Math problem set Grade 9 Science

Orrick Treatment Plant: Detention Time and Filter Loading

A grade 9 problem set where students find a sedimentation basin's detention time and a sand filter's loading rate for a fictional treatment plant.

Grade: Grade 9
Subject: Science
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

HSG-MG.A.1 Common Core Math

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

How this material aligns: Items 1 and 2 have students model the rectangular sedimentation basin as a geometric solid to find its volume in cubic feet and gallons, the geometric-modeling task this standard describes.

All materials for HSG-MG.A.1 →

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 3 through 9 chain a flow conversion, a detention-time calculation, and a filter-loading rate across gallons, minutes, and gallons per minute, requiring the consistent unit tracking this standard specifies.

All materials for HSN-Q.A.1 →

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, 8, and 9 evaluate the basin's detention time and the filters' loading rates against the published design ranges, and item 10 weighs the finished-water consequence of running a filter past that constraint.

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 find a rectangular basin's volume in cubic feet and gallons.
Students will calculate detention time from a basin volume and a plant flow.
Students will calculate a filter loading rate and compare it to a typical design range.

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.
Flow rate: Flow rate measures how much water moves past a point in a certain amount of time, like gallons per minute through a garden hose. Bigger pipes and stronger pushes give bigger flow rates.

Also: sedimentation basin, filter loading rate

Teacher overview

Before water is filtered, a treatment plant slows it down in a sedimentation basin so heavy particles can settle out. How long the water sits there is the detention time, found by dividing the basin's volume by the plant's flow. After settling, the water passes through sand filters, and operators track the filter loading rate to be sure it stays in a safe range. This set works through those calculations for the fictional town of Orrick using the same formulas operators use on the job.

A common misconception is to compare two flows or volumes that are in different units. Students must convert the basin volume to gallons and the flow to gallons per minute before dividing, or the detention time will be wrong.

Orrick Treatment Plant: Detention Time and Filter Loading — Grade 9 Science

Name: ____________________________ Date: ______________

Problems

The town of Orrick (a fictional town) runs a treatment plant with a rectangular sedimentation basin and several rapid sand filters. Use these facts: rectangular volume = length × width × depth, 1 cubic foot = 7.48 gallons, 1 MGD = 694 gpm, detention time = volume ÷ flow, and filter loading rate = filter flow ÷ filter area. Sedimentation basins are usually designed for 2 to 4 hours of detention, and rapid filters usually run between 2 and 6 gpm per square foot.

The basin is 80 feet long, 30 feet wide, and 12 feet deep. Find its volume in cubic feet.
Convert the basin volume to gallons, using 1 cubic foot = 7.48 gallons.
The plant treats 1.5 MGD. Convert this flow to gallons per minute, using 1 MGD = 694 gpm.
Using the basin volume in gallons (item 2) and the flow in gallons per minute (item 3), find the detention time in minutes. Round to the nearest minute.
Convert the detention time from item 4 to hours. Round to the nearest tenth.
Sedimentation basins are usually designed for 2 to 4 hours of detention. Does Orrick's basin fall within that range?
Each rapid sand filter has a surface area of 200 square feet. If one filter passes 800 gpm, find its filter loading rate in gallons per minute per square foot.
Rapid filters usually run between 2 and 6 gpm per square foot. Is the filter in item 7 within that range?
During peak demand, one filter must pass 1,300 gpm. Find its loading rate, and state whether it is still within the 2 to 6 gpm per square foot range.
Explain why running a filter above its design loading rate can let more particles pass through into the finished water.

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: 28,800 cubic feet. Volume = 80 × 30 × 12 = 28,800 cubic feet.
Answer: 215,424 gallons. 28,800 cubic feet × 7.48 gallons per cubic foot = 215,424 gallons.
Answer: 1,041 gpm. 1.5 MGD × 694 gpm per MGD = 1,041 gallons per minute.
Answer: 207 minutes. 215,424 gallons ÷ 1,041 gallons per minute = 206.9, which rounds to 207 minutes.
Answer: 3.5 hours. 207 minutes ÷ 60 minutes per hour = 3.45, which rounds to 3.5 hours.
Answer: Yes. 3.5 hours falls within the usual 2 to 4 hour design range.
Answer: 4 gpm per square foot. 800 gpm ÷ 200 square feet = 4 gallons per minute per square foot.
Answer: Yes. 4 gpm per square foot falls within the 2 to 6 range.
Answer: 6.5 gpm per square foot, which is above the range. 1,300 gpm ÷ 200 square feet = 6.5, which is higher than the 6 gpm per square foot upper limit.
Answer: At a higher loading rate the water moves through the sand faster, so particles have less time to be trapped. Some of them are carried through the filter instead of being caught, which lets more particles reach the finished water.

Differentiation

Support

Provide the basin volume from item 1 already calculated and a conversion reference card listing "1 cubic foot = 7.48 gallons" and "1 MGD = 694 gpm" so students can focus on the detention-time and loading-rate steps.

Extension

Have students find the largest plant flow, in MGD, that would still keep the basin's detention time at or above the 2-hour minimum, working backward from the detention-time formula.

ELL supports

Pre-teach "sedimentation basin," "detention time," and "filter loading rate" with a labeled diagram of water settling in a basin and then passing down through sand. Provide the formulas as arrow rules on a printed strip.