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Worksheet Grade 11 Math

Kestrel Bend's Clearwell: Chlorine Dosing and Detention-Time Math

Grade 11 students chain unit conversions through the pounds formula and detention-time formula to check a fictional plant's chlorine dose and clearwell sizing.

Objectives

  1. Students will convert plant flow between million gallons per day and gallons per minute.
  2. Students will apply the pounds formula to calculate a daily chemical feed rate.
  3. Students will calculate detention time in days, hours, and minutes from volume and flow.

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: chlorine demand, residual, MRDL

Teacher overview

Kestrel Bend (a fictional water treatment plant used for this worksheet) treats an average flow of 3.2 million gallons per day. Its operators dose chlorine after filtration and hold the water in a clearwell tank long enough to guarantee disinfection before it enters the distribution system. This worksheet chains together three operator-certification formulas (unit conversion, the pounds formula, and detention time), so students practice carrying consistent units through a multistep problem rather than treating each formula as an isolated fact. A common misconception to watch for: students often plug MGD directly into a formula written for gallons per day, forgetting that "million gallons" needs to be expanded to a plain gallon figure before the arithmetic is correct.

Kestrel Bend's Clearwell: Chlorine Dosing and Detention-Time Math — Grade 11 Math
Name: ____________________________ Date: ______________

Student Worksheet

Use these facts about Kestrel Bend's plant (a fictional facility created for this worksheet) for every item below:

  • Average flow: 3.2 MGD
  • Chlorine dosage applied: 2.5 mg/L
  • Chlorine residual measured in the clearwell: 1.1 mg/L
  • Clearwell volume: 150,000 gallons
  1. Convert the plant's average flow of 3.2 MGD to gallons per minute, using the conversion 1 MGD = 694 gpm.
  2. Calculate the chlorine demand using Chlorine demand (mg/L) = dosage (mg/L) − residual (mg/L).
  3. Using the pounds formula (Loading in lbs/day = dose in mg/L × flow in MGD × 8.34), calculate how many pounds of chlorine the plant feeds each day at the stated dose and flow.
  4. The clearwell holds 150,000 gallons. First convert the flow to gallons per day (3.2 MGD = 3,200,000 gal/day), then calculate the detention time in days using Detention time = Volume ÷ Flow.
  5. Convert your answer from item 4 into hours.
  6. Convert your answer from item 4 into minutes.
  7. State the typical chlorine residual range utilities maintain in distribution and the maximum residual disinfectant level allowed. Is Kestrel Bend's measured residual (1.1 mg/L) within both bounds?
  8. Suppose a second, nearby plant instead doses chlorine at 3.0 mg/L on the same 3.2 MGD flow. Calculate its daily chlorine feed in pounds.
  9. Using your answers to items 3 and 8, calculate the difference in pounds of chlorine fed per day between the two dosing choices.
  10. Explain in one or two sentences why an operator setting a chlorine dose needs to think about detention time, not just the concentration applied.

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: 2,221 gpm. 3.2 MGD × 694 gpm/MGD = 2,220.8 gpm, which rounds to 2,221 gpm.
  2. Answer: 1.4 mg/L. Chlorine demand = 2.5 mg/L − 1.1 mg/L = 1.4 mg/L.
  3. Answer: 66.72 lbs/day. 2.5 mg/L × 3.2 MGD × 8.34 = 8.0 × 8.34 = 66.72 pounds of chlorine per day.
  4. Answer: 0.046875 days. 150,000 gal ÷ 3,200,000 gal/day = 0.046875 days.
  5. Answer: 1.125 hours. 0.046875 days × 24 hr/day = 1.125 hours.
  6. Answer: 67.5 minutes. 0.046875 days × 1,440 min/day = 67.5 minutes.
  7. Answer: Yes. Utilities typically maintain a residual of 0.2 to 2.0 mg/L in distribution, and the maximum residual disinfectant level is 4.0 mg/L. Kestrel Bend's 1.1 mg/L residual sits within the typical operating range and well below the maximum allowed.
  8. Answer: 80.06 lbs/day. 3.0 mg/L × 3.2 MGD × 8.34 = 9.6 × 8.34 = 80.064 pounds, which rounds to 80.06 lbs/day.
  9. Answer: 13.34 lbs/day. 80.064 − 66.72 = 13.344 pounds per day, which rounds to 13.34 lbs/day.
  10. Answer: A longer detention time gives chlorine more contact time with pathogens before the water leaves the clearwell, so a plant with a short detention time may need a higher dose (or a different disinfection step) to reach the same level of disinfection as a plant where the water sits longer.

Differentiation

Support (below grade level)

Give students a labeled sequence of steps for items 1 through 6 ("first convert MGD to gallons, then divide, then multiply by 24 or 1,440") printed as a reference strip, and allow a calculator for every item.

Extension (above grade level)

Ask students to work backward: if Kestrel Bend's operators want the clearwell's detention time to be exactly 1.5 hours without changing the tank's 150,000-gallon volume, what flow rate (in MGD) would the plant need to run at? Have them show every conversion step.

ELL supports

Pre-teach "dosage," "residual," "demand," and "detention time" with a simple diagram of water entering a clearwell tank, chlorine being added, and water leaving after a delay. Provide a printed unit-conversion reference card (MGD to gpm, days to hours, days to minutes) for items 1, 5, and 6.