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Lesson plan Grade 12 Engineering & Design

Water Age in the Quintrell Ridge Tank: A Turnover Lesson

A grade 12 lesson where students compute water age in a fictional storage tank from volume and daily throughput, then weigh storage size against disinfectant residual.

Objectives

  1. Students will calculate the water age of a storage tank as volume divided by daily throughput.
  2. Students will predict how lowering a tank's operating depth changes water age.
  3. Students will connect water age to chlorine residual loss and explain the storage-versus-freshness trade-off.

Vocabulary

Chlorine residual
Chlorine residual is the small amount of chlorine still left in the water after it leaves the treatment plant. It keeps protecting the water from germs all the way to your faucet.

Also: water age, turnover, operating depth, throughput

Teacher overview

Storage tanks give a distribution system reserve capacity for peak demand, fire flow, and outages, yet water that sits in a tank ages, and as it ages its chlorine residual decays toward the point where the water is no longer well protected. This lesson uses the fictional Quintrell Ridge tank to put a number on that aging: students compute water age as volume divided by daily throughput, then test how an operational change, lowering the normal operating depth, trades stored volume for fresher water. The common misconception addressed here is that a bigger or fuller tank is always better; the mathematics shows that oversized storage can push water age past the point where residual targets hold. Teaching note: the guided example and the handout use different tanks on purpose, so keep the guided numbers on the board as a worked pattern rather than letting students copy results across.

Procedure

Hook (5 min): Write two facts about the fictional Quintrell Ridge tank on the board: it holds several days of the neighborhood's demand, and complaints about chlorine taste stopped last year while complaints about "stale" water began. Ask students what could make water in a full, clean tank become a problem. Take three or four ideas without evaluating them.

Direct instruction (12 min): Define water age as the average time a gallon spends in storage, computed as tank volume divided by daily throughput. Review why age matters: chlorine residual decays over time, and systems typically maintain a residual of 0.2 to 2.0 mg/L in distribution, well under the regulatory maximum of 4.0 mg/L, so a tank that adds days of age can consume most of the protective residual before water reaches the last customer. Review the cylinder volume formula, Volume (cu ft) = 0.785 × Diameter² × depth, and the 7.48 gallons-per-cubic-foot conversion.

Guided example (10 min): Work one full calculation for a different fictional tank: 40 feet in diameter, 24-foot operating depth, 90,000 gallons per day of throughput. Volume = 0.785 × 1,600 × 24 = 30,144 cubic feet, which is 30,144 × 7.48 = 225,477 gallons. Age = 225,477 ÷ 90,000 = 2.5 days. Ask a checking question before moving on: if throughput doubled, what would happen to the age? (It would halve.)

Handout work (18 min): Students complete the five handout questions individually or in pairs, showing every unit. Circulate and watch for the two predictable errors: substituting the radius for the diameter in the 0.785 × Diameter² formula, and dividing throughput by volume instead of volume by throughput.

Discussion (6 min): Compare answers to handout questions 2 and 4. Ask: the lower operating depth improved freshness, so what did the utility give up? Draw out that the tank now holds less water for fire flow and outages, which is the real design trade-off operators manage.

Exit ticket (4 min): Each student writes two operational changes that would reduce water age in a storage tank and one cost or risk of each. Collect and scan for volume-side answers (lower the operating band) and throughput-side answers (cycle the tank harder); either is acceptable with a stated trade-off.

Water Age in the Quintrell Ridge Tank: A Turnover Lesson — Grade 12 Engineering & Design
Name: ____________________________ Date: ______________

Student Handout

The fictional Quintrell Ridge tank serves a hillside pressure zone. Answer every question with units shown. Use Volume (cu ft) = 0.785 × Diameter² × depth, and one cubic foot = 7.48 gallons.

  1. The tank is a cylinder 50 feet in diameter with a normal operating depth of 30 feet. Find its volume at normal depth, in gallons.
  2. On an average day, 110,000 gallons flow through the tank. Compute the tank's water age in days, to the nearest tenth.
  3. The utility's water-quality goal is a water age of 3.0 days or less at the 30-foot depth. What daily throughput, in gallons per day, would meet that goal exactly?
  4. Instead of changing throughput, operators lower the normal operating depth to 18 feet. Find the new water age at 110,000 gallons per day, to the nearest tenth of a day. Show the new volume as part of your work.
  5. Water enters the tank carrying a chlorine residual of 1.2 mg/L and loses about 0.15 mg/L for each day of age. Using the age from question 2, what residual remains when water leaves the tank, and is it inside the typical 0.2 to 2.0 mg/L distribution range?

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: 440,385 gallons. Volume = 0.785 × 50² × 30 = 0.785 × 2,500 × 30 = 58,875 cubic feet, and 58,875 × 7.48 = 440,385 gallons.
  2. Answer: 4.0 days. 440,385 ÷ 110,000 = 4.003, which rounds to 4.0 days of water age.
  3. Answer: 146,795 gallons per day. To hold age at 3.0 days, throughput must be volume ÷ age = 440,385 ÷ 3.0 = 146,795 gallons per day.
  4. Answer: 2.4 days. New volume = 0.785 × 2,500 × 18 = 35,325 cubic feet, which is 35,325 × 7.48 = 264,231 gallons. Age = 264,231 ÷ 110,000 = 2.402, about 2.4 days.
  5. Answer: 0.6 mg/L. Loss = 4.0 days × 0.15 mg/L per day = 0.6 mg/L, so the leaving residual is 1.2 − 0.6 = 0.6 mg/L, which is inside the typical 0.2 to 2.0 mg/L range.

Differentiation

Support

Provide the volume from handout question 1 already computed so students who stall on geometry can still practice the age and residual reasoning in questions 2 through 5. Keep the guided example visible and label its three stages: volume, age, interpretation.

Extension

Have students combine both levers for the fictional tank: find the water age if the depth stays at 18 feet while throughput also rises to 146,795 gallons per day, and explain in a sentence whether the utility would want water that young. (264,231 ÷ 146,795 = 1.8 days.)

ELL supports

Pre-teach "age," "turnover," and "residual" with a three-panel sketch of a tank: water entering with a full chlorine label, sitting as days pass, and leaving with a smaller label. Provide a sentence frame for question 5: "The water is ___ days old, so it loses ___ mg/L and leaves with ___ mg/L."