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Math problem set Grade 9 Careers & CTE

Tollesby Plant Exam Prep: Operator Conversion and Dosage Drills

Ten grade 9 careers problems drilling the conversions an operator certification exam asks for, all drawn from one fictional plant's tanks, flows, and chlorine feed.

Objectives

  1. Students will convert plant flow between million gallons per day and gallons per minute.
  2. Students will calculate basin volumes and detention times from tank dimensions and plant flow.
  3. Students will apply the pounds formula to a chlorine dose and convert the result into days of chemical supply.

Vocabulary

Detention time
Detention time is how long water stays inside a tank or basin before flowing out. Water must stay long enough for each treatment step, like settling or disinfecting, to finish its job.
Clearwell
A clearwell is a large storage tank at a treatment plant that holds finished water right after it comes out of the filters. It gives the disinfectant enough time to work before the water is pumped out to homes and businesses.

Also: pounds formula, design flow, day tank, dosage

Teacher overview

The math questions on state operator certification exams are largely built from a small set of conversions and formulas applied to a real plant's dimensions, and candidates who know the formulas still fail on units. These ten problems put a candidate at the fictional Tollesby Water Treatment Plant, working from that plant's own tanks and flows, in the order an operator would meet them on a shift. The error worth naming before students start is dividing a tank volume in cubic feet by a flow in gallons per day, which produces a number that looks like a detention time and is wrong by a factor of about seven. Converting cubic feet to gallons first, and then multiplying the result in days by 24, is the habit the exam is testing. Water typically spends 2 to 4 hours in a sedimentation basin, and problem 7 asks students to judge a result against that range rather than only to report it.

Tollesby Plant Exam Prep: Operator Conversion and Dosage Drills — Grade 9 Careers & CTE
Name: ____________________________ Date: ______________

Problems

Use the following information about the fictional Tollesby Water Treatment Plant for every problem. Write the unit beside every number you calculate, and round to one decimal place unless the problem says otherwise.

