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Math problem set Grade 12 Math

Wraymont Plant: Chlorine Dose, Demand, and Hypochlorite Feed

A grade 12 problem set on a fictional treatment plant, using the pounds formula to size chlorine dose, demand, hypochlorite feed, and clearwell contact time.

Objectives

  1. Students will apply the pounds formula to find daily chlorine feed from dose and flow.
  2. Students will convert a percent hypochlorite strength into gallons of solution per day.
  3. Students will compute clearwell detention time and check a residual against the standard.

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.

Also: chlorine dose, chlorine demand, residual, hypochlorite

Teacher overview

The fictional Wraymont Water Treatment Plant chlorinates its finished water, and its operators size the chemical feed with the same pounds formula that appears on certification exams. This set moves from dose and demand through the daily pounds of chlorine, the gallons of hypochlorite that deliver those pounds, and the contact time the clearwell provides. A common error is confusing dose with demand: the dose is all the chlorine added, while the demand is only the part consumed before a residual is left, and the pounds formula must be fed the right one for each question.

Wraymont Plant: Chlorine Dose, Demand, and Hypochlorite Feed — Grade 12 Math
Name: ____________________________ Date: ______________

Problems

All figures describe the fictional Wraymont plant, which treats 3.5 MGD. The operator adds a chlorine dose of 2.4 mg/L and measures a residual of 0.6 mg/L leaving the clearwell. The plant feeds 10 percent sodium hypochlorite. The clearwell holds 100,000 gallons. Use: pounds per day = mg/L × MGD × 8.34; demand = dose − residual; 1 percent = 10,000 mg/L; detention time = volume ÷ flow. The chlorine standard sets a maximum residual disinfectant level of 4.0 mg/L, with systems usually holding 0.2 to 2.0 mg/L in distribution.

  1. Find the chlorine demand, in mg/L.

  2. Find the pounds of chlorine fed per day, using the dose and the plant flow.

  3. Find the pounds of chlorine per day actually consumed by the demand.

  4. Express the 10 percent hypochlorite strength in mg/L, and find the pounds of available chlorine in one gallon of it (use 8.34 lb/gal for the solution).

  5. Find the gallons of 10 percent hypochlorite the plant must feed per day to deliver the chlorine from problem 2. Round to the nearest tenth.

  6. Find the clearwell detention time, in minutes, at the plant's flow.

  7. Is the 0.6 mg/L residual within the usual 0.2 to 2.0 mg/L distribution range and below the 4.0 mg/L maximum? State the margin below the maximum.

  8. Suppose the source worsens and demand rises to 2.6 mg/L, while the plant still wants a 0.6 mg/L residual. Find the new required dose and the new pounds of chlorine per day.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

  1. Answer: 1.8 mg/L.
    Demand = dose − residual = 2.4 − 0.6 = 1.8 mg/L. This is the chlorine consumed before the residual remains.

  2. Answer: 70.1 lb/day.
    Pounds per day = dose × flow × 8.34 = 2.4 mg/L × 3.5 MGD × 8.34 = 70.056, which rounds to 70.1 lb/day.

  3. Answer: 52.5 lb/day.
    Pounds consumed = demand × flow × 8.34 = 1.8 × 3.5 × 8.34 = 52.542, which rounds to 52.5 lb/day. The rest of the fed chlorine remains as residual.

  4. Answer: 100,000 mg/L; 0.834 lb of chlorine per gallon.
    10 percent × 10,000 mg/L per percent = 100,000 mg/L. Available chlorine per gallon = 0.10 × 8.34 lb/gal = 0.834 lb of chlorine per gallon of solution.

  5. Answer: 84.0 gal/day.
    Gallons per day = chlorine pounds ÷ pounds per gallon = 70.056 ÷ 0.834 = 84.0 gallons of 10 percent hypochlorite per day.

  6. Answer: 41.1 min.
    Flow = 3.5 MGD = 3,500,000 gallons per day. Detention time = 100,000 ÷ 3,500,000 = 0.02857 day. Times 1,440 minutes per day = 41.1 minutes in the clearwell.

  7. Answer: yes, 3.4 mg/L below the maximum.
    The 0.6 mg/L residual sits inside the usual 0.2 to 2.0 mg/L range and well under the 4.0 mg/L maximum. The margin below the maximum is 4.0 − 0.6 = 3.4 mg/L.

  8. Answer: 3.2 mg/L dose; 93.4 lb/day.
    New dose = demand + residual = 2.6 + 0.6 = 3.2 mg/L. New pounds per day = 3.2 × 3.5 × 8.34 = 93.408, which rounds to 93.4 lb/day, so the feed must rise from about 70 to about 93 pounds per day.

Differentiation

Support

Provide the pounds formula and the demand relationship on a reference card, and pre-compute problem 1 so the demand of 1.8 milligrams per liter is available for problem 3. Walk one full pounds-formula calculation before students begin, using neutral numbers.

Extension

Ask students to find how many days a 500-gallon hypochlorite storage tank would last at the daily feed rate from problem 5, and how that run time would change if the demand rise in problem 8 became permanent. Have them explain why storage planning depends on source-water quality.

ELL supports

Pre-teach "dose," "demand," "residual," and "hypochlorite" with a simple flow diagram showing chlorine added, chlorine used up, and residual leaving. Provide a worked pounds-formula example with the units written under each number so students can match their own work step by step.