Math problem set Grade 11 Science

Ashcombe Plant Expansion: Filter Loading Rate and Area Design

Grade 11 students convert a fictional plant's flow to gallons per minute and design a filter's minimum surface area that satisfies its loading-rate constraint.

Grade: Grade 11
Subject: Science
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: calculator

Standards

HSG-MG.A.3 Common Core Math

Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost).

How this material aligns: Problems 6 and 7 require students to design the minimum filter surface area and side length that satisfy Ashcombe's 2-to-6-gpm-per-square-foot loading constraint, an explicit design-under-constraint problem.

All materials for HSG-MG.A.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 1 and 5 require converting the plant's flow from million gallons per day to gallons per minute before it can be combined with a square-foot area, carrying units consistently through the formula.

All materials for HSN-Q.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 2026-07-16.

Objectives

Students will convert plant flow from million gallons per day to gallons per minute.
Students will calculate filter loading rate and compare it to the standard operating range.
Students will design a minimum filter area and dimensions that satisfy a loading-rate constraint.

Vocabulary

Key words: filter loading rate, square feet, constraint, gallons per minute

Teacher overview

Ashcombe Water Treatment Plant (a fictional facility created for this problem set) is planning an expansion, and its engineers need to check whether the existing filter bed can handle the new flow before deciding whether to build additional filter capacity. This problem set walks students through calculating loading rate, the flow passing through each square foot of filter surface each minute, and then using that same relationship in reverse to design a filter area that meets the standard operating range. A common misconception this math is designed to correct: students often divide a flow given in million gallons per day directly by an area in square feet without first converting to gallons per minute, producing a loading-rate number that is off by a factor of 694, the number of gallons per minute in one MGD.

Ashcombe Plant Expansion: Filter Loading Rate and Area Design — Grade 11 Science

Name: ____________________________ Date: ______________

Problems

Ashcombe's plant (a fictional facility used for this problem set) currently treats an average flow of 2.16 MGD through a single rectangular filter bed measuring 20 feet by 15 feet. Conventional filters are designed to operate between 2 and 6 gpm per square foot.

Convert the plant's current flow of 2.16 MGD to gallons per minute, using the conversion 1 MGD = 694 gpm.
Calculate the current filter bed's surface area in square feet.
Calculate the current filter loading rate in gallons per minute per square foot, using your answers to items 1 and 2.
Is Ashcombe's current filter loading rate within the standard 2-to-6-gpm-per-square-foot range?
The plant plans to expand to a new flow of 3.6 MGD. Convert this new flow to gallons per minute.
To keep the loading rate at or below 5 gpm per square foot at the new flow, calculate the minimum filter surface area needed.
If the new filter is built as a square, calculate the minimum whole-number side length, in feet, needed to reach at least the area from item 6.
Suppose instead the plant keeps its original 300-square-foot filter bed and builds one more identical 300-square-foot filter bed, running the two in parallel at the new 3.6 MGD flow with the flow split evenly between them. Calculate the loading rate on each filter bed, and state whether this design meets the 2-to-6-gpm-per-square-foot range.

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: 1,499.04 gpm. 2.16 MGD × 694 gpm/MGD = 1,499.04 gpm.
Answer: 300 sq ft. 20 ft × 15 ft = 300 sq ft.
Answer: 5.00 gpm/sq ft. 1,499.04 gpm ÷ 300 sq ft = 4.9968, which rounds to 5.00 gpm/sq ft.
Answer: yes. 5.00 gpm/sq ft falls within the standard 2-to-6-gpm-per-square-foot range.
Answer: 2,498.4 gpm. 3.6 MGD × 694 gpm/MGD = 2,498.4 gpm.
Answer: 499.68 sq ft. Minimum area = flow ÷ maximum loading rate = 2,498.4 ÷ 5 = 499.68 sq ft.
Answer: 23 ft. A 22-foot square gives 484 sq ft, which is less than the required 499.68 sq ft, so the plant needs at least a 23-foot square, which gives 529 sq ft.
Answer: 4.16 gpm/sq ft; yes, it meets the range. Each filter receives half the new flow: 2,498.4 ÷ 2 = 1,249.2 gpm. Loading rate per filter = 1,249.2 ÷ 300 = 4.164 gpm/sq ft, which rounds to 4.16 gpm/sq ft and falls within the 2-to-6-gpm-per-square-foot range.

Differentiation

Support (below grade level)

Provide the loading-rate formula already written as "gpm ÷ sq ft = loading rate" with the unit-conversion step for item 1 fully worked as an example. Allow a calculator for every item.

Extension (above grade level)

Ask students to determine, using the 2-to-6-gpm-per-square-foot range, the maximum flow (in MGD) the original 300-square-foot filter bed alone could handle without exceeding the upper limit, and to compare that maximum to the fictional Ashcombe plant's planned expansion flow from item 5.

ELL supports

Pre-teach "loading rate," "square foot," and "constraint" using a simple diagram of a filter bed drawn as a grid of one-foot squares with an arrow showing water flowing down through it. Provide a printed step list ("convert MGD to gpm, then divide by area") for items 1 through 3.