  • Tollesby has a design flow of 4.0 MGD and is treating 3.2 MGD today.
  • The clearwell is rectangular: 60 feet long, 30 feet wide, with water 12 feet deep.
  • The sedimentation basin is rectangular: 80 feet long, 25 feet wide, with water 14 feet deep.
  • The chlorine day tank is a cylinder 8 feet in diameter holding solution 10 feet deep.
  • Today's chlorine dose is 2.2 mg/L.
  • The chemical room holds 940 pounds of chlorine in stock.
  • Conversions Tollesby's operators use: 1 MGD equals 694 gallons per minute; 1 cubic foot holds 7.48 gallons; loading in pounds per day equals concentration in mg/L times flow in MGD times 8.34; a rectangular basin's volume in cubic feet equals length times width times depth; a cylinder's volume in cubic feet equals 0.785 times the diameter squared times the depth; detention time equals volume divided by flow.
  1. Tollesby is treating 3.2 MGD. Using 694 gallons per minute per MGD, convert today's flow to gallons per minute.
  2. The clearwell is 60 feet long, 30 feet wide, and holds water 12 feet deep. Calculate its volume in cubic feet.
  3. A clearwell holds 21,600 cubic feet of water. Using 7.48 gallons per cubic foot, convert that volume to gallons.
  4. A clearwell holds 161,568 gallons and the plant is treating 3,200,000 gallons per day. Calculate the detention time in hours.
  5. The sedimentation basin is 80 feet long, 25 feet wide, and holds water 14 feet deep. Using 7.48 gallons per cubic foot, calculate its volume in gallons.
  6. A sedimentation basin holds 209,440 gallons and the plant is treating 3,200,000 gallons per day. Calculate the detention time in hours.
  7. Water typically spends 2 to 4 hours in a sedimentation basin. A basin is running at 1.6 hours of detention time. State whether that basin meets the typical range.
  8. Tollesby applies a chlorine dose of 2.2 mg/L at a flow of 3.2 MGD. Using the pounds formula with the constant 8.34, calculate the pounds of chlorine fed per day.
  9. The chlorine day tank is a cylinder 8 feet in diameter holding solution 10 feet deep. Using 0.785 times the diameter squared times the depth, and 7.48 gallons per cubic foot, calculate the tank's volume in gallons.
  10. The chemical room holds 940 pounds of chlorine and the plant feeds 58.7 pounds per day. Calculate the days of supply on hand, rounded to one decimal place.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 2,220.8 gpm.
    Multiply the flow by the conversion: 3.2 MGD times 694 gallons per minute per MGD equals 2,220.8 gallons per minute.
  2. Answer: 21,600 cu ft.
    Multiply length by width by depth: 60 feet times 30 feet equals 1,800 square feet, and 1,800 square feet times 12 feet equals 21,600 cubic feet.
  3. Answer: 161,568 gallons.
    Multiply the volume by the conversion: 21,600 cubic feet times 7.48 gallons per cubic foot equals 161,568 gallons.
  4. Answer: 1.2 hours.
    Divide volume by flow: 161,568 gallons divided by 3,200,000 gallons per day equals 0.0505 days. Multiply by 24 hours per day to get 1.2 hours.
  5. Answer: 209,440 gallons.
    Multiply length by width by depth: 80 feet times 25 feet equals 2,000 square feet, and 2,000 square feet times 14 feet equals 28,000 cubic feet. Then 28,000 cubic feet times 7.48 gallons per cubic foot equals 209,440 gallons.
  6. Answer: 1.6 hours.
    Divide volume by flow: 209,440 gallons divided by 3,200,000 gallons per day equals 0.0654 days. Multiply by 24 hours per day to get 1.6 hours.
  7. Answer: No.
    A detention time of 1.6 hours falls below the typical 2 to 4 hour range, so solids have less time to settle than typical practice allows, and the operator would expect more load to carry onto the filters.
  8. Answer: 58.7 lbs/day.
    Apply the pounds formula: 2.2 mg/L times 3.2 MGD equals 7.04, and 7.04 times 8.34 equals 58.7136, which rounds to 58.7 pounds per day.
  9. Answer: 3,758 gallons.
    Square the diameter: 8 feet times 8 feet equals 64 square feet. Then 0.785 times 64 equals 50.24, and 50.24 times 10 feet equals 502.4 cubic feet. Finally 502.4 cubic feet times 7.48 gallons per cubic foot equals 3,757.95 gallons, which rounds to 3,758 gallons.
  10. Answer: 16.0 days.
    Divide the stock by the daily feed: 940 pounds divided by 58.7 pounds per day equals 16.01 days, which rounds to 16.0 days. Reporting more decimal places would suggest a precision the stock count does not have.

Differentiation

Support

Give these students a conversion card listing each fictional Tollesby conversion with one worked example, and let them mark which conversion each problem needs before computing anything. For problem 4, write the division already set up with the units showing, since the step students lose is multiplying the answer in days by 24. Allow problems 2, 3, 5, and 9 to be completed as a labeled chain rather than in sentences.

Extension

Ask these students to recompute problems 4 and 6 at the fictional Tollesby plant's full design flow of 4.0 MGD and state what happens to both detention times. Then have them find the flow, to the nearest tenth of an MGD, at which the sedimentation basin would just reach 2 hours of detention, and explain what an operator would do on a day when raw water demand pushed the plant past that flow.

ELL supports

Pre-teach clearwell, detention time, dose, day tank, and design flow using a side-view sketch of the fictional Tollesby plant with water moving left to right through each tank. Provide a units card showing MGD, gpm, cubic feet, gallons, hours, and pounds per day with a picture or example beside each. Allow answers to be written as labeled arithmetic, and accept a short phrase for problem 7.

Extensions

Have students rebuild problems 2 through 6 using the dimensions of a tank they can actually measure, such as a school swimming pool or a classroom aquarium, and a flow rate they choose. Comparing the detention time of a familiar container against the fictional Tollesby basin gives the number a size students can picture, which is what operators rely on when a reading looks wrong.