Virginia Wastewater Treatment Examination Formula Sheet

 

1. Circumference, Area, Volume

a. Circumference C = 3.1416 × Diameter
b. Perimeter P = [2 × Length] + [2 × Width]

c. Area

 
     Rectangle Area = Length × Width
     Circle Area = 0.785 × Diameter × Diameter
     Triangle Area = ½ × Base × Height
d. Volume  
     Rectangle Volume = Length × Width × Depth
     Cylinder Volume = 0.785 × Diameter × Diameter × Depth
     Cone Volume = 0.262 × Diameter × Diameter × Height
     Sphere Volume = 0.524 × Diameter × Diameter × Diameter

 

2. Conversion Factors

a. ft to gallons Volume, Gallons = Volume, ft3 × 7.48 gallons/ft3
b. Gallons to pounds Pounds = Gallons × 8.34 lbs/gallon
c. mg/L to pounds Pounds = Concentration, mg/L × TAnk Volume, MG × 8.34 lbs/MG/mg/L
d. mg/L to pounds/day Pounds/Day = Concentration, mg/L × Flow, MGD × 8.34 lbs/MG/mg/L
e. mg/L to kilograms/day Kilograms/Day = Conc., mg/L × Flow, MGD × 3.785 lbs/MG/mg/L
f. mg/Kg to pounds/ton Pounds/Ton = Concentration, mg/KG × 0.002 lbs/ton/mg/KG
g. Pounds to mg/L
h. Pounds/Day to mg/L
i. Pounds/Day to MGD

 

3. Flow

a. MGD to GPD Flow, GPD = Flow, MGD × 1,000,000 gallons/MG
b. MGD to GPM
c. MGD to CFS Flow, cfs = Flow, MGD × 1.55 cfs/MGD

 

4. Chemical Weight

Using Specific Gravity Weight/lbs/gallon = Specific gravity × 8.34 lbs/gallon

 

5. Population Equivalent

 

 

6. Percent to Decimal Percent

 

 

7. Percent Removal (Wastewater)

a. Based on Concentration
b. Based on Quantity (lbs, lbs/day, KG or KG/day)

 

8. Hydraulic Detention Time

a. HDT, Minutes
b. HDT, Hours
c. HDT, Days

 

9. Flow Measurement

a. Flow, (Fill and Draw), GPM
b. Flow (Velocity), cfs Flow (Q), cfs = Channel Width, ft × Water Depth, ft × Velocity, fps

 

10. Grit Removal

a. Velocity (float method)
b. Velocity
c. Settling Time*
d. Required Channel Length*
*The settling velocity must be given or determined experimentally.

 

11. Settling

a. Weir Overflow Rate
b. Surface Loading Rate
c. Solids Loading Rate

 

12. Ponds

a. Area in Acres
b. Volume in Acre-Feet
c. Flow in Acre-Feet/Day Flow, Acre Feet/Day = Flow, MGD × 3.069 Acre Feet/MG
d. Flow, Acre-Inches/Day Flow, Acre Inches/Day = Flow, MGD × 36.8 Acre Inches/MG
e. Hydraulic Detention Time, Days
f. Hydraulic Loading
g. Organic Loading
h. Population Loading

 

 

13. Trickling Filter

a. Total Flow (given flows) Total Flow, MGD = Influent Flow, MGD + Recirculation Flow, MGD
b. Total Flow (given ratio) Total Flow, MGD = Influent Flow, MGD × (1.0 + Recirculation Rate)
c. Hydraulic Loading

Total Flow always includes recirculated flow.
d. Organic Loading

Organic loading does not include recirculated flows.

