Math problem set Grade 9 Engineering & Design

Ash Creek Treatment Plant: Detention, Filters, Chlorine

A grade 9 engineering set on a surface water plant: students size a sedimentation basin's detention time, a filter loading rate, and a chlorine feed in pounds per day.

Grade: Grade 9
Subject: Engineering & Design
Material: Math problem set
Time: 50 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 units through the volume, detention time, filter loading, and pounds-formula work in problems 1 through 6, converting cubic feet to gallons and days to hours consistently.

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: Problems 3, 4, and 7 ask students to report detention time, loading rate, and a break-even flow at a level of accuracy that matches the plant's design ranges and rounding needs.

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: Problems 3, 4, and 6 test the detention time, filter loading rate, and chlorine residual against the plant's stated design ranges and the 4.0 mg/L limit, and problems 7 and 8 evaluate the flow ceiling and a proposed third filter against those same constraints.

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 2026-07-17.

Objectives

Students will calculate a sedimentation basin's detention time and a filter's loading rate from a design flow.
Students will use the pounds formula to find a chlorine feed rate and compare a residual to the regulatory limit.

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.
Sedimentation: Sedimentation is the step where water sits almost still in a big basin so the heavy clumps of dirt can sink to the bottom. The cleaner water on top then moves on to the filters.

Also: filter loading rate, chlorine dose, residual

Teacher overview

A conventional surface water plant slows water down in a sedimentation basin so heavy particles settle, filters the water, then adds chlorine to disinfect it. Engineers size each step from the plant's design flow. This set uses one fictional plant to find a basin's detention time, a filter's loading rate, and a chlorine feed rate in pounds per day, then checks each result against a normal design range.

A common error in this math is leaving detention time in days when the design range is stated in hours, which makes a basin look far too small. Detention time comes out in days when volume in gallons is divided by flow in gallons per day, so the result must be multiplied by 24 to compare it with the usual 2 to 4 hour range for sedimentation.

Ash Creek Treatment Plant: Detention, Filters, Chlorine — Grade 9 Engineering & Design

Name: ____________________________ Date: ______________

Problems

The Ash Creek Water Treatment Plant (a fictional plant used for this set) treats river water. Use these values for all problems:

Design flow: 2.0 MGD.
Sedimentation basin (rectangular): length 80 feet, width 25 feet, water depth 12 feet.
Filters: two filters, each 10 feet by 15 feet.
Conversions: 1 cubic foot = 7.48 gallons; 1 MGD = 694 gpm; 1 gallon of water weighs 8.34 pounds.
Design ranges: sedimentation detention 2 to 4 hours; filter loading 2 to 6 gpm per square foot.

Find the sedimentation basin volume in cubic feet. Volume = length x width x depth.
Convert the basin volume to gallons.
Find the detention time in hours at the design flow. Detention time in days = volume in gallons / flow in gallons per day; multiply by 24 for hours. State whether it falls in the 2 to 4 hour range.
Find the filter loading rate in gpm per square foot. First convert 2.0 MGD to gpm, then divide by the total filter area (two filters). State whether it falls in the 2 to 6 range.
The operator feeds chlorine at a dose of 2.2 mg/L. Use the pounds formula, pounds per day = dose (mg/L) x flow (MGD) x 8.34, to find the chlorine feed in pounds per day.
The plant targets a chlorine residual of 1.0 mg/L leaving the plant. Chlorine demand = dose - residual. Find the demand, and confirm the 1.0 mg/L residual stays below the 4.0 mg/L maximum residual disinfectant level.
The state asks the plant to keep sedimentation detention at 2.0 hours or more. Using detention time = volume / flow, find the flow in MGD at which the detention time drops to exactly 2.0 hours.
The plant plans to add a third filter of the same size (10 feet by 15 feet). Recompute the filter loading rate at 2.0 MGD with three filters, and explain how adding filter area changes the loading rate.

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: 24,000 cu ft.
Volume = 80 ft x 25 ft x 12 ft = 24,000 cubic feet.
Answer: 179,520 gallons.
24,000 cubic feet x 7.48 gallons per cubic foot = 179,520 gallons.
Answer: 2.2 hours.
Detention in days = 179,520 gallons / 2,000,000 gallons per day = 0.08976 day. In hours: 0.08976 x 24 = 2.15, about 2.2 hours. This falls inside the 2 to 4 hour range.
Answer: 4.6 gpm/sq ft.
Flow = 2.0 MGD x 694 = 1,388 gpm. Total filter area = 2 x (10 ft x 15 ft) = 300 square feet. Loading = 1,388 / 300 = 4.63, about 4.6 gpm per square foot, inside the 2 to 6 range.
Answer: 36.7 lb/day.
Pounds per day = 2.2 mg/L x 2.0 MGD x 8.34 = 36.7 pounds per day.
Answer: 1.2 mg/L.
Chlorine demand = dose - residual = 2.2 mg/L - 1.0 mg/L = 1.2 mg/L. The 1.0 mg/L residual is below the 4.0 mg/L maximum residual disinfectant level.
Answer: 2.15 MGD.
Set detention to 2.0 hours = 2.0 / 24 day, about 0.0833 day. Flow = volume / time = 179,520 gallons / (2.0 / 24 day) = 179,520 x 12 = 2,154,240 gallons per day, about 2.15 MGD. Above this flow the detention time drops below 2.0 hours.
Answer: 3.1 gpm/sq ft.
Three filters give 3 x 150 = 450 square feet. Loading = 1,388 / 450 = 3.08, about 3.1 gpm per square foot. Adding filter area lowers the loading rate, so water passes through more slowly and the filters remove particles more effectively.

Differentiation

Support

Provide the basin volume in gallons (179,520) already computed so students can begin at problem 3, and give a worked reminder that a detention time in days is multiplied by 24 to reach hours. Allow a calculator for every step.

Extension

Ask students to find the detention time and filter loading rate if the plant's design flow rose to 3.0 MGD, and to explain which result moves outside its recommended range first as flow increases, and what upgrade would bring it back in range.

ELL supports

Pre-teach "detention time," "sedimentation," "loading rate," "dose," and "residual" with a labeled side-view diagram of a basin, a filter, and a chlorine feed point. Allow students to record answers as numbers with unit labels rather than full sentences.