Worksheet Grade 12 Science

Alum Coagulant Dosing at the Penhallow Treatment Plant

A grade 12 worksheet applying the pounds formula, flow conversions, and turbidity removal efficiency across a fictional plant's coagulation and disinfection train.

Grade: Grade 12
Subject: Science
Material: Worksheet
Time: 45 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: Items 1 through 5 carry units through the pounds formula and the MGD-to-gpm and MGD-to-cfs conversions, the consistent-unit discipline this standard names.

All materials for HSN-Q.A.1 →

HSN-Q.A.3 Common Core Math

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

How this material aligns: Items 6 through 10 ask students to report turbidity and chlorine residual to an accuracy matched to the stated readings rather than to false precision.

All materials for HSN-Q.A.3 →

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: Items 6, 7, and 11 evaluate the plant's jar-test alum dose against prioritized criteria, settled and finished turbidity versus the 0.3 NTU limit set against the chemical cost and the restabilized floc that overdosing causes, the trade-off evaluation this standard names.

All materials for HS-ETS1-3 →

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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 calculate a chemical feed rate in pounds per day using the pounds formula.
Students will convert a plant flow among MGD, gpm, and cfs and use it to find detention time.
Students will compute turbidity removal efficiency and check finished water against the EPA standard.

Vocabulary

Coagulation: Coagulation is the first cleaning step at a drinking water plant. Operators quickly mix in a chemical that makes tiny bits of dirt stop pushing each other away so they can start sticking together.
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.
Turbidity: Turbidity is a measure of how cloudy or murky water looks because of tiny particles floating in it. Clear water has low turbidity, and muddy water has high turbidity.

Also: pounds formula, chlorine demand

Teacher overview

This worksheet follows raw river water through the fictional Penhallow Water Treatment Plant, from rapid mix through disinfection. Students size the alum feed with the pounds formula, convert the plant flow to the units an operator actually reports, and judge the finished water against the EPA turbidity standard. A common error to watch for is skipping the flow-unit conversion: the pounds formula needs flow in MGD, while detention time needs flow in gpm, and students who reuse the wrong version of the flow get answers off by a large factor.

Alum Coagulant Dosing at the Penhallow Treatment Plant — Grade 12 Science

Name: ____________________________ Date: ______________

Student Worksheet

The town of Penhallow runs a surface-water plant treating a steady flow of 6.2 MGD. A jar test set the optimum alum dose at 22 mg/L. Use these constants throughout: one gallon of water weighs 8.34 pounds, one cubic foot holds 7.48 gallons, one MGD equals 694 gpm, and one MGD equals 1.547 cfs.

Convert the plant flow of 6.2 MGD to gallons per minute (gpm). Round to the nearest whole gpm.
Convert the same 6.2 MGD flow to cubic feet per second (cfs). Round to the nearest hundredth.
Using the pounds formula, feed rate (lbs/day) = dose (mg/L) x flow (MGD) x 8.34, find the alum feed rate at the 22 mg/L jar-test dose.
The plant orders alum by the month. At the feed rate from item 3, how many pounds of alum does Penhallow use across a 30-day month?
The flocculation basin measures 60 ft long, 30 ft wide, and 14 ft deep. Find its volume in gallons, then find the detention time in minutes at the flow you found in item 1. Detention time = volume (gal) / flow (gpm).
The water entering sedimentation reads 12 NTU, and the settled water reads 0.8 NTU. Calculate the turbidity removal efficiency across the sedimentation basin, using removal efficiency (%) = (influent - effluent) / influent x 100.
After filtration, the finished water reads 0.18 NTU. EPA rules require finished water at or below 0.3 NTU in most monthly samples. Does Penhallow's finished water meet that limit, and by how much?
The plant adds chlorine at a dose of 2.4 mg/L and measures a residual of 0.9 mg/L. Find the chlorine demand, where chlorine demand = dose - residual.
Using the pounds formula again, find the chlorine feed rate in pounds per day at the 2.4 mg/L dose and the 6.2 MGD flow.
The chlorine MRDL is 4.0 mg/L. Is Penhallow's measured residual of 0.9 mg/L within that limit? State the margin.
Explain why raising the alum dose well past the jar-test optimum can actually increase settled turbidity rather than lower it.
Explain why the plant flow must be expressed in gpm before you calculate detention time in minutes, even though the pounds formula used MGD.

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: 4,303 gpm.
6.2 MGD x 694 gpm/MGD = 4,302.8 gpm, which rounds to 4,303 gpm.
Answer: 9.59 cfs.
6.2 MGD x 1.547 cfs/MGD = 9.5914 cfs, which rounds to 9.59 cfs.
Answer: 1,138 lbs/day.
22 mg/L x 6.2 MGD x 8.34 = 1,137.58 lbs/day, rounding to about 1,138 lbs/day.
Answer: 34,127 lbs.
1,137.58 lbs/day x 30 days = 34,127.4 lbs, or about 34,127 pounds of alum for the month.
Answer: 43.8 min.
Volume = 60 x 30 x 14 = 25,200 cu ft; 25,200 x 7.48 = 188,496 gal. Detention time = 188,496 gal / 4,302.8 gpm = 43.8 minutes.
Answer: 93.3%.
(12 - 0.8) / 12 x 100 = 11.2 / 12 x 100 = 93.33%, or about 93.3 percent removal.
Answer: yes, by 0.12 NTU.
0.18 NTU is below the 0.3 NTU limit, clearing it by 0.3 - 0.18 = 0.12 NTU.
Answer: 1.5 mg/L.
Chlorine demand = 2.4 mg/L - 0.9 mg/L = 1.5 mg/L.
Answer: 124.1 lbs/day.
2.4 mg/L x 6.2 MGD x 8.34 = 124.10 lbs/day.
Answer: yes, 3.1 mg/L below the limit.
0.9 mg/L is within the 4.0 mg/L MRDL, with a margin of 4.0 - 0.9 = 3.1 mg/L.
Answer: Overdosing reverses the charge on the particles.
At the jar-test optimum, the alum neutralizes the negative charge on the suspended particles so they clump and settle. Adding much more alum can push the particle charge positive, which restabilizes the colloid, so the floc breaks up and settled turbidity rises again.
Answer: The units must match the formula's time base.
Detention time in minutes requires a flow in gallons per minute, so a gallon count divided by a per-minute flow yields minutes. The pounds formula is written for MGD, so each formula needs the flow in its own matching unit before the numbers mean anything.

Differentiation

Support

Provide a printed constant sheet listing the four conversions and the two formulas, and work item 3 aloud as a model before students attempt item 9, since the two use the same pounds formula with different numbers.

Extension

Ask students to find the alum dose that would exactly double the monthly pounds used in item 4 while the flow stays fixed, then explain why doubling the dose does not double the removal efficiency in item 6.

ELL supports

Pre-teach "coagulation," "floc," "turbidity," and "residual" with a labeled diagram of the treatment train from rapid mix to disinfection. Allow students to answer items 11 and 12 with a labeled sketch plus a short caption rather than a full paragraph.

Extensions

Invite students to request a local plant's most recent Consumer Confidence Report and locate its reported finished-water turbidity, then compare that real value with the finished-water reading in this worksheet and discuss why a plant aims well below the 0.3 NTU limit rather than right at it.