Wastewater Operator Wastewater Math and Calculations Questions and Answers — Questions and Answers
Question 1: A treatment plant's influent flow of 4.2 MGD has an average Biochemical Oxygen Demand (BOD) concentration of 210 mg/L. How many pounds of BOD enter the plant each day?
- 7,356 lbs/day (Correct answer)
- 882 lbs/day
- 73,560 lbs/day
- 8,820 lbs/day
Correct answer: 7,356 lbs/day
The 'pounds formula' is used to calculate the pounds of a substance in wastewater. The formula is: Pounds/day = Flow (MGD) × Concentration (mg/L) × 8.34 lbs/gal. Calculation: 4.2 MGD × 210 mg/L × 8.34 lbs/gal = 7,355.88 lbs/day, which is rounded to 7,356 lbs/day.
Question 2: An activated sludge system has the following characteristics: Influent flow to the aeration basin is 1.5 MGD, primary effluent BOD is 150 mg/L, the aeration tank volume is 0.5 MG, and the Mixed Liquor Suspended Solids (MLSS) is 2,800 mg/L. What is the Food to Microorganism (F/M) ratio?
- 0.05
- 0.16 (Correct answer)
- 1.25
- 6.22
Correct answer: 0.16
The F/M ratio is calculated by dividing the pounds of incoming food (BOD) by the pounds of microorganisms (MLSS) under aeration. 1. Calculate Food (BOD) in lbs/day: 1.5 MGD × 150 mg/L × 8.34 = 1,876.5 lbs/day. 2. Calculate Microorganisms (MLSS) in lbs: 0.5 MG × 2,800 mg/L × 8.34 = 11,676 lbs. 3. Calculate F/M Ratio: 1,876.5 lbs/day ÷ 11,676 lbs = 0.16.
Question 3: A circular clarifier is 60 feet in diameter and 12 feet deep. If the influent flow rate is 2.5 MGD, what is the detention time in hours?
- 0.1 hours
- 4.1 hours
- 2.4 hours (Correct answer)
- 1.8 hours
Correct answer: 2.4 hours
Detention time is calculated by dividing the tank volume by the flow rate. 1. Calculate Tank Volume in cubic feet (cu ft): Volume = π × r² × depth = 3.14 × (30 ft)² × 12 ft = 33,912 cu ft. 2. Convert Volume to gallons (gal): 33,912 cu ft × 7.48 gal/cu ft = 253,662 gal. 3. Calculate Detention Time in days: 253,662 gal ÷ 2,500,000 gal/day = 0.101 days. 4. Convert Detention Time to hours: 0.101 days × 24 hrs/day = 2.43 hours.
Question 4: An operator performs a 30-minute settleability test on a mixed liquor sample, and the settled solids occupy a volume of 320 mL/L. The MLSS concentration is determined to be 2,500 mg/L. What is the Sludge Volume Index (SVI) in mL/g?
- 7.8 mL/g
- 0.13 mL/g
- 80 mL/g
- 128 mL/g (Correct answer)
Correct answer: 128 mL/g
The Sludge Volume Index (SVI) formula is: SVI (mL/g) = (Settled Sludge Volume, mL/L × 1,000 mg/g) ÷ MLSS (mg/L). Calculation: (320 mL/L × 1,000 mg/g) ÷ 2,500 mg/L = 128 mL/g.
Question 5: A pump is required to move 500 gallons per minute (gpm) against a total head of 45 feet. What is the water horsepower (WHP) required?
- 5.7 WHP (Correct answer)
- 2.8 WHP
- 88.0 WHP
- 11.4 WHP
Correct answer: 5.7 WHP
Water Horsepower (WHP) is calculated using the formula: WHP = (Flow, gpm × Total Head, ft) ÷ 3,960. Calculation: (500 gpm × 45 ft) ÷ 3,960 = 5.68 WHP, which rounds to 5.7 WHP.
Question 6: What is the weir overflow rate (WOR) in gpd/ft for a circular clarifier that has a diameter of 80 feet and receives a flow of 3.0 MGD?
- 37,500 gpd/ft
- 15,000 gpd/ft
- 11,943 gpd/ft (Correct answer)
- 5,971 gpd/ft
Correct answer: 11,943 gpd/ft
Weir Overflow Rate (WOR) is the flow per foot of weir length. 1. First, calculate the weir length, which is the circumference of the clarifier: Circumference = π × Diameter = 3.14 × 80 ft = 251.2 ft. 2. Then, calculate WOR: WOR = Flow (gpd) ÷ Weir Length (ft) = 3,000,000 gpd ÷ 251.2 ft = 11,942.7 gpd/ft. This is rounded to 11,943 gpd/ft.
Wastewater Operator Wastewater Math and Calculations Questions and Answers
A treatment plant's influent flow of 4.2 MGD has an average Biochemical Oxygen Demand (BOD) concentration of 210 mg/L.
How many pounds of BOD enter the plant each day?