Worksheet Grade 12 Science

Chlorine Feed Rate and Detention Time at Blackstone Falls

A grade 12 worksheet using the pounds formula, the detention-time formula, and chlorine demand to size disinfection feed at a fictional treatment plant.

Grade: Grade 12
Subject: Science
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

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: Students carry consistent units through the chained flow, detention-time, and pounds-formula conversions in items 1 through 10, the multi-step dimensional analysis this standard requires.

All materials for HSN-Q.A.1 →

HS-ESS3-4 NGSS

Evaluate or refine a technological solution that reduces impacts of human activities on natural systems.

How this material aligns: Items 4 through 11 evaluate chlorine disinfection as the treatment solution protecting finished water, sizing the feed, checking the 1.2 mg/L residual against the 4.0 mg/L federal maximum, and reading a rising demand as a change in the source water the dose must overcome.

All materials for HS-ESS3-4 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will calculate chemical feed loading in pounds per day using the pounds formula.
Students will calculate detention time from tank volume and flow rate, in both days and minutes.
Students will determine chlorine demand from a stated dosage and 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.
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, loading rate

Teacher overview

Blackstone Falls, a fictional town used for this worksheet, operates a small treatment plant that disinfects its water with chlorine before it reaches the clearwell, the tank that holds finished water long enough for disinfection to work before distribution. This worksheet uses two real operator-certification formulas, the pounds formula and the detention-time formula, along with the federal maximum residual disinfectant level of 4.0 mg/L, to size the plant's chlorine feed and check how long water actually sits in the clearwell at different flow rates.

A common misconception in this math is assuming detention time is fixed once a tank is built. Detention time depends on flow as well as volume, so the same clearwell gives water less contact time whenever flow rises, which is exactly what items 8 and 9 ask students to demonstrate with numbers rather than take on faith.

Chlorine Feed Rate and Detention Time at Blackstone Falls — Grade 12 Science

Name: ____________________________ Date: ______________

Student Worksheet

Blackstone Falls (a fictional town used for this worksheet) operates a treatment plant that normally treats a flow of 2.4 MGD and holds finished water in a clearwell with a volume of 150,000 gallons before it enters the distribution system. Use these facts, plus the formulas below, for all items.

Pounds formula: Loading (lbs/day) = Concentration (mg/L) x Flow (MGD) x 8.34
Detention time: t (days) = Volume (gal) / Flow (gal/day); multiply by 1440 to convert days to minutes
Chlorine demand (mg/L) = dosage (mg/L) - residual (mg/L)
Conversion: 1 MGD = 694 gallons per minute (gpm)

Convert the plant's normal flow of 2.4 MGD to gallons per minute. Round to the nearest whole gpm.
The clearwell holds 150,000 gallons, which equals 0.15 million gallons (MG). At the normal flow of 2.4 MGD, calculate the detention time in days.
Convert your answer from item 2 into minutes.
The plant doses chlorine at 3.0 mg/L. Operators want a residual of 1.2 mg/L entering distribution. Calculate the chlorine demand.
Using the pounds formula, calculate the chlorine feed loading (lbs/day) needed at the 3.0 mg/L dose and the 2.4 MGD normal flow.
The federal maximum residual disinfectant level for chlorine is 4.0 mg/L. By how much margin does the plant's 1.2 mg/L target residual stay under that maximum?
During a summer demand peak, flow rises to 3.0 MGD while the dose stays at 3.0 mg/L. Calculate the new chlorine feed loading at this higher flow.
At the same 3.0 MGD peak flow, and with the clearwell volume unchanged at 150,000 gallons, calculate the new detention time in minutes.
Compare your answers to items 3 and 8. Explain in a sentence or two why detention time changed even though the clearwell's volume stayed exactly the same.
One morning, the chlorine analyzer reads a residual of only 0.9 mg/L instead of the target 1.2 mg/L, with the dose still set at 3.0 mg/L. Calculate the new chlorine demand.
Explain what a rising chlorine demand on an unchanged dose might indicate about the water entering the plant that day.

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: 1,666 gpm.
2.4 MGD x 694 gpm per MGD = 1,665.6 gpm, which rounds to 1,666 gpm.
Answer: 0.0625 days.
Detention time = Volume / Flow = 0.15 MG / 2.4 MGD = 0.0625 days.
Answer: 90 minutes.
0.0625 days x 1,440 minutes/day = 90 minutes.
Answer: 1.8 mg/L.
Chlorine demand = dosage - residual = 3.0 mg/L - 1.2 mg/L = 1.8 mg/L.
Answer: 60.0 lbs/day.
Loading = Concentration x Flow x 8.34 = 3.0 mg/L x 2.4 MGD x 8.34 = 60.048 lbs/day, which rounds to 60.0 lbs/day.
Answer: 2.8 mg/L.
4.0 mg/L (maximum) - 1.2 mg/L (target residual) = 2.8 mg/L of margin before the plant would reach the federal maximum.
Answer: 75.1 lbs/day.
Loading = 3.0 mg/L x 3.0 MGD x 8.34 = 75.06 lbs/day, which rounds to 75.1 lbs/day. Raising the flow while holding the dose constant raises the total pounds of chlorine fed each day.
Answer: 72 minutes.
Detention time = 0.15 MG / 3.0 MGD = 0.05 days; 0.05 days x 1,440 minutes/day = 72 minutes.
Answer: Detention time drops as flow rises.
The clearwell's volume did not change, but at 3.0 MGD, water enters and leaves the tank faster than it did at 2.4 MGD, so each gallon spends less time inside before moving on to distribution. Detention time depends on the relationship between volume and flow, not on volume alone.
Answer: 2.1 mg/L.
Chlorine demand = 3.0 mg/L - 0.9 mg/L = 2.1 mg/L.
Answer: Something in the source water is consuming more chlorine.
A rising demand on the same dose usually means the water entering the plant that day carries more organic matter, more microbial load, or is warmer than usual, all of which consume chlorine faster. Operators who see this trend typically need to raise the dose to keep the target residual steady.

Differentiation

Support (below grade level)

Provide the three formulas on a printed reference card with each variable labeled, and work through item 1 as a demonstration before students begin independently. Allow a calculator for every item and accept unrounded decimal answers alongside the rounded ones.

Extension (above grade level)

Ask students to find the flow rate, in MGD, at which the plant's detention time would drop to exactly 60 minutes, holding the clearwell volume at 150,000 gallons. They should set up and solve the detention-time equation for the unknown flow rather than guess and check.

ELL supports

Pre-teach "detention time," "residual," "demand," and "clearwell" with a simple diagram showing water entering a tank, sitting for a period, and leaving through a pipe to homes. Allow students to show item 9 and item 11 as a labeled diagram or bulleted list rather than full sentences.