1. Mass, Lbs/Day = (Vol, MGD) x ( Conc., mg/l) x ( 8.

34 lbs/gal)
(BOD)/(SS), Lbs/Day = (Vol, MGD) x ( SS, mg/l) x ( 8.34 lbs/gal)
2. Dosage, mg/l = ( Feed, lbs/day )
( Vol, MGD ) X ( 8.34 lbs/gal )
3. Rectangular Tank = (Length, ft) x (Width, ft) x (Height, ft)
Volume, cu. ft.
i) Vol, Gals = Multiply the above by the factor 7.48 gals/cu.ft.
4. Right Cylinder = (0.785) x (D
2
,ft) x (Height or Depth,ft)
Volume, cu. ft.
i) Vol, Gals = Multiply the above by the factor 7.48 gals/cu.ft.
5. Conical Base = (0.785) x (D
2
,ft) x (Height or Depth,ft)
Volume, Cu. ft. ( 3 )
i) Vol, Gals = Multiply the above by the factor 7.48 gals/cu.ft.
SUMMARY OF KEY WASTEWATER
MATH FORMULAS
General:
6. Removal, Percent = ( In - Out ) x 100
In
7. Decimal Fraction = ( Percent )
100
8. Population = ( Population ) x BOD or TSS, lbs/day/capita
Equivalent, BOD/TSS
Lbs. Loading
a) Population = (Vol, MGD) x ( Conc., mg/l) x 8.34 lbs/gal)
Equivalent, No. ( BOD or TSS, 0.17 lbs/day/capita )
of People
b) Population = (Population) x (BOD or TSS, lbs/day per capita)
Equivalent - ( Flow, MGD ) x ( 8.34 lbs/day )
BOD, mg/l
9. Daily Hydraulic = ( Population, No. of People ) x ( 100 GPCD )
Loading, GPD
a) Population, = ( Daily Hydraulic Loading, GPD )
No. of People ( 100 GPCD )
10. GPD = ( 2nd Meter Reading - 1st Meter Reading)
( Elapsed Time, Days )
11. Supply, Hrs = ( Storage Volume, Gallons )
(Full or Tank Dry) ( Flow In, GPM - Flow Out, GPM ) x 60 Min/Hr.
12. Percent (%) = ( Larger Amount ) - 1.0 x 100
of Increase ( Smaller Amount )
1. Velocity
Q,cfs = ( Area,sq.ft. ) x ( Velocity,fps ), or
( GPM ) = ( 0.785 ) x ( D,ft )
2
x ( Distance, ft )
( 448.8 GPM/cfs ) or . . . ( Base x Height, ft.) ( Time, sec. )
Q = ( A ) x ( V )
A = ( Q )
( V )
V = ( Q )
( A )
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Rectangular Horizontal-Flow Grit Chambers:
IMPORTANT CONVERSIONS: 1.55 CFS/MGD 448.8 gpm / CFS
2. 1.0 FPS = 3.0 sq. ft. of area for
every 3.0 cfs of flow.
3. Velocity = At 1.25 fps, or greater, bottom
scour begins to occur.
4. Flow Conversions:
Flow, GPM = ( Q, cfs ) X ( 448.8 GPM/cfs )
Q, cfs = ( Flow, GPM )
( 448.8 GPM/cfs )
5. Cubic Yards = ( Cubic Feet )
( 27 cubic ft./Cu. Yd )
1. Hydraulics:
Head, ft. = (2.31 ft/psi) x PSI, or
PSI = (0.433 PSI/Ft) x ( Head, ft. )
2. Pumping: Rates:
Volume, Gals = GPM x Time, minutes
Fill Rate, GPM = ( Tank Volume, Gals )
( Time, minutes )
Fill Time, Minutes = ( Tank Volume, Gals )
( Fill Rate, GPM )
3. Pump Size:
Water Hp. = (GPM) x ( Head,ft)
( 3,960 )
Brake Hp. = ( GPM ) x ( Head,ft )
( 3,960 x ( %, Effic. )
%, Effic. = ( GPM ) x ( Head,ft ) x 100
( 3,960 x ( Brake Hp. )
GPM = ( Brake Hp. ) x (3,960) x ( %, Efffic)
( Head, ft. )
Head, ft. = ( Brake Hp. ) x (3,960 ) x ( %, Efffic)
( GPM )
4. Vol, GPM = (0.785) x ( Bore,ft )
2
x ( Stroke, ft. ) x 7.48 x
S/min x %, Effic.
