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Worksheet Grade 11 Math

Wendover Valley Hypochlorite Feed: Dose and Pump-Setting Math

A grade 11 operator-math worksheet: turn a chlorine dose at a fictional plant into pounds per day, gallons of 12.5% hypochlorite, and a feed-pump setting.

Objectives

  1. Students will apply the pounds formula to find the daily chlorine feed at a stated dose and flow.
  2. Students will convert a chlorine demand into gallons of 12.5% hypochlorite and a feed-pump setting.
  3. Students will check a working dose against the regulatory maximum residual disinfectant level.

Vocabulary

Key words: hypochlorite, dose, available chlorine, feed pump, pounds formula

Teacher overview

Many small plants disinfect with liquid sodium hypochlorite, a form of bleach, rather than chlorine gas. Turning a target dose into a pump setting takes three linked steps: the pounds formula, a correction for the solution's strength, and a conversion to gallons of product. This worksheet walks grade 11 students through that chain for the Wendover Valley Water Treatment Plant, a fictional plant. A common student error is to stop at pounds of chlorine and forget that a 12.5% solution is mostly water, so the plant must feed far more pounds of product than pounds of actual chlorine.

Wendover Valley Hypochlorite Feed: Dose and Pump-Setting Math — Grade 11 Math
Name: ____________________________ Date: ______________

Student Worksheet

The Wendover Valley Water Treatment Plant is a fictional plant. Use these facts for every item:

  • Plant flow: 1.8 MGD.
  • Target free-chlorine dose: 2.4 mg/L.
  • Disinfectant: sodium hypochlorite, 12.5% available chlorine.
  • The 12.5% solution weighs 10.0 pounds per gallon.
  • Pounds formula: pounds per day = dose (mg/L) x flow (MGD) x 8.34.
  • Strength conversion: a 1% solution equals 10,000 mg/L.
  • Feed-pump maximum output: 5.0 gallons per hour.
  1. Using the pounds formula, how many pounds of chlorine per day must the plant feed to hold a 2.4 mg/L dose at 1.8 MGD? Round to the nearest tenth.
  2. Express the strength of a 12.5% hypochlorite solution in mg/L, using the rule that a 1% solution equals 10,000 mg/L.
  3. The hypochlorite is only 12.5% available chlorine. How many pounds of the 12.5% solution per day are needed to deliver the chlorine from item 1? Divide by 0.125 and round to the nearest pound.
  4. The 12.5% solution weighs 10.0 pounds per gallon. How many gallons of solution per day does that require? Round to the nearest tenth.
  5. Convert the daily solution use from item 4 into gallons per hour. Round to the nearest hundredth.
  6. The feed pump's maximum output is 5.0 gallons per hour. What percent of the pump's maximum is the setting from item 5? Round to the nearest whole percent.
  7. A delivery fills a 500-gallon day tank with the 12.5% solution. At the item 4 usage rate, how many days will one full tank last? Round to the nearest tenth.
  8. Explain in one or two sentences why the plant feeds far more pounds of hypochlorite solution than pounds of actual chlorine.
  9. For a summer taste-and-odor episode the plant raises its target dose to 3.0 mg/L. Recalculate the pounds of chlorine per day at 1.8 MGD. Round to the nearest tenth.
  10. Using your item 9 answer, how many gallons of 12.5% solution per day are now needed? Divide by 0.125, then by 10.0 pounds per gallon. Round to the nearest tenth.
  11. The maximum residual disinfectant level (MRDL) for chlorine is 4.0 mg/L, a limit on the chlorine left in the water in the distribution system. Because the residual can never be more than the dose, can the summer dose of 3.0 mg/L produce a residual above the MRDL? By at least how much would the residual stay below it?

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: 36.0 lb/day.
    2.4 mg/L x 1.8 MGD x 8.34 = 36.03 pounds per day, which rounds to 36.0.
  2. Answer: 125,000 mg/L.
    12.5% x 10,000 mg/L per 1% = 125,000 mg/L of available chlorine. The 10,000 mg/L rule assumes the solution weighs about as much as water. Because this solution is denser (10.0 lb/gal), items 3 and 4 work by weight instead, as operator math problems commonly do.
  3. Answer: 288 lb/day.
    36.03 pounds of chlorine divided by 0.125 (the 12.5% strength) = 288.2, which rounds to 288 pounds of solution per day.
  4. Answer: 28.8 gal/day.
    288.23 pounds per day divided by 10.0 pounds per gallon = 28.82, which rounds to 28.8 gallons per day.
  5. Answer: 1.20 gal/hr.
    28.82 gallons per day divided by 24 hours = 1.201, which rounds to 1.20 gallons per hour.
  6. Answer: 24%.
    1.20 divided by the 5.0 gallons-per-hour maximum = 0.240, or about 24% of the pump's output.
  7. Answer: 17.3 days (accept 17.4).
    500 gallons divided by 28.82 gallons per day = 17.35, which rounds to 17.3 days; using the rounded 28.8 from item 4 gives 17.36, or 17.4 days.
  8. Answer: Because the solution is only 12.5% available chlorine.
    The other 87.5% of the product is water and inert material, so delivering one pound of chlorine takes eight pounds of solution.
  9. Answer: 45.0 lb/day.
    3.0 mg/L x 1.8 MGD x 8.34 = 45.04 pounds per day, which rounds to 45.0.
  10. Answer: 36.0 gal/day.
    45.04 divided by 0.125 = 360.3 pounds of solution; 360.3 divided by 10.0 pounds per gallon = 36.03, or about 36.0 gallons per day.
  11. Answer: no; the residual stays at least 1.0 mg/L below the limit.
    The residual equals the dose minus the chlorine demand, so it cannot exceed 3.0 mg/L, which is 1.0 mg/L under the 4.0 mg/L MRDL.

Differentiation

Support

Give students a labeled flow strip that names the three moves in order: pounds of chlorine (dose x flow x 8.34), then pounds of solution (divide by 0.125), then gallons of solution (divide by 10.0). Provide item 1 already worked so students can focus on the strength and gallons steps.

Extension

Ask students to build a single combined formula that goes straight from dose and flow to gallons of solution per day, then use it to find the gallons needed if the plant switched to a 10% hypochlorite that weighs 9.5 pounds per gallon at the plant's original dose.

ELL supports

Pre-teach "dose," "available chlorine," "solution," and "feed pump" with a simple labeled diagram of a day tank, a metering pump, and the pipe carrying plant flow. Allow students to record each step's result in a three-box graphic organizer rather than in full sentences.

Extensions

Invite a local operator or a public works staff member to describe how their plant sets and checks a chemical feed pump, including how they calibrate the pump against a graduated cylinder. Students can compare the plant's real day-tank size and dose to the fictional Wendover Valley numbers used here.