimetres(mm) 1 metre (m) 100 centimetres (cm) 1 metre (m) 1 dekametre (dam) 10 metres (m) metres (m) 1 kilometre (km) sq. m (m ) 1 hectare (ha) 1 cu. meter (m) 1,000,000 cu. cm (cm ) cu. cm (cm ) 1 Litre (L) BBREVITIONS m m ml L ML MLD min/d METRIC CONVERSION FCTORS metre cubic metre millilitre litre megalitre megalitre (1,000,000 L) per day minutes per day millilitres (ml) 1 Litre (L) liters 1 cu. m (m ) liters (L) 1 Megalitre (ML) 1 milligram (mg) micrograms (ug) 1 gram (g) milligrams (mg) 1 kilogram (kg) grams (g) kilograms (kg) 1 tonne (t) 1 kilowatt (kw) watts 1 litre (L) of water weighs grams 1 kg 1 litre (L) of water weighs milligrams 1kg 1 cu. m (m ) of water weighs kg 1 metre of hydraulic head (m) 9.81 kpa MESURES OF CONCENTRTION 1 mg/l 1 ppm (1 part per million) 1 mg/l 1 gram / m 1 ppm 1 part /1 million parts 1% mg/l Volume Detention Time (seconds) FlowRate Velocity (m/s) DETENTION TIME / RETENTION TIME V V Volume (m ) Flow Rate (m /s) VELOCITY Distance L L Length (m) Time T T Time (s) v Velocity (m/s) Velocity (m/s) Flow Rate rea Flow Rate (m /s) Cross Sectional rea (m ) v Velocity (m/s)

3 PIPE Flow Rate (m /s) (m /s) rea x Velocity x v FLOW RTE Flow Rate (m /s) Cross Sectional rea (m D ) π 4 v Velocity (m/s) CHNNEL Flow Rate (m /s) rea x Velocity (m /s) (Width x Depth) x v (W x d ) x v Clarifier Rise Rate (m /m xd) Weir Overflow Rate (m /dxm) Flow Rate (m /s) Cross Sectional rea (m ) W x d W Width of channel (m) d Depth of liquid in channel (m) v Velocity (m/s) OVERFLOW RTE / SURFCE LODING RTE WL Force (Newtons) (Volume x Density) x (ccel. of Gravity) (V x ρ ) x g Uplift Force (kilo-newtons) (rea x Height) x 9.81 kpa/m ( x H) x P I E E I R Water Power (kw) x H 615 Water Horsepower (Hp) x H 4570 (This equation assumes 100% motor and pump efficiency) FORCE POWER CLCULTIONS I E R Clarifier Surface rea (m ) Flow Rate (m /d) WL weir length (m) V Volume (m ) ρ density (kg/ m ) g cceleration of Gravity 9.81 m/s cross sectional area (m ) H Liquid Depth (m) P Power (watts) E Voltage (volts) I Current (amps) R Resistance (ohms) flow rate (L/min) H head of water (m) 1 Hp (electric) kw 1watt1Joule/sec. 1 kw- hr.6mj (Mega Joule) Pump Power (W) Force Height F h Time T Brake Power (kw) x H Water Power 615Ep Pump Effic( Ep) Motor Power Brake Power WaterPower Motor Effic.(Em) (Ep) x (Em) Overall Efficiency (%) Output x 100 Input F Force (N) h height of lift (m) T Time (s) Ep pump efficiency This equation does not assume 100% motor or pump efficiency. pump efficiency (Ep) of 100% 1 motor efficiency (Em) of 100% 1 EFFICIENCY Ci concentration in the influent Ce - concentration in the effluent Treatment (Ci - Ce) x 100 Efficiency (%) Ci

