Math problem set Grade 11 Science

Cresswick Clearwell Disinfection: Chlorine Dose and CT Math

A grade 11 problem set on chlorine demand, the pounds formula, contact time, and CT values in a fictional plant's clearwell, with equations for a required residual.

Grade: Grade 11
Subject: Science
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

HS-ETS1-3 NGSS

Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics as well as possible social, cultural, and environmental impacts.

How this material aligns: Problems 5 and 8 evaluate whether Cresswick's clearwell still meets its 36 mg/L-min disinfection-safety target once peak demand cuts the contact time, weighing that criterion against the higher residual a shorter contact time would demand.

All materials for HS-ETS1-3 →

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Problems 2, 3, and 4 carry milligrams per liter, million gallons per day, gallons, and minutes through the pounds formula and the CT calculation, the consistent-unit multi-step reasoning this standard requires.

All materials for HSN-Q.A.1 →

HSA-CED.A.1 Common Core Math

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

How this material aligns: Problems 6 and 8 have students write and solve a one-variable equation for the minimum chlorine residual needed to meet a required CT value, exactly the equation-building this standard targets.

All materials for HSA-CED.A.1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will apply the pounds formula and chlorine-demand relationship to a treatment scenario.
Students will calculate contact time and CT values and solve for a required residual concentration.

Vocabulary

CT value: CT value is a way operators check that water has been disinfected long enough. It is found by multiplying how much disinfectant is in the water by how many minutes the water has been in contact with it.
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, contact time

Teacher overview

Disinfection depends on two things together: how much chlorine stays in the water and how long the water sits in contact with it. Operators combine these into a single CT value, the residual concentration multiplied by the contact time, and compare it to a required target. This set follows the fictional town of Cresswick through one pass of its clearwell, from chlorine feed to CT check. A common misconception it corrects is confusing the chlorine dose with the residual; the dose is what is added, while the residual is what remains after demand is satisfied, and only the residual counts in the CT calculation. Regulators credit only the T10 contact time, which is shorter than the theoretical detention time because some water short-circuits through the clearwell; this set uses the full detention time to keep the math simple.

Cresswick Clearwell Disinfection: Chlorine Dose and CT Math — Grade 11 Science

Name: ____________________________ Date: ______________

Problems

Use the fictional town of Cresswick and these values for every problem.

Normal plant flow: 2.0 MGD; peak plant flow: 3.0 MGD
Clearwell volume: 150,000 gallons
Chlorine dose: 3.0 mg/L
Free chlorine residual leaving the clearwell: 0.8 mg/L
Required CT for the target inactivation in this scenario: 36 mg/L-min
1 gallon of water weighs 8.34 pounds.
Detention time t = volume / flow; multiply a time in days by 1,440 to get minutes.
CT = residual concentration (mg/L) x contact time (min); chlorine demand = dose - residual.

Find the chlorine demand of the Cresswick water.
Using the pounds formula (feed = dose x flow x 8.34), find the chlorine feed rate in pounds per day at the normal flow of 2.0 MGD.
Find the contact time, in minutes, that water spends in the clearwell at the normal flow of 2.0 MGD.
Using the contact time from problem 3 and the 0.8 mg/L residual, calculate the CT value the clearwell achieves.
Does Cresswick meet the required CT of 36 mg/L-min at normal flow? State by what factor it clears or misses the target.
Write and solve a one-variable equation for the minimum residual concentration that would just meet the required CT of 36 mg/L-min at the normal-flow contact time from problem 3.
During peak demand the flow rises to 3.0 MGD. Recompute the contact time in the clearwell.
Write and solve a one-variable equation for the minimum residual needed to meet the required 36 mg/L-min CT at the peak-flow contact time from problem 7, and explain why peak flow demands a higher minimum residual.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Answer: 2.2 mg/L.
Chlorine demand = dose - residual = 3.0 - 0.8 = 2.2 mg/L.
Answer: 50 lbs/day.
Feed = dose x flow x 8.34 = 3.0 mg/L x 2.0 MGD x 8.34 = 50.04, which rounds to about 50 pounds per day.
Answer: 108 min. t = volume / flow = 150,000 gallons / 2,000,000 gallons per day = 0.075 day; 0.075 x 1,440 = 108 minutes.
Answer: 86.4 mg/L-min.
CT = residual x contact time = 0.8 mg/L x 108 min = 86.4 mg/L-min.
Answer: yes, by about 2.4 times.
86.4 mg/L-min divided by the required 36 mg/L-min = 2.4, so Cresswick clears the target by a factor of about 2.4 at normal flow.
Answer: 0.33 mg/L.
Let C be the residual. C x 108 = 36, so C = 36 / 108 = 0.333, about 0.33 mg/L. Any residual at or above this value meets the target at normal flow.
Answer: 72 min. t = 150,000 gallons / 3,000,000 gallons per day = 0.05 day; 0.05 x 1,440 = 72 minutes.
Answer: 0.5 mg/L.
Let C be the residual. C x 72 = 36, so C = 36 / 72 = 0.5 mg/L. Peak flow shortens the contact time from 108 to 72 minutes, so a higher residual is needed to reach the same CT; the achieved CT at peak with the 0.8 mg/L residual is 0.8 x 72 = 57.6 mg/L-min, still above 36.

Differentiation

Support

Provide the detention-time formula and the pounds formula pre-labeled with where each Cresswick value goes, and work problem 1 as a model. Allow students to keep contact time in days until the final minute conversion.

Extension

Have students find the peak flow, in MGD, at which the town of Cresswick's clearwell would exactly meet the required 36 mg/L-min CT with the 0.8 mg/L residual, by writing an equation that sets the CT equal to 36 and solving for the flow.

ELL supports

Provide a labeled diagram of a clearwell showing water entering, the contact path, and the residual test point. Pair the terms dose, demand, residual, and contact time with a simple before-and-after picture, and give the CT formula with each symbol labeled.