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Lesson plan Grade 10 Math

Harrowgate Chlorine Dose and Contact Time Lesson

A 50-minute grade 10 lesson on chlorine chemistry: students find feed rate with the pounds formula, compute the demand, and find detention time for a fictional plant.

Objectives

  1. Students will calculate a chlorine feed rate in pounds per day using the pounds formula.
  2. Students will compute chlorine demand from dose and residual and find a contact tank's detention time.

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.

Also: chlorine dose, residual, chlorine demand

Teacher overview

In drinking-water treatment, disinfection depends on chemistry: an operator adds enough chlorine to kill pathogens, then measures what is left over as the residual. This lesson has students at the fictional Harrowgate plant use the pounds formula to size a chlorine feed, find the chlorine demand, and calculate how long water sits in the contact tank. A common misconception is confusing dose with residual, or plugging flow into the pounds formula in gpm instead of MGD; both errors are addressed directly during instruction and practice.

Procedure

Hook (5 min): Ask students how a plant knows it added "enough" chlorine. Collect a few ideas, then introduce the residual: the small amount of chlorine still measurable after the demand has been met. Explain that too little leaves pathogens, while too much can exceed a federal limit.

Direct instruction (12 min): Present three ideas using the fictional Harrowgate plant as the running example. First, the pounds formula: feed (lbs/day) = dose (mg/L) × flow (MGD) × 8.34. Model it once: at 2.0 MGD with a dose of 2.5 mg/L, feed = 2.5 × 2.0 × 8.34 = 41.7 lbs/day. Stress that flow must be in MGD. Second, chlorine demand = dose − residual. Third, the maximum residual disinfectant level for chlorine is 4.0 mg/L, so residuals in distribution stay well below that. Do not solve the handout numbers; those are for students.

Guided practice (13 min): Hand out the student page. Work items 1 through 3 together, pausing after item 1 so pairs can check that they used MGD, not gpm, in the pounds formula.

Independent practice (12 min): Students complete items 4 through 6 on their own, including the detention-time calculation for the contact tank. Circulate and check that students subtract to find demand rather than reusing the dose.

Closure and formative check (8 min): As an exit check, ask students to compare their feed rates from item 1 and item 4 and state, in one sentence, why the higher dose needs more chlorine per day. Collect the handouts and scan item 4: if more than a quarter of the class used the wrong flow units, reteach the pounds formula before moving on.

Harrowgate Chlorine Dose and Contact Time Lesson — Grade 10 Math
Name: ____________________________ Date: ______________

Student Handout

At the fictional Harrowgate plant, the flow is 1.5 MGD. Use the pounds formula, feed (lbs/day) = dose (mg/L) × flow (MGD) × 8.34; chlorine demand = dose − residual; and detention time (minutes) = volume (gallons) / flow (gallons per day) × 1,440. The maximum residual disinfectant level for chlorine is 4.0 mg/L.

  1. The operator sets a chlorine dose of 3.0 mg/L. Find the chlorine feed rate in pounds per day at 1.5 MGD.

  2. After the chlorine reacts, the measured residual is 0.8 mg/L. Find the chlorine demand.

  3. Is the 0.8 mg/L residual within the maximum residual disinfectant level of 4.0 mg/L? Answer yes or no.

  4. The operator raises the dose to 4.5 mg/L. Find the new chlorine feed rate in pounds per day at 1.5 MGD.

  5. At the higher dose, the residual rises to 2.1 mg/L. Find the new chlorine demand.

  6. The chlorine contact tank holds 50,000 gallons, and the plant flow is 1.5 MGD, which is 1,500,000 gallons per day. Find the detention time in minutes.

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: 37.5 lb/day. 3.0 mg/L × 1.5 MGD × 8.34 = 37.53, about 37.5 pounds per day.

  2. Answer: 2.2 mg/L. Chlorine demand = dose − residual = 3.0 − 0.8 = 2.2 mg/L.

  3. Answer: Yes. The 0.8 mg/L residual is well below the 4.0 mg/L maximum, so it is within the limit.

  4. Answer: 56.3 lb/day. 4.5 mg/L × 1.5 MGD × 8.34 = 56.295, about 56.3 pounds per day.

  5. Answer: 2.4 mg/L. Chlorine demand = 4.5 − 2.1 = 2.4 mg/L.

  6. Answer: 48 min. Detention time = 50,000 / 1,500,000 × 1,440 = 0.03333 × 1,440 = 48 minutes.

Differentiation

Support

Give students a filled-in example of the pounds formula with different numbers beside the handout, so the structure is visible while they work. Provide the detention-time formula with the item 6 values already placed, leaving only the arithmetic.

Extension

Ask students to find the dose, in mg/L, that would produce a feed rate of exactly 50 pounds per day at the fictional plant's 1.5 MGD, working backward through the pounds formula. Then have them discuss why an operator would not simply add as much chlorine as possible.

ELL supports

Pre-teach "dose," "residual," and "demand" with a simple picture: chlorine added, chlorine used up fighting germs, and chlorine left over. Provide a sentence frame for item 3: "The residual is within the limit because ___."

Extensions

Invite students to research how contact time and chlorine concentration work together in the disinfection idea operators call CT, then explain why a larger contact tank lets a plant use a lower chlorine concentration while still disinfecting the water. The detention-time answer from item 6 gives them a concrete contact time to reason about.