Math problem set Grade 12 Engineering & Design

Kingsley Bend Plant Chlorine Feed: Pounds-Formula and Demand Problems

A grade 12 problem set on chlorine disinfection at a fictional plant: students apply the pounds formula, find chlorine demand, and set a feed to hit a target residual.

Grade: Grade 12
Subject: Engineering & Design
Material: Math problem set
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: Problems 1, 2, and 6 apply the pounds formula, carrying mg/L, MGD, and the 8.34 constant through to pounds per day, the multi-step unit work this standard requires.

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: Problem 7 evaluates the proposed dose against the 0.2-to-2.0 mg/L distribution range and the 4.0 mg/L regulatory limit to judge whether the dosing plan is acceptable, the constraint-based solution evaluation this standard requires.

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 plant's chlorine feed in pounds per day using the pounds formula.
Students will find chlorine demand and set a dose that meets a target residual within regulatory limits.

Vocabulary

Key words: pounds formula, chlorine demand, dose, residual

Teacher overview

The fictional Kingsley Bend water treatment plant adds chlorine to disinfect its finished water before it enters the distribution system. This set has students calculate the chlorine feed with the standard pounds formula, then use a measured chlorine demand to set a dose that reaches a target residual without exceeding the regulatory limit. A common misconception in this math is confusing dose, demand, and residual, so watch for that in problems 4 and 5, where dose equals demand plus the residual an operator wants to keep.

Kingsley Bend Plant Chlorine Feed: Pounds-Formula and Demand Problems — Grade 12 Engineering & Design

Name: ____________________________ Date: ______________

Problems

Use these facts about the fictional Kingsley Bend plant for every problem:

The plant treats a flow of 3.0 million gallons per day (MGD).
The starting chlorine dose is 2.5 mg/L.
The pounds formula is: Loading (pounds per day) = Concentration (mg/L) x Flow (MGD) x 8.34.
Chlorine demand = dose - residual. Dose needed = demand + desired residual.
The regulatory limit (MRDL) for chlorine is 4.0 mg/L. Systems typically keep a distribution residual of 0.2 to 2.0 mg/L.

Find the chlorine feed, in pounds per day, at a dose of 2.5 mg/L and a flow of 3.0 MGD.
During peak season the flow rises to 4.0 MGD at the same 2.5 mg/L dose. Find the new chlorine feed in pounds per day.
How many more pounds of chlorine per day does the plant use at 4.0 MGD than at 3.0 MGD?
A jar test at the 2.5 mg/L dose leaves a residual of 0.8 mg/L. Find the chlorine demand.
The operator wants a 1.0 mg/L residual leaving the plant. Using the demand from problem 4, find the dose needed.
Find the chlorine feed, in pounds per day, at the new dose from problem 5 and the original flow of 3.0 MGD.
Is the plan in problems 5 and 6 acceptable? Check the 1.0 mg/L residual against the 0.2 to 2.0 mg/L distribution range and the 4.0 mg/L limit.
Explain why an operator measures chlorine demand before setting a feed rate, rather than just dosing to the target residual.

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: 62.55 pounds per day.
Loading = 2.5 mg/L x 3.0 MGD x 8.34 = 62.55 pounds per day.
Answer: 83.4 pounds per day.
Loading = 2.5 mg/L x 4.0 MGD x 8.34 = 83.4 pounds per day.
Answer: 20.85 pounds per day.
83.4 - 62.55 = 20.85 pounds per day. The higher flow needs more chlorine to hold the same dose.
Answer: 1.7 mg/L.
Demand = dose - residual = 2.5 mg/L - 0.8 mg/L = 1.7 mg/L. This is the chlorine used up by the water before any residual is left.
Answer: 2.7 mg/L.
Dose needed = demand + desired residual = 1.7 mg/L + 1.0 mg/L = 2.7 mg/L.
Answer: 67.55 pounds per day.
Loading = 2.7 mg/L x 3.0 MGD x 8.34 = 67.554, which rounds to 67.55 pounds per day.
Answer: Yes, acceptable.
The 1.0 mg/L residual falls inside the typical 0.2 to 2.0 mg/L distribution range and is well below the 4.0 mg/L limit, so the plan is acceptable.
Answer: Demand must be met first.
Accept any sound explanation: some chlorine is consumed by material in the water (the demand) before any residual remains, so dosing only to the target residual would leave too little chlorine. The operator must add enough to cover the demand and then the desired residual on top of it.

Differentiation

Support

Provide a printed reference card with the pounds formula and the demand relationships spelled out, and work problem 1 as a class example before students continue. Allow a calculator for every step.

Extension

Suppose the fictional plant's demand rises to 2.2 mg/L during a warm spell while the operator still wants a 1.0 mg/L residual. Ask students to find the new dose and the new feed in pounds per day, and to confirm the residual still fits the distribution range.

ELL supports

Pre-teach "dose," "demand," and "residual" with a simple picture: chlorine going in, part used up, part left over. Provide a sentence frame for problem 8: "Demand is the chlorine that gets ___, so the operator must add ___ before the residual."