Gals = (0.785) x ( Bore,ft )
2
x ( Stroke, ft. ) x 7.48 gals/cu. ft. x
( Strokes/minute ) x ( %, Effic. ) x ( Pumping Minute )
5. Cost/day = ( Brake Hp.) x (0.746 Kw/Hp.) x Operating Time, Hrs.
x ( /Kw- Hr. )
100
6. Speed, RPM (N
2
) = ( N
1
x D
1
)
( D
2
)
7. Drawdown, ft. = Pumping Level, ft. - Static Level, ft.
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Pumps and Pumping:
Strength of Solutions:
1. Chemical Feed Pumps:
GPD = ( Required Feed, Lbs/Day ) = (MGD) x mg/L x 8.34
( Dry lbs/Gal ) ( Dry lbs/Gal )
2. Chemical Feed Rate:
GPD = ( Feed, ml/minute x 1,440 min/day )
( 1,000 ml/L x 3.785 L/gallon )
ml/min = ( GPD x 1,000 ml/L x 3.785 L/Gallon )
( 1,440 min/day )
ml/min = ( GPM x 3,785 ml/gal )
3. Lbs/gallon = ( % Solution ) x 8.34 lbs/gallon x (Specific Gravity, if needed)
( 100 )
4. Lbs Chemical = Specific Gravity x 8.34 lbs/gallons x Gallons of Solution
5. Specific Gravity = ( 8.34 lbs/gallon + Chemical Wt., Lbs/gallon )
( 8.34 lbs/gallon )
6. Specific Gravity, = ( S.G. x 8.34 lbs/gal ) - ( 8.34 lbs/gal )
Lbs/gallon
7. % Percent of = ( Dry Chemical, Lbs ) x 100
Chemical in ( Dry Wt. Chemical, Lbs ) + ( Water, Lbs )
Solution from Dry Stock
8. Mixture Gals = ( Gals of Dilute Solution x Lower Concentration, % )
for Percentage (%) ( Higher Concentration Solution, % )
9. Two-Normal Equations:
a) C
1
V
1
= C
2
V
2
b) Q
1
= Q
2

V
1
V
2

10. Three Normal equations:
a) ( Q
1
C
1
) + ( Q
2
C
2
) = ( Q
3
C
3
)
b) Q
1
= Q
2
= Q
3

V
1
V
2
V
3
Hydraulic Cross- Check Formulas
1. Detention = (Volume, gals) x ( 24 Hrs./day )
Time, Hrs. ( Total 24 Hr. Flow, gals/day )
Design Data: 1 - 2.5 Hours; Average 1.5 hours.
2. Total Flow, GPD = (Volume, gals) x ( 24 Hrs./day )
( Detention Time, Hrs. )
3. Surface Loading = ( Total Flow, GPD )
Rate, GPD/sq ft. ( Surface Area, sq.ft.)
Design Data: 800 - 1,200 GPD/Sq. Ft.
4. Weir Overflow = ( Flow, GPD )
Rate, GPD/Ft ( Weir Length, ft )
Weir Length, ft = Circumference, ft. = B x Diameter, ft
Design Data: 10,000 - 20,000 GPD/LF; Average 15,000 GPD/L.F.
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Sedimentation Tanks and Clarifiers:
5. Solids Loading = ( Solids into Clarifier, lbs/day )
Rate, lbs/day/sq. ft. ( Surface Area, sq. ft. )
Design Rate: Primary Clarifiers: Not a design consideration.
2nd. Clarifiers: 12 - 30 lbs/day/sq. ft.
6. Sludge Solids, lbs = (Flow, Gals) x ( 8.34 lbs/gal ) x ( Sludge, % )
or GPD 100
7. Raw Sludge = ( Settleable Solids, ml/L ) x ( Plant Flow, GPM )
Pumping, gpm ( 1,000 mls/L )
1. Organic Loading = ( BOD In, lbs/day )
Rate, Lbs/day/acre ( Pond Area, acres )
Design Data: 25 - 50 Lbs/day of BOD
2. Pond Area, Acres = ( BOD In, Lbs/day )
( Organic Loading Rate, lbs/day/acre )
Design Data: 20 - 50 Acres ( Range )
3. Detention Time, = ( Volume, Acre-ft )
Days ( Flow, Acre-ft/Day )
Design Data: 60 - 180 Days
4. Surface Area, Acres = (Flow, MGD) x (BOD Conc. mg/l) x (8.34 lbs/gal)
(BOD Loading) ( Loading Rate, Lbs/Acre/Day )
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Ponds and Lagoons:
5. Hydraulic Loading = ( Pond Depth, Inches )
Rate, Inches/day ( Detention Time, Days )
