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Division of Drinking and Ground Waters
APPLIED WASTEWATER MATH FORMULA SHEET
AND CONVERSION FACTORS
12 in = 1 ft 27 cu ft = 1 cu yd 1,000 mg = 1 gm 60 sec = 1 min
3 ft = 1yd 7.48 gal = 1 cu ft 1,000 gm = 1 kg 60 min = 1 hour
5,280 ft = 1 mi 8.34 lbs = 1 gal water 1,000 ml = 1 liter 1,440 min = 1 day
144 sq in = 1ft
2
62.4 lbs = 1 ft
3
water 2.31 ft water = 1 psi 10,000 mg/L = 1%
43,560 ft
2
= 1 acre 746 watts = 1hp 0.433 psi = 1 ft water 454 gm = 1 lb
L = Length B = Base π = 3.14 W = Width H = Height R = Radius
Q = Flow Rate A = Area V = Volume v = velocity SG = Specific Gravity
Chlorine Demand (mg/L) = dosage (mg/L) – residual (mg/L)
AREA
Rectangle: A = L x W Triangle: A = ½ B x H Circle: Area = πR
2
VOLUME
Cylinder: V = πR
2
H Rectangle: V = L x W x H Cone: V = 1/3πR
2
H
VELOCITIES and FLOW RATES
1. Velocity = distance
time
2. Q = v x A
DETENTION TIME
Detention Time = V
Q
PARTS PER MILLION / POUNDS
lbs = 8.34 lbs / gal x mg/L x MG x SG
SEDIMENTATION AND LOADINGS
1. Weir overflow rate = total flow
length of weir
2. Surface overflow rate = Influent flow
surface area
3. Solids Loading rate = solids applied
surface area
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SEDIMENTATION AND LOADINGS (continued)
4. Efficiency, % = (in) – (out) x 100%
(in)
5. Organic loading rate (activated sludge) = CBOD applied
V
6. Hydraulic loading rate = Q
A
7. Centrifuge hydraulic loading: hydraulic loading rate = Q x run time
run time + skim time
ACTIVATED SLUDGE
1. SVI = 30 min settling, ml/L x 1,000 mg
MLSS, mg/L gram
2. SDI = 100
SVI
3. Solids inventory, lbs = (Tank volume, MG) x (solids concentration, mg/L) x (8.34 lbs / gal)
4. Sludge age, days = solids under aeration, lbs
solids added, lbs / day
5. F/M = CBOD applied
Organic solids under aeration
6. MCRT = solids inventory
[effluent solids + WAS solids]
7. Change, WAS rate, MGD = (current solids inventory, lbs) – (desired solids inventory, lbs)
WAS, mg/L x 8.34 lbs / gal
8. Return sludge rate, MGD = (settleable solids, mL) x Q
(1,000 mL) – (settleable solids, mL)
SLUDGE DIGESTION
1. Dry solids, lbs = (sludge, gal) x (sludge, % solids) x (8.34 lbs / gal) x SG
100%
2. Seed Sludge, lbs volatile solids = volatile solids pumped (lbs volatile solids / day)
loading factor (lbs VS / day) / lb VS in digester
3. Seed Sludge, gal = seed sludge (lbs volatile solids)
seed sludge (lbs / gal) x (solids %) x (volatile solids %)
100% (
100%)
4. Digested sludge removed = Total sludge in – volatile solids destroyed
5. Lime required, lbs = (sludge, MG) x (volatile acids, mg/L) x (8.34 lbs / gal)
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SLUDGE DIGESTION (continued)
6. Percent volatile solids reduction = (in - out) x 100%
in - (in x out)
7. VS destroyed, lbs / day / cu ft = volatile solids added (lbs / day) x volatile solids reduction (%)
digester volume (ft
3
) x 100%
8. Gas production (cu ft / lb VS) = gas produced (ft
3
/ day)
VS destroyed (lbs / day)
HORSEPOWER, FORCE, CHEMICAL PUMPS
1. Water HP = Q(gpm) x 8.34 lbs / gal x head (ft)
33,000 ft-lbs / min
2. Break HP = Water HP
pump efficiency
3. Motor HP = BHP
motor efficiency
4. Upward force = 62.4 (lbs / ft
3
) x height (ft) x area (ft
2
)
5. Side wall force = 31.2 (lbs / ft
3
) x volume (ft
3
)
6. Chemical solution, lbs / gal = (solution %) x 8.34 lbs / gal)
100%
7. Feed pump flow, gal / day = chemical feed (lbs / day)
Chemical solution (lbs / gal)
8. Scale setting, % = desired flow (gal / day) (100%)
maximum feed rate (gal/day)
9. Total Dynamic Head = Static Head + Friction Losses
10. Static Head = Suction Lift + Discharge Head
11. Polymer solution % = dry polymer (lb)
100% Vol of solution (gal) x 8.34 (lbs / gal)
LAB PROCEDURES AND MEASUREMENTS
1. TSS, mg/L = (RDD – DD) x 1M
sample vol (mL)
2. VSS, mg/L = (RDD – FDD) x 1M
sample vol (mL)
where: RDD = dried residue + dish + disc (filter)(grams)
DD = dish + disc, grams
FDD = fired residue + dish + disc (grams)
1M = 1,000,000
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LAB PROCEDURES AND MEASUREMENTS (continued)
3. VSS, % = volatile solids (mg/L) x 100%
total suspended solids (mg/L)
4. CBOD sample size (mL) = 1,200
estimated CBOD (mg/L)
5. Seed correction, mg/L for 1 mL seed = seed initial D.O. – seed final D.O.
mL seed added
6. CBOD, mg/L = [(Initial D.O. – Final D.O.) – seed correction factor] x bottle volume (mL)
sample volume (mL)
7. Initial D.O. = (mL sample x D.O. sample) + (mL dilution water x D.O. dilution water)
bottle volume (mL)
8. Temperature Conversion: Temperature, F = (temperature C)(1.8) + 32
