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Math problem set Grade 11 Math

Corbett Springs Plant: Detention, Filter Loading, and Chlorine Math

A grade 11 math set sizing the fictional Corbett Springs treatment plant: basin volume, detention time, filter loading rate, and a chlorine feed calculation.

Objectives

  1. Students will calculate basin volume in cubic feet and gallons and use it to find detention time.
  2. Students will compute a filter loading rate and compare it against typical design ranges.
  3. Students will apply the pounds formula to find a chlorine feed rate and interpret a residual reading.

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: filter loading rate, pounds formula, chlorine demand, residual

Teacher overview

Corbett Springs is a fictional surface-water treatment plant that clarifies river water and disinfects it before sending it to town. This set walks students through the same sizing math a plant operator or design engineer uses: how long water sits in a settling basin, how fast water passes through the filters, and how much chlorine to feed. Each answer is checked against a real design range, because a number that is technically correct can still be a poor design if it falls outside accepted practice. A common mistake in this work is mixing units, for example dividing a volume in gallons by a flow in cubic feet per second; the detention-time answer only makes sense when the volume and the flow are expressed in matching units.

Corbett Springs Plant: Detention, Filter Loading, and Chlorine Math — Grade 11 Math
Name: ____________________________ Date: ______________

Problems

Use these facts about the fictional Corbett Springs plant for every problem:

  • The plant's design flow is 6 MGD (million gallons per day).
  • The rectangular settling basin measures 120 feet long, 40 feet wide, and 14 feet deep.
  • One cubic foot holds 7.48 gallons. One MGD equals 694 gpm.
  • The plant has four filters with a combined surface area of 800 square feet. Conventional filters typically run at 2 to 6 gpm per square foot.
  • Water typically spends about 2 to 4 hours in a settling basin, though many state design rules call for at least 4 hours in a conventional basin.
  • A chlorine feed follows the pounds formula: feed (lbs/day) = dose (mg/L) × flow (MGD) × 8.34.
  • The maximum residual disinfectant level for chlorine is 4.0 mg/L, and distribution systems usually hold a residual of 0.2 to 2.0 mg/L.
  1. Find the volume of the settling basin in cubic feet.
  2. Convert the basin volume to gallons, using 7.48 gallons per cubic foot.
  3. Convert the plant's 6 MGD design flow to gallons per minute, using 694 gpm per MGD.
  4. Find the detention time in the basin in hours, dividing the basin volume in gallons by the flow in gallons per minute, then converting minutes to hours. Is it inside the typical 2-to-4-hour range, and does it meet the 4-hour minimum for a conventional basin?
  5. Find the filter loading rate in gpm per square foot, dividing the flow in gpm by the 800 square feet of filter area. Is it inside the usual 2-to-6 range?
  6. The operator wants a chlorine dose of 2.5 mg/L at the 6 MGD flow. Use the pounds formula to find the chlorine feed rate in pounds per day.
  7. A sample point in town reads a chlorine residual of 0.8 mg/L. Find the chlorine demand, using demand = dose − residual, and state whether the 0.8 mg/L residual sits inside the usual 0.2-to-2.0 mg/L distribution range and below the 4.0 mg/L limit.
  8. The chlorine test kit reads to the nearest 0.1 mg/L. A student records the residual as 0.83 mg/L. Explain why that is false precision and state what the student should report instead.

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: 67,200 cu ft. Volume = length × width × depth = 120 × 40 × 14 = 67,200 cubic feet.
  2. Answer: 502,656 gal. 67,200 cubic feet × 7.48 gallons per cubic foot = 502,656 gallons.
  3. Answer: 4,164 gpm. 6 MGD × 694 gpm per MGD = 4,164 gallons per minute.
  4. Answer: 2.0 hours. Detention time = 502,656 gallons ÷ 4,164 gpm = 120.7 minutes; 120.7 ÷ 60 = 2.01 hours, which rounds to about 2.0 hours. That is at the low end of, but still inside, the typical 2-to-4-hour range, though it falls short of the 4-hour minimum many state design rules set for conventional basins.
  5. Answer: 5.2 gpm per sq ft. Loading rate = 4,164 gpm ÷ 800 square feet = 5.205, about 5.2 gpm per square foot, which is inside the usual 2-to-6 range and near its high end.
  6. Answer: 125.1 lbs/day. Feed = dose × flow × 8.34 = 2.5 × 6 × 8.34 = 125.1 pounds per day.
  7. Answer: 1.7 mg/L. Chlorine demand = dose − residual = 2.5 − 0.8 = 1.7 mg/L. The 0.8 mg/L residual is inside the usual 0.2-to-2.0 mg/L distribution range and well below the 4.0 mg/L maximum residual disinfectant level.
  8. Answer: 0.8 mg/L. A kit that reads to the nearest 0.1 mg/L cannot distinguish 0.83 from 0.80, so the second decimal place is not real information. The student should report 0.8 mg/L, matching the reported accuracy to the instrument's precision.

Differentiation

Support

Provide a units checklist next to each problem naming the unit the answer should carry (cubic feet, gallons, gpm, hours, gpm per square foot, pounds per day, mg/L). Give the pounds formula and the two conversions on a reference strip so students focus on setting up each calculation.

Extension

Ask students to find the largest design flow, in MGD, at which the settling basin would still provide 4 hours of detention, and to explain what the plant would have to change if the town's demand grew past that flow.

ELL supports

Pre-teach "detention time," "loading rate," "dose," "demand," and "residual" with a labeled plant diagram that shows where in the treatment train each quantity is measured. Allow students to answer item 8 with a short sentence using the frame "The kit only reads to ___, so the answer should be ___."