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Worksheet Grade 11 Engineering & Design

Rensford Falls Clearwell: A Chlorine CT Compliance Worksheet

A grade 11 worksheet on disinfection contact time: students size a clearwell, apply a baffling factor, compute CT achieved, and solve for a passing residual.

Objectives

  1. Students will compute a clearwell volume and its theoretical detention time.
  2. Students will apply a baffling factor to find effective contact time and CT achieved.
  3. Students will solve for the chlorine residual that meets a required CT ratio.

Vocabulary

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: contact time, baffling factor, CT ratio, chlorine demand

Teacher overview

Adding chlorine is only part of disinfection, because a plant must also show that enough chlorine stayed in contact with the water for long enough, which is what a CT calculation demonstrates. This worksheet walks students through the CT check for a clearwell at a fictional plant, from tank dimensions through to the residual needed to pass. The misconception the sequence is built to correct is the belief that the contact time the chlorine actually gets equals tank volume divided by flow. Real tanks short-circuit, so part of the water races from inlet to outlet in far less than the average time, and the baffling factor exists to account for that gap between the average and the fastest water.

Rensford Falls Clearwell: A Chlorine CT Compliance Worksheet — Grade 11 Engineering & Design
Name: ____________________________ Date: ______________

Student Worksheet

Use these figures from the fictional Rensford Falls water plant for every item. All values are hypothetical.

  • Clearwell dimensions: 80 feet long, 30 feet wide, 12 feet of water depth.
  • Flow through the clearwell: 1,200 gpm.
  • Baffling factor assigned to the clearwell: 0.50.
  • Free chlorine residual leaving the clearwell: 1.2 mg/L.
  • Chlorine dose applied at the clearwell inlet: 2.4 mg/L.
  • Suppose the plant's permit requires a CT of 95 mg/L-min at this water temperature and pH.
  • Conversions: one cubic foot holds 7.48 gallons, one MGD equals 694 gpm, and one gallon of water weighs 8.34 pounds.
  • Formulas: CT achieved equals residual times effective contact time. CT ratio equals CT achieved divided by CT required.
  1. Find the clearwell volume in cubic feet.
  2. Find the clearwell volume in gallons.
  3. Find the theoretical detention time in minutes at the stated flow.
  4. Find the effective contact time in minutes using the 0.50 baffling factor.
  5. Find the CT achieved, in mg/L-min, using the residual leaving the clearwell.
  6. Find the CT ratio against the required value. Round to two decimal places.
  7. Does the clearwell meet the permit requirement at these conditions?
  8. Convert the clearwell flow to million gallons per day. Round to two decimal places.
  9. Find the chlorine feed rate in pounds per day at the stated dose, using the flow in million gallons per day.
  10. Find the chlorine demand through the clearwell.
  11. Suppose baffle walls are added and the baffling factor rises to 0.70. Find the new effective contact time in minutes.
  12. Find the CT achieved with the improved baffling factor and the same residual.
  13. Find the CT ratio with the improved baffling factor. Round to two decimal places.
  14. Return to the 0.50 baffling factor. Find the free chlorine residual that would make the CT ratio exactly 1.00. Round to two decimal places.
  15. Explain why two clearwells holding the same volume and passing the same flow can have different effective contact times.

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: 28,800 cubic feet.
    Volume is length times width times depth, so 80 feet times 30 feet times 12 feet equals 28,800 cubic feet.
  2. Answer: 215,424 gallons.
    Multiplying 28,800 cubic feet by 7.48 gallons per cubic foot gives 215,424 gallons.
  3. Answer: 179.52 minutes.
    Detention time is volume divided by flow, so 215,424 gallons divided by 1,200 gpm equals 179.52 minutes.
  4. Answer: 89.76 minutes.
    Effective contact time is the theoretical time times the baffling factor, so 179.52 minutes times 0.50 equals 89.76 minutes.
  5. Answer: 107.7 mg/L-min.
    CT achieved is the residual times the effective contact time, so 1.2 mg/L times 89.76 minutes equals 107.712, which rounds to 107.7 mg/L-min.
  6. Answer: 1.13.
    The CT ratio is 107.712 divided by 95, which equals 1.1338 and rounds to 1.13.
  7. Answer: Yes.
    A CT ratio of 1.13 is greater than 1.00, so the clearwell delivers more contact than the permit requires at these conditions.
  8. Answer: 1.73 MGD.
    Dividing 1,200 gpm by 694 gpm per MGD gives 1.7291, which rounds to 1.73 MGD.
  9. Answer: 34.6 pounds per day.
    The pounds formula gives dose times flow times 8.34, so 2.4 mg/L times 1.73 MGD times 8.34 pounds per gallon equals 34.63, which rounds to 34.6 pounds per day.
  10. Answer: 1.2 mg/L.
    Chlorine demand is dose minus residual, so 2.4 mg/L minus 1.2 mg/L equals 1.2 mg/L consumed inside the clearwell.
  11. Answer: 125.66 minutes.
    The theoretical time does not change, so 179.52 minutes times 0.70 equals 125.664, which rounds to 125.66 minutes.
  12. Answer: 150.8 mg/L-min.
    CT achieved is 1.2 mg/L times 125.664 minutes, which equals 150.797 and rounds to 150.8 mg/L-min.
  13. Answer: 1.59.
    The CT ratio is 150.797 divided by 95, which equals 1.5873 and rounds to 1.59.
  14. Answer: 1.06 mg/L.
    Setting the residual times 89.76 minutes equal to 95 mg/L-min gives a residual of 95 divided by 89.76, which equals 1.0584 and rounds to 1.06 mg/L.
  15. Answer: Their baffling differs.
    Baffle walls, inlet position, and outlet position decide how much of the water short-circuits from inlet to outlet. A tank with good baffling holds a larger share of its water for close to the average time, so its effective contact time is a larger fraction of the theoretical time.

Differentiation

Support

Give these students items 1 and 2 worked out, and provide a formula strip listing volume, detention time, effective contact time, CT achieved, and CT ratio in the order the worksheet uses them. Allow the theoretical detention time from item 3 to be carried forward as a printed value so an early arithmetic slip does not spoil the later items in the fictional scenario.

Extension

Ask these students to find the highest flow, in gallons per minute, at which the fictional clearwell would still reach a CT ratio of 1.00 with the original 0.50 baffling factor and a residual of 1.2 mg/L. Then have them explain why a plant's CT compliance is hardest to meet at peak hourly flow rather than at average daily flow.

ELL supports

Provide a labeled plan-view sketch of the fictional clearwell showing the inlet, the outlet, and a dashed short-circuit path between them, with the words inlet, outlet, and baffle wall labeled. Allow item 15 to be answered with the frame "The two tanks are different because the water inside ___."

Extensions

Have students compare the CT approach with the contact time used for ultraviolet disinfection, where dose is measured in energy per unit area and contact lasts seconds rather than an hour. Students can then explain why a plant that switches to ultraviolet light still keeps a chlorine residual in the distribution system. A further task is to sketch two baffling arrangements for the fictional clearwell and predict which would earn the higher baffling factor, then justify the prediction using the short-circuit path they drew.