4 Volume 1 x Conc. 1 Volume x Conc. V 1 x C 1 V x C CD (mg/l) CD (mg/l) C ( kg) V ( m ) C ( kg / d) ( m / d) Chemical Feed Rate (ml/min) 4 CHEMICL/ VOLUME REUIREMENT V 1 Volume 1 (L) V Volume (L) CHEMICL REUIREMENT CD x c x d x 1440 Chemical Required (kg) Pure Chemical % Purity Note: Pure Chemical expressed in kilograms % Purity expressed as a decimal Flow Loading (m /day x cap) BOD Loading (kgbod/d x cap) Yield (kg/m x h) (C/100) x CHEMICL FEEDING CHLORINTION C 1 Concentration 1 (mg/l) C Concentration (mg/l) CD Dosage (mg/l) C Mass of Chemical dded (kg or kg/d) V Volume (m ) Flow Rate (m /d) CD Dosage (mg/l) Flow Rate (m /d) c % active chemical expressed as a decimal d relative density of chemical feed (g/cm ) Total Chlorine Dosage Chlorine Demand + Chlorine Residual Chlorine Residual Combined Chlorine + Free Chlorine UNIT LODING population C population Filter Loading Rate (L/m xs) x Note: If flow rate is in L/s then the equation is: Filter Loading Rate (L/m xs) Method 1. Filter Backwash Rate (L/m x s) Method. Filter Backwash Rate R (m/h) T FILTER YIELD (VCUUM) FILTER LODING RTE FILTER BCKWSH RTE Flow Rate (m /d) C Concentration of BOD in the influent (mg/l) Note: Population and Capita (cap) are similar C concentration of solids in sludge feed (%) sludge feed rate to filter (L/h) surface area of filter (m ) (This formula assumes there are no solids in the filtrate and the specific gravity of sludge is equal to water.) flow rate (m /d) surface area of the filter (m ) rate of upflow of backwash water (L/s) surface area of filter (m ) R water rise (m) T time (h)

5 5 SOLIDS LODING Solids loading refers to the daily mass of suspended solids entering the clarifier or sedimentation basin. xc Solids Loading (kg /d) Flow of settled wastewater (m /d) C Solids Concentration of SS in settled sewage (mg/l) Organic Loading, F (BOD 5 kg/d) ORGNIC LODING Organic loading of an aeration tank refers to the daily mass of BOD entering the aeration tank volume. xc Volumetric Organic Loading (kg BOD/m x d) xc Vx Note:Volumetric Organic Loading applies to Trickling filters. SVI volume of settled sludge x MLSS SVI volume of settled sludge (%) mixed liquor suspended solids (%) F ratio M SDI 100 SVI BOD 5 kg MLVSS kg SLUDGE VOLUME INDEX SLUDGE DENSITY INDEX F/M RTIO flow of settled sewage to aeration tank (m /d) C concentration of BOD in settled sewage (mg/l) V volume of aeration tank (m ) F organic loading (BOD 5 kg/d) MLSS mixed liquor suspended solids (mg/l) volume of settled sludge expressed in ml SVI sludge volume index F BOD 5 kg/d x C where flow of settled wastewater (m /d) C BOD 5 concentration of settled sewage (mg/l) x B V x VSS M MLVSS kg mixed liquor volatile suspended solids MLVSS is assumed to be equal to the mass of microorganisms in the aeration tank V x VSS where V volume of aeration tank (m ) VSS mixed liquor volatile suspended solids (mg/l)