6. Pond Depth, Ft. = ( Daily Flow Into The Pond, Cu.ft.
( Total Surface Area of the Pond, Sq.ft. )
7. Volume, = ( Area, acres ) x ( Depth, ft. )
Acre-Ft
8. Flow Rate, = ( Daily Flow into Pond, GPD )
Acre-Ft/Day ( 7.48 Gal/cu.ft.) x ( 43,560 cu.ft/acre-ft.)
Evaporation / Percolation Rates
9. Inches/Day = ( Volume lost, Gallons/Day )
( No. of Acres x 325,828 gals/Ac-ft ) x ( 12"/ft )
10. Vol, Gals = ( Acres, sq.ft. ) x ( Evap. Rate, inches/day ) x 7.48 gals/cf
Lost/Day ( 12" )
1. Organic Loading = ( BOD, Lbs/Day )
Rate, Lbs/Day/1,000 cu.ft. ( Media Volume, 1,000's of cu.ft. )
Same as . . . = ( MGD ) x ( mg/L BOD ) x 8.34 lbs/gal)
( Media Volume, 1,000's of cu.ft. )
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Trickling Filters:
2. Hydraulic Loading = ( GPM )
Rate, GPM/sq.ft. ( Surface Area, sq. ft. )
3. Hydraulic Loading = ( GPM x 1,440 min/day )
Rate, GPD/Sq. Ft. ( Surface Area, sq. ft. )
a) Hydraulic Loading = ( GPM )
Rate, GPM/sq.ft. ( Surface Area, sq. ft. )
4. Recirculation = ( Recirculation Flow, Q
1
)
Ratio ( Average Influent Flow, Q
2
)
5. Total Flow = ( Recirculation Flow, Q
1
) + ( Average Influent Flow, Q
2
)
1. Organic BOD = ( Soluble BOD Applied, lbs BOD/Day )
Loading Rate, ( Media Surface Area/1,000 sq. ft. )
Lbs/Day/1,000 sq.ft.
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Rotating Biological Contactors:
2. Hydraulic Loading = ( GPM )
Rate, GPM/sq.ft. ( Surface Area, sq. ft. )
3. Hydraulic Loading = (Total Flow, GPD ) Including Recirculation
Rate, GPD/sq.ft. ( Surface Area, sq.ft. )
4. BOD Applied, = ( Flow, MGD ) x (Soluble BOD, mg/l) x (8.34 lbs/gal)
Lbs/Day
5. Soluble BOD, mg/l = Total BOD, mg/l - Suspended BOD, mg/l, or
Soluble BOD, mg/l = ( Total BOD, mg/l) - ( K x Suspended Solids, mg/l )
6. Suspended BOD, = K x Suspended Solids, mg/l
mg/l ( K = 0.5 - 0.7 for most domestic wastewaters. )
1. F/M = ( BOD, lbs/day )
( MLVSS, lbs )
2. BOD = ( BOD, lbs/day )
Loading Rate, ( Ditch Volume, in 1,000 Cu. ft. )
Lbs/Day/1,000 Cu. Ft.
3. Ditch Detention = ( Ditch Vol, MG ) x 24 Hours/Day )
Time, Hours Flow, MGD
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Oxidation Ditches:
4. Determine Sludge Age:
a) Aeration Solids, = (Vol, MG) x ( MLSS, mg/l ) x ( 8.34 lbs/gal)
lbs.
b) Solids Added, = ((Vol, MG) x ( Inf. SS, mg/l ) x ( 8.34 lbs/gal)
lbs/day
c) Sludge Age, = ( Solids Under Aeration, lbs )
Days Solids Added, lbs/day
5. Calculate Ditch Volume:
a) Average Width, ft. = ( Bottom, ft. ) + ( Depth, ft )
( Slope )
b) Area Determination
i) Area, sq. ft. = Width, ft x Depth, Ft., or
ii Area, sq. ft. = (B,Width
1
, ft. + T,Width
2
, ft.)