 

14. Rotating Biological Contactors

a. Soluble BOD SBOD, mg/L = Total BOD5, mg/L - ('K' Factor × Influent TSS mg/L)
b. Total Media
c. Hydraulic Loading
d. Soluble Organic Loading
e. Total Organic Loading

 

15. Activated Sludge

a. Settled Sludge Volume
b. Settled Sludge Volume
c. Return Rate (By SSV)

d. Return Rate (By SVI)

 

 

e. Return Rate (Clarifier Mass Balance)
f. Clarifier Solids (Core Sample) SolidsC, lbs = Core Sample TSS, mg/L × VolumeC MG × 8.34 lbs/ mg/L/ MG
g. Clarifier Solids (MLSS) SolidsC = MLSS, mg/L × Volume C, MG × 8.34 lbs/ mg/L/ MG

h. Clarifier Solids (MLSS and RASSS)

 

 

 

C = Clarifier or Settling Tank
MLSS = Mixed Liquor Suspended Solids in milligrams/Liter
RASSS = Return Activated Sludge Suspended Solids in milligrams/Liter

i. Sludge Volume Index
j. F:M Ratio
k. Desired MLVSS, (lbs)
l. Desired MLVSS (mg/L)
m. Waste Volatile Solids (Based on F:M) Waste, lbs = Actual MLVSS, lbs - Required MLVSS, lbs
n. Waste Rate, MGD (Based on F:M)
o. MCRT, Days
p. Waste Solids, lbs/day (Based on MCRT)
q. Waste Rate, MGD (Based on MCRT)
r. Waste Rate, GPM

 

16. Chemical Addition

a. Demand Demand, mg/L = Dose, mg/L - Residual, mg/L
b. Dose, mg/L
c. Required Chemical (Feed Rate, lbs/day)
d. Feed Rate, gpd
e. Feed Rate, gpm
f. Feed Rate, mL/minute
g. Supply Required
h. Supply on Hand
i. Increases, (price, usage, or for safety) Increase = Current Amount × [1.0 + % (decimal) Increase]
j. Chemical Cost  
k. Chemical Makeup (dry chemical)
l. Chemical Makeup (solution)
m. Active Ingredient Chemical UsedActive Ingredient = Chemical Used, lbs × %Active Ingredient

 

17. Solids Pumping

a. Estimated Pump Rate (gallons/minute)
b. Gallon pumped GPD GPD = Pump Rate, gpm × Cycles, Cycles/day × Cycle Time, minutes/cycle
c. Solids Pumped lbs/day Solids, lbs/day = Solids Volume, gpd × 8.34 lbs/gal × % (decimal) Solids
d. Volatile Solids Pumped, lbs/day

Volatile Solids, lbs/day = Solids Volume, gpd × 8.34 lbs/gal × %Solids × %Volatile Matter

*All % values must be in decimal form.

 

18. Thickening

a. Solids Loading Rate (SLR) lbs/day/ft2
b. Solids Loading Rate (SLR) lbs/hour/ft2
c. Solids Volume Ratio (SVR)
d. Hydraulic Loading
e. Air: Solids Ratio
f. Concentration Factor

 

19. Aerobic Digestion

a. Volatile Solids Loading lbs/day/ft3
b. Digestion Time (based on flow)
c. Digestion Time (based on solids)
d. Chemical Requirement
e. Volatile Matter Reduction

 

20. Anaerobic Digestion

a. Seed Volume Seed, gallons = Digester Volume, gallons × Desired % Seed Volume
b. Volatile Solids Loading
c. Volatile Acids/Alkalinity Ratio
d. Chemical Requirement
e. Volatile Matter Reduction
f. Gas Production ft3/Day Gas, ft3 = Volatile SolidsIn, lbs/day × % V.M. Reduction × Rate, ft3/lb V.M. Destroyed

21. Land Application

a. Solids Production (dry tons/year)
b. Solids Production (wet tons/year)

c. Plant Available Nitrogen (PAN) (lbs/dry ton)

 

[(Organic - N, mg/kg × f1) + (Ammonia - N, mg/kg × V1)] × 0.002

f1= Mineralization Rate (assume 0.20)
V1 = Volatilization Rate
Injected Sludge = 1.0
Incorporated Within 24 hours = 0.85
Incorporated Within 7 days = 0.70

d. Application Rate (nitrogen basis)
e. Metals Loading lbs/acre Loading, lbs/Acre = Concentration, mg/kg × Application Rate, D.T./acre × 0.002 mg/kg/dry ton
f. Allowable Applications (Metals Basis)
g. Site LIfe (metal basis)

 

