Math problem set Grade 10 Math

Whitmore Bend Plant Chlorine Dosing: A Grade 10 Pounds-Formula Set

A grade 10 math set sizing chlorine disinfection at a fictional plant: the pounds formula, chlorine demand, flow conversions, and clearwell contact time.

Grade: Grade 10
Subject: Math
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: Item 4 models the clearwell as a cylinder and applies the cylinder-volume relationship to estimate its capacity from a measured diameter and depth, 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 2 through 5 require carrying consistent units through the pounds formula and a flow-to-detention-time chain, the unit-guided multi-step reasoning this standard names.

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 2026-07-17.

Objectives

Students will apply the pounds formula to calculate a plant's daily chlorine feed from a dose and flow.
Students will calculate a clearwell's volume and use it to find disinfection contact time in minutes.
Students will relate a target chlorine residual to the federal maximum residual disinfectant level.

Vocabulary

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.
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.

Also: pounds formula, chlorine demand, residual

Teacher overview

The fictional Whitmore Bend Water Treatment Plant is planning the chlorine feed for its disinfection stage. This set walks students through finding the required chlorine dose from the water's demand and a target residual, converting that dose into a daily feed weight with the pounds formula, and checking that water spends long enough in the clearwell to be disinfected. A common misconception in this math is confusing dose, demand, and residual: the dose is the total chlorine added, the demand is the amount consumed by the water, and the residual is what remains, so dose must equal demand plus the residual the operator wants to keep. Watch for that mix-up in items 1 and 7.

Whitmore Bend Plant Chlorine Dosing: A Grade 10 Pounds-Formula Set — Grade 10 Math

Name: ____________________________ Date: ______________

Problems

Whitmore Bend (a fictional plant created for this set) treats a steady flow of 3.5 MGD. Its water has a measured chlorine demand of 1.8 mg/L, and operators want a chlorine residual of 0.8 mg/L leaving the clearwell. The clearwell is a cylinder 50 feet in diameter with a water depth of 14 feet.

Find the required chlorine dose in mg/L, using the rule that dose equals chlorine demand plus the target residual.
Using the pounds formula, Loading (lbs/day) = Concentration (mg/L) × Flow (MGD) × 8.34, calculate the pounds of chlorine the plant must feed per day at the dose from item 1 and the flow of 3.5 MGD.
Convert the plant's flow of 3.5 MGD to gallons per minute (gpm), using the conversion that 1 MGD equals 694 gpm.
Find the clearwell's volume in gallons. Use the cylinder-volume relationship Volume (cu ft) = 0.785 × Diameter² × depth, then convert to gallons with 1 cubic foot holding 7.48 gallons.
Using the detention-time formula, detention time = Volume ÷ Flow, calculate how many minutes water spends in the clearwell at 3.5 MGD. Convert the plant's flow to gallons per day, divide the clearwell volume by it to get days, then multiply by 1,440 minutes per day.
Whitmore Bend's disinfection plan calls for at least 30 minutes of clearwell contact time. Does the plant meet that target at 3.5 MGD? Justify your answer with your result from item 5.
The federal maximum residual disinfectant level (MRDL) for chlorine is 4.0 mg/L. How far below that MRDL is the plant's 0.8 mg/L target residual?
Convert the daily chlorine feed from item 2 into an hourly feed rate in pounds per hour, using 24 hours per day.
During a summer peak, the plant's flow rises to 4.2 MGD while operators hold the dose from item 1 steady. Recalculate the pounds of chlorine needed per day at the higher flow.
Explain why operators track chlorine demand, not just the dose they add, when they want a specific residual to remain in the water leaving the plant.

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: 2.6 mg/L.
Dose = demand + residual = 1.8 mg/L + 0.8 mg/L = 2.6 mg/L.
Answer: 75.9 lbs/day.
Loading = 2.6 mg/L × 3.5 MGD × 8.34 = 9.1 × 8.34 = 75.894, which rounds to 75.9 pounds of chlorine per day.
Answer: 2,429 gpm.
3.5 MGD × 694 gpm/MGD = 2,429 gpm.
Answer: 205,513 gallons.
Volume = 0.785 × 50² × 14 = 0.785 × 2,500 × 14 = 27,475 cubic feet. Converting to gallons: 27,475 × 7.48 = 205,513 gallons.
Answer: about 84.6 minutes.
Flow of 3.5 MGD is 3,500,000 gallons per day. Detention time = 205,513 ÷ 3,500,000 = 0.05872 days. Converting to minutes: 0.05872 × 1,440 = 84.55, which rounds to about 84.6 minutes.
Answer: Yes.
The clearwell provides about 84.6 minutes of contact time, which is well above the 30-minute minimum the plan requires, so the plant meets its contact-time target at 3.5 MGD.
Answer: 3.2 mg/L.
4.0 mg/L (the MRDL) − 0.8 mg/L (the target residual) = 3.2 mg/L, so the target residual sits 3.2 mg/L below the federal limit.
Answer: about 3.16 lbs/hr.
75.9 lbs/day ÷ 24 hours/day = 3.1625, which rounds to about 3.16 pounds per hour.
Answer: 91.1 lbs/day.
Loading = 2.6 mg/L × 4.2 MGD × 8.34 = 10.92 × 8.34 = 91.07, which rounds to 91.1 pounds per day at the peak flow.
Answer: Accept any answer explaining that the water itself consumes part of the chlorine added, so if operators dosed only the amount they wanted left over, the demand would use it up and little or no residual would remain. Tracking demand lets them add enough to satisfy that demand and still leave the target residual for continued disinfection in the distribution system.

Differentiation

Support (below grade level)

Provide the pounds formula, the cylinder-volume formula, and the detention-time steps on a printed reference card with each constant already written in, and work item 4's volume calculation through the cubic-feet step as a class before students convert to gallons and continue to item 5.

Extension (above grade level)

Ask students to find what steady flow, in MGD, would drop the clearwell's contact time to exactly the 30-minute minimum, working backward from the detention-time formula and the clearwell volume from item 4, then explain what that result means for the plant during very high demand.

ELL supports

Provide a labeled diagram of the treatment train showing where the clearwell sits and marking the terms dose, demand, and residual with a short plain-language definition beside each. Allow students to show items 1 through 9 as numbered calculations and answer item 10 with a labeled sketch plus a short sentence.