6 6 RECYCLE RTE R E x MLSS RSSS-MLSS R return or recycle sludge flow rate (m /d) E effluent flow rate (m /d) (may be assumed to equal influent flow rate) MLSS mixed liquor suspended solids (mg/l) RSSS return or recycle sludge suspended solids (mg/l) SOLIDS RETENTION TIME (or Mean Cell Residence Time) Solids Retention Time (SRT) or Mean Cell Retention Time (MCRT) is the length of time that biological solids are held within a process. SRT and MCRT is stated in days. MCRT (V x MLSS) + (V C x MLSS) ( W x WSSS) + ( E x FESS) or in simplified form by omitting sludge in clarifier SRT V x MLSS ( W x WSSS) + ( E x FESS) Waste Sludge Rate Required (M 1 - M ) x V R Oxygen Uptake Rate or Specific Uptake Rate (SUR) Oxygen Uptake Rate (mgo /Lx h) (DO 1 - DO ) x 60 T Specific Uptake Rate Loading (kg/m x d) SUR (mgo /h g MLVSS) Oxygen Uptake Rate x MLVSS (mg/l) C x P x V x 10 Reduction (%) (P I - P D ) x 100 P I - (P I x P D ) SLUDGE WSTING RESPIRTION RTES SRT solids retention time in days V volume of aeration tank(s) (m ) V C volume of final settling tank (m ) W daily waste sludge flow (m /d) E effluent (or influent) flow (m /d) MLSS mixed liquor suspended solids (mg/l) WSSS waste sludge suspended solids (mg/l) FESS final effluent suspended solids (mg/l) M 1 present MLSS (mg/l) M desired MLSS (mg/l) V volume of aeration tank (m ) R suspended solids in sludge recycle or return (mg/l) DO 1 dissolved oxygen in mixed liquor sample at start of test (mg/l) DO dissolved oxygen in mixed liquor sample at end of test (mg/l) T duration of the test (min.) Oxygen Uptake Rate rate of oxygen utilization (mgo /hxg) DIGESTER LODING (volatile solids) MLVSS mixed liquor volatile suspended solids (mg/l) C concentration of solids in sludge feed (%) P concentration of volatile solids in sludge feed (%) volume of sludge feed (m /d) V volume of digester (m ) REDUCTION OF VOLTILE SOLIDS IN DIGESTER P D volatile matter in digested sludge (%) P I volatile matter in feed (raw) sludge (%)

7 IMPERIL - METRIC CONVERSION FCTORS Imperial Units 1 mile 580 ft 1 mile 1760 yds. 1 Imperial gallon of water 10 lbs. 1 cubic foot of water 6.4 lbs. 1 cubic foot of water 6.4 Imperial gallons 1 Imperial gallon 77 cubic inches 1 million gallons per day Imperial 700 gallons per minute 1 million gallons per day Imperial 1.85 cubic feet per second 1 cubic foot per second 75 Imperial gallons per minute Length Equivalents 1 kilometre 0.61 mile 1 metre.8 feet 1 metre 9.7 inches 1 centimetre 0.97 inch 1 millimetre inch rea Equivalents 1 km 47 acres 1 hectare.47 acres 1 m ft 1 cm in. 1 ft 99 cm Volume Equivalents 1 kilolitre 0. gallons 1 L 0.0 gallons 1 L quarts 1 m 5. ft 1 cm in 1 m 1.08 yd 1 MG 4.54 ML Weight Equivalents 1 metric tonne 1.10 tons 1 kg.05 pounds 1 gm 0.05 ounces Velocity Equivalents 1 ft/sec 0.05 m/sec 1 ft/sec 05 mm/sec 1 mile/hr 0.45 m/sec Pressure and Head Equivalents 7 1 mile 1.61 kilometre 1 foot 0.05 metre 1 inch metre 1 foot 0.5 centimetres 1 inch.54 cm or 5.4 mm 1 mile.56 km 1 acre ha 1 ft 0.09 m 1 in 6.45 cm 1 gallon 4.54 L 1 quart 1.15 L 1 ft 8.17 L 1 ft 0.08 m 1 in cm 1 yd m 1 ML 0. MG 1 ton tonne 1 pound 45.6 gm 1 ounce 8.5 gm 1 pound per inch [psi] 6.9 kpa [or].1 ft [or]0.704 m 1 kpa psi [or]0.8 ft [or]0.1 m 1 foot of hydraulic head [ft] 0.4 psi [or].05 kpa [or]0.05 m 1 metre of hydraulic head [m] 1.4 psi [or]9.81 kpa Flow Rate Equivalents 1 ft /sec 8. L/s 1 ft /sec 0.08 m /sec 1 gpm L/s 1 MGD 4.54 MLD 1 gpm/ft 0.81 mm/s 1 ft /sec 75 gpm 1 m/sec.8 ft/sec 1 km/hr 0.6 miles/hr 1 mile/hr 1.61 km/hr 1 m /sec 11 gpm 1 m /sec 5. ft /sec 1 L/s 1. gpm 1 MLD 0.0 MGD 1 mm/s 1. gpm/ft