( 2 )
c) End Lengths, ft. = ( 2 B ) x Radius, ft.
d) Total Length, ft. = Ends Lengths, ft + ( 2 Lengths, ft.)
e) Volume, cu. ft. = ( Length, ft. ) x ( Area, sq. ft. )
1. F/M RATIO = ( BOD in Primary Effluent, lbs/day )
(Lbs of Mixed liquor VSS in the Aeration Tanks)
2. Mean Cell = (Aeration Tank TSS, lbs + Clarifier TSS, lbs )
Residence Time, (TSS Wasted, lbs/day + Effluent TSS, lbs/day)
Days, (MCRT)
a) TSS Wasted, = (Aer. Tnk TSS,lbs ) + ( Clar.TSS, lbs) - Effluent TSS, Lbs
( MCRT, Days )
b) MCRT, Days = ( Aeration Tank TSS, lbs ) + ( RAS, Lbs )
( TSS Wasted, lbs + Effluent TSS, lbs )
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Activated Sludge:
3. Sludge Volume = (Settled Volume, ml/L ) x ( 1,000 Mg/G )
Index (SVI), ml/g ( MLSS, Mg/L )
MLSS, mg/l = ( 1,000,000 )
SVI
4. Sludge Density = ( 100 )
Index (SDI) SVI
5. Sludge to Waste, = ( Secondary SS, lbs ) - Effluent SS, lbs/day
lbs/day ( MCRT, days )
6. Sludge Age, Days = ( Aeration Tank TSS, lbs ) (Refer to MCRT )
( Primary Clarifer Effluent TSS, lbs/day )
7. Return Sludge = ( Aerator Flow, MGD ) x ( Settable Solids, % ) Ra t e ,
MGD
8. Desired MLSS, = ( Desired MLSS in Aerator, lbs. )
mg/l ( Aerator Vol., MG ) x ( 8.34 lbs/gal )
9. Cu.ft. Air/ = ( Air, Cu.ft. )
Lb. BOD Removed ( Primary Effl., lbs BOD - Secondary Effl., lbs. BOD )
1. Volatile Solids = (Feed Sludge VS, lbs/day )
Loading, ( Digester Volume, cu.ft. )
Lbs VS/Day/Cu.Ft.
2. Detention Time, = ( Digester Volume, Gallons )
Days ( Sludge Feed, GPD )
3. Digester Loading, = ( Lbs of Volatile Matter Added/Day )
Lbs Vol. Matter/ ( Volume of Digester, Cu. Ft. )
Cu. Ft./day
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Anaerobic Digesters:
4. Volatile Solids = ( VS In - VS Out ) x 100
Reduced, % ( VS In ) - ( VS, In x VS, Out )
5. Gas Production, = ( Gas Produced, cu.ft./day )
Cu.Ft./lb VS Reduced ( VS Feed, lbs/day ) x ( Reduction/100 )
6. Gas, Lbs = Volatile Solids, lbs x % Reduction of Volatile Matter
7. VA/Alk Ratio = ( Volatile Acids, mg/L )
( Alkalinity, mg/L )
8. Volatile Matter = Sludge Pumped, gals/day x % Solids x
Destroyed, lbs/day/cu.ft. % Volatile x % Reduction x 8.34 lbs/gal
( Digester Volume, cu. ft. )
9. Pumping, = (Flow, MGD) x (Inf. SS, mg/L - Effl, SS, mg/L) x 100%
Minutes ( Pump, GPM ) x ( Sludge Solids, % x (24 Hours/day )
10. V.S. Destroyed, = (VS Added, lbs/day)( VS Reduction, % )
Lbs/day/cu. ft. ( Disgester Volume, Cu. ft. 100% )
11. Digested Sludge = (VS Added, lbs/day) x (Loading, Lbs Digester Sludge )
in Storage, Lbs. ( Lbs VS / Day )
12. Volatile Solids, Lbs = ( Dry Solids, lbs ) x ( Raw Sludge, % VS )
( 100 % )
1. Filter Flow Rate:
Filtration Rate, = (Filter Area,sq.ft.) x (GPM/sq.ft.)
GPM
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Tertiary Filtration:
2. Filter Backwash:
Backwash, gals = (Filter Area,sq.ft.) x (Backwash Rate, gpm) x (Time, min)
Backwash = ( Backwash Volume, gpm )
Rate, gpm/sq.ft. ( Filter Area, sq.ft. )
Backwash,gals = (Filter Area, sq.ft.) x (Rise/Fall,ft/min)
x (7.48 gals/cu.ft.)
