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Worksheet Grade 12 Careers & CTE

Operator Exam Math at Wexmoor Water Plant

A grade 12 careers worksheet of operator-certification math at a fictional plant, using the pounds formula, flow, tank volume, and pressure conversions.

Objectives

  1. Students will apply the pounds formula to find a plant's daily chlorine feed.
  2. Students will convert among flow, volume, and pressure units used on operator exams.

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.
Flow rate
Flow rate measures how much water moves past a point in a certain amount of time, like gallons per minute through a garden hose. Bigger pipes and stronger pushes give bigger flow rates.

Also: pounds formula, head pressure

Teacher overview

Operator certification exams test the same handful of conversions again and again: turning a chemical dose into pounds per day, moving between cubic feet and gallons, and converting the height of water into pressure. This worksheet drills those skills on one fictional plant so the numbers stay connected. A common error is using a tank's diameter in the volume formula without squaring it correctly, or reporting a volume in cubic feet when the question asks for gallons. Encourage students to write the unit next to every number as they work.

Operator Exam Math at Wexmoor Water Plant — Grade 12 Careers & CTE
Name: ____________________________ Date: ______________

Student Worksheet

Wexmoor Water Plant is a fictional plant used for this worksheet. It treats 3.5 million gallons per day (MGD). Use these standard operator conversions and formulas for every problem:

  • One gallon of water weighs 8.34 pounds.
  • Chlorine feed in pounds per day = dose (mg/L) times flow (MGD) times 8.34.
  • Flow Q = area times velocity.
  • Pressure (psi) = height of water (ft) times 0.433.
  • One MGD = 694 gallons per minute.
  • Cylindrical tank volume (cubic feet) = 0.785 times diameter squared times depth.
  • One cubic foot holds 7.48 gallons.
  1. The plant doses chlorine at 2.4 mg/L across its 3.5 MGD flow. How many pounds of chlorine per day does it feed? Round to the nearest tenth.
  2. Convert the plant's flow of 3.5 MGD to gallons per minute.
  3. A main pipe leaving the plant has a cross-sectional area of 0.8 square feet, and water moves through it at 3.5 feet per second. Using Q = area times velocity, find the flow in cubic feet per second (cfs).
  4. The plant's clearwell is a cylinder 30 feet in diameter and 16 feet deep. Using volume = 0.785 times diameter squared times depth, find its volume in cubic feet.
  5. Convert the clearwell volume from problem 4 (11,304 cubic feet) to gallons.
  6. The Wexmoor water tower holds its surface 150 feet above the Birch Street neighborhood. Find the water pressure at Birch Street, to the nearest whole psi.
  7. Distribution systems generally run between 40 and 80 psi. Is the Birch Street pressure from problem 6 within that range? Explain in one sentence.
  8. The plant's 3.5 MGD flow (3,500,000 gallons per day) passes through the clearwell, which holds 84,554 gallons. Find the detention time in hours, using detention time = volume divided by flow. First convert the daily flow to gallons per hour by dividing by 24.

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: 70.1 lb/day. Chlorine feed = 2.4 mg/L times 3.5 MGD times 8.34 = 70.056, which rounds to 70.1 pounds per day.
  2. Answer: 2,429 gpm. 3.5 MGD times 694 gallons per minute per MGD = 2,429 gallons per minute.
  3. Answer: 2.8 cfs. Q = 0.8 square feet times 3.5 feet per second = 2.8 cubic feet per second.
  4. Answer: 11,304 cu ft. Volume = 0.785 times 30 squared times 16 = 0.785 times 900 times 16 = 11,304 cubic feet.
  5. Answer: 84,554 gal. 11,304 cubic feet times 7.48 gallons per cubic foot = 84,553.92, which rounds to 84,554 gallons.
  6. Answer: 65 psi. Pressure = 150 feet times 0.433 = 64.95, which rounds to 65 psi.
  7. Answer: Yes. The Birch Street pressure of about 65 psi falls between 40 and 80 psi, so it is within the usual distribution range.
  8. Answer: 0.58 hr. The flow is 3,500,000 gallons per day divided by 24, which is about 145,833 gallons per hour. Detention time = 84,554 divided by 145,833 = about 0.58 hours, or roughly 35 minutes.

Differentiation

Support

Provide a conversion reference strip listing "1 cubic foot = 7.48 gallons," "1 MGD = 694 gpm," and "psi = feet times 0.433," and give the value 30 squared (900) already computed for problem 4 so students focus on the full volume calculation.

Extension

Ask students to find what chlorine dose, in mg/L, would raise the plant's feed to exactly 100 pounds per day at the fictional plant's 3.5 MGD flow, working backward through the pounds formula, and to show the algebra.

ELL supports

Pre-teach "dose," "flow," "detention time," and "head pressure" with a labeled plant diagram that shows where each is measured. Allow students to answer problem 7 by circling "within range" or "outside range" and adding a short reason.

Extensions

Have students look up the certification formula sheet their state gives operators for the entry-level exam and compare which of the formulas on this worksheet appear on it. Most state programs publish the sheet for free, which shows students that this math is exactly what the licensing exam expects.