22. Pumping

a. Head to Pressure
b. Total Dynamic Head

TDH, ft = Static Head, ft + Friction Head, ft + Velocity Head, ft

c. Water Horsepower
d. Brake Horsepower
e. Motor Horsepower

 

23. Electrical Energy

a. Hp to kilowatts (kW) Kilowatts = Horsepower × 0.746 Kw/hp
b. kW to kilowatt hrs Kilowatt Hour = Kilowatts Used × Hours Operated
c. Power Cost Cost = Kilowatt hours used × Cost/Kilowatt

24. Sampling

a. Composite Sample Volume, mL

 

T = Sample Collection Time

b. Proportioning Factor (PF)

c. Sample Volume (Using PF)

 

Sample Volume, mL = FlowT × PF

T = Time sample is collected

 

25. Alkalinity

Conventional

 

 

A = Volume of Standard Acid Used
N = Normality of Standard Acid

Low Level

 

 

B = Volume of Standard Acid Used to reach pH 4.3 - 4.5
C = Total Volume of Standard Acid for titration
N = Normality of Standard Acid

 

26. Hardness

a. EDTA Standardization
b. Hardness, mg/L Calcium Carbonate

A = EDTA used in Titration, mL
B = EDTA CaCO3 Equivalence, mL/mL

 

27. Ammonia Nitrogen

a. Nesslerization

 

 

 

A = Micrograms of N from calibration curve
B = Volume of distillate collected
C = Volume of distillate used for nesslerization
Sample Volume = Original sample volume placed in distillation flask

b. Titration

 

 

A = Volume of titrant used for sample
B = Volume of titrant used for blank
Sample Volume = Volume of sample used for titration

28. Biochemical Oxygen Demand

a. Unseeded Samples
b. Seed Correction Factor
c. Seeded Samples

29. Chemical Oxygen Demand

a. FAS Standardization (Open Reflux)
b. FAS Standardization (Closed Reflux)

c. COD

 

 

A = FAS Used for Blank, mL
B = FAS Used for Sample, mL
C = FAS Molarity

 

30. Total Residual Chlorine

a. Iodometric Direct Titration
b. Iodometric Back Titration (No Iodine correction)
c. Iodine Correction
d. Iodometric Back Titration (With Iodine correction)
e. Iodometric Back Titration Iodate Titrant

 

31. Dissolved Oxygen

Winkler Titration

 

 

If N = 0.0250 & Sample Volume = 200 mL
then: Titrant Used = D.O., mg/L

 

32. Fecal Coliform

a. Multiple Tube
b. Membrane Filtration

33. Nitrate Nitrogen

a. Brucine Sulfate
b. Cadmium Reduction

 

34. Nitrite Nitrogen

Diazotization Diluted Sample

 

 

C = NO2 - N Concentration, mg/L
V = Total volume after dilution, mL
S = Sample Volume in dilution, mL

35. Phosphorous

Phosphorous

 

36. Total Suspended Solids

TSS, mg/L

37. Total Kjeldahl Nitrogen

a. Nesslerization

 

 

 

A = Micrograms of N from calibration curve
B = Volume of distillate collected
C = Volume of distillate used for nesslerization
Sample Volume = Original sample volume placed in distillation flask

b. Titration

 

 

A = Volume of titrant used for sample
B = Volume of titrant used for blank
Sample Volume = Volume of sample used for titration

 

38. Total Volatile Suspended Solids

TVSS, mg/L

 

 

A = Weight of Dried Solids & Support
C = Weight of Ash & Support

 

39. Residual (Sludge) Solids Tests

a. % Solids
b. % Volatile Matter

c. % Moisture

 

 

 

 

40. VPDES Reporting

a. Average Monthly Concentration
b. Average Weekly Concentration
c. Average Daily Concentration
d. Average Hourly Concentration

e. Daily Quantity

 

 

Daily Quantity, KG/Day = Conc., mg/L × Flow, MGD × 3.785 lbs/MG/mg/L

Conc. = Individual Test Result in mg/L
Flow = Flow on day sample was collected in MGD

f. Average Monthly Quantity
g. Average Weekly Quantity
h. Geometric Mean (Xy)
i. Geometric Mean (log)