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Land Application:
1. Required Acres = ( Total Volume of sludge, tons/year )
( Limit, tons per acre )
2. Sludge Application, = (Gal. of Sludge) x (8.34 lbs/gal) x (% Solids in Sludge)
Lbs.
Waterways Discharge:
1. Diluted = ( Stream Conc. 1 x Stream, Q
1
) + ( Waste Conc. 2 x Waste, Q
2
)
Concentration, ( Stream Q
1
+ Waste Q
2
)
mg/l or g/l
2. Lbs O
2
/Day = ( Flow, MGD ) x ( Conc. O
2
, mg/l ) x ( 8.34 lbs/gal )
Gas Chlorine Feed, Lbs/day
1. Lbs/Day = (Vol, MGD) x ( Conc., mg/l) x (8.34 lbs/gal)
Dosage, mg/l = ( Lbs/day )
( MGD ) x ( 8.34 lbs/gal )
65% HTH Feed, Lbs/day - Calcium Hypochlorite
2. HTH, lbs/Day = (Vol, MGD) x ( Conc., mg/l) x (8.34 lbs/gal)
0.65
Dosage, mg/l = ( Lbs/day x 0.65 )
( MGD ) x ( 8.34 lbs/gal )
HTH, Lbs = ( Gals, H
2
O x 8.34 lbs/gal x % Solution )
( 0.65 )
5-1/4% Liquid Chlorine - Sodium Hypochlorite
3. Lbs/Gal = ( Solution Percentage ) x 8.34 lbs/gal
100
GPD = (Vol, MGD) x ( Conc., mg/l) x (8.34 lbs/gal)
( Lbs/gal )
Dosage/Demand/Residual
4. Dosage, mg/l = ( Demand, mg/l ) + ( Residual, mg/l )
5. Demand, mg/l = ( Dosage, mg/l ) - ( Residual, mg/l )
6. Residual, mg/l = ( Dosage, mg/l ) - ( Demand, mg/l )
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Effluent Disinfection
7. Sulphur Dioxide:
Lbs/day = (MGD) x (Cl
2
Residual, mg/l) x (8.34 lbs/gal) x 0.90
0.9 mg/l of SO
2
is required to dechlorinate 1.0 mg/l of chlorine.
1. BOD, mg/l = ( Initial DO, mg/l - Final DO, mg/l ) x 300 ml
Sample, ml
Volume
BOD, mg/l = ( Initial DO, mg/l - Final DO, mg/l ) x Dilution
Factor
mg/l = ( ml x 1,000,000 )
( ml of Sample )
mg/l = ml x 1,000 ml/L
SUMMARY OF KEY WASTEWATER
MATH FORMULAS - Continued
Laboratory:
2. TSS (mg/l) = Paper Wt. and Dried Solids(g) - Paper Wt.(g) x 1,000,000
( Milliliters [ml] of Sample )
3. BOD (mg/l) = ( Initial D.O. - Final (D.O. ) x 300
(Unseeded) ( Milliliters [ml] of Sample )
4. mg/l Total Solids = ( Residue, mg ) x 1,000
( ml sample )
5. %, Solids = ( MLSS )
( 10,000 mg/L per 1% )
6. Geometric Mean = ( X
1
! X
2
! X
3
! . . . X
n
)
1/n
7. Temperature:
F = ( C x 1.8 ) + 32
C = ( F - 32 )
( 1.8 )
ABBREVIATIONS
Ac-ft Acre feet M Meter
AFC Actual fluoride content M Mile
C Celsius mg/l Milligram per Liter
CCF Hundred Cubic Feet MGD Million Gals/Day
Cf Cubic feet (ft
3
) ml Milliliter
CFS Cubic Feet Per Second msl Mean Sea Level
F Fahrenheit ppm Parts per Million
Gal Gallon(s) Q Flow, cu. ft/sec.
GPM Gallons Per Minute B Pi (3.141)
GPD Gallons Per Day Sq. ft. Square feet (ft
2
)
GPH Gallons Per Hour Sq. Yd Square Yards (ft
3
)
GPCD Gallons per capita per day SWD Side Wall Depth
H Height g/L Microgram/Liter
Hp Horsepower V Velocity
BHp Brake Horsepower V Volume
Whp Water Horse power
KW-Hrs Kilowatt hours
Lbs Pounds
Lbs/Day Pounds per day
L Liter
END
Updated: December, 2002