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Worksheet Grade 12 Math

Operator Unit Conversions at the Oswell Water Authority

A grade 12 math worksheet drilling the flow, volume, weight, and concentration conversions on operator-certification exams, all built around one fictional utility.

Objectives

  1. Students will convert among MGD, gpm, and cfs using standard operator conversion factors.
  2. Students will convert among cubic feet, gallons, acre-feet, and pounds of water.
  3. Students will convert between percent strength, mg/L, and ppm for a treatment solution.

Vocabulary

Acre-foot
The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.

Also: MGD, cfs, percent strength, dimensional analysis

Teacher overview

Operator-certification exams lean heavily on unit conversions, because a treatment plant reports flow in several units at once and dosing math depends on getting them right. This worksheet gives students focused practice using the conversion factors printed on state exam formula sheets, all set at the fictional Oswell Regional Water Authority. A common error is mixing up which factor multiplies and which divides. Carrying the units through each step, so the unwanted units cancel, is the habit that prevents it, and students should show that cancellation on every item.

Operator Unit Conversions at the Oswell Water Authority — Grade 12 Math
Name: ____________________________ Date: ______________

Student Worksheet

Use these standard conversion factors from an operator formula sheet for the fictional Oswell Regional Water Authority. Show your unit cancellation on each item.

  • 1 MGD = 694 gpm
  • 1 MGD = 1.547 cfs
  • 1 cfs = 448.8 gpm
  • 1 acre-foot = 325,851 gallons
  • 1 cubic foot = 7.48 gallons
  • 1 gallon of water weighs 8.34 pounds
  • 1 percent solution strength = 10,000 mg/L
  • 1 mg/L = about 1 ppm in fresh water and other dilute solutions

  1. Convert a plant flow of 5.5 MGD to gallons per minute (gpm).

  2. Convert the same 5.5 MGD flow to cubic feet per second (cfs). Round to the nearest hundredth.

  3. A source stream runs at 12 cfs. Convert this flow to gallons per minute (gpm). Round to the nearest whole gpm.

  4. Convert your answer from item 3 back to MGD. Round to the nearest hundredth.

  5. A basin holds 60,000 cubic feet of water. Convert this volume to gallons.

  6. Convert your answer from item 5 to acre-feet. Round to the nearest hundredth.

  7. A chemical day tank holds 500 gallons of solution. Using 8.34 pounds per gallon, find the weight of that volume of water, in pounds.

  8. A sodium hypochlorite solution is rated at 0.8 percent strength. Express this strength in mg/L.

  9. A laboratory reports water hardness as 120 ppm. Express this value in mg/L.

  10. A reservoir holds 2,500 acre-feet. Convert this volume to gallons.

  11. A well pumps at 900 gpm. Convert this rate to MGD. Round to the nearest hundredth.

  12. Explain how carrying units through a calculation, so the unwanted units cancel, helps you catch an error before you report a wrong number. Use one item above as your example.

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: 3,817 gpm.
    5.5 MGD x 694 gpm per MGD = 3,817 gpm.

  2. Answer: 8.51 cfs.
    5.5 MGD x 1.547 cfs per MGD = 8.5085, which rounds to 8.51 cfs.

  3. Answer: 5,386 gpm.
    12 cfs x 448.8 gpm per cfs = 5,385.6, which rounds to 5,386 gpm.

  4. Answer: 7.76 MGD.
    5,385.6 gpm / 694 gpm per MGD = 7.76 MGD. (Checking against item 2's factor, 12 cfs / 1.547 also gives about 7.76 MGD.)

  5. Answer: 448,800 gallons.
    60,000 cubic feet x 7.48 gallons per cubic foot = 448,800 gallons.

  6. Answer: 1.38 acre-feet.
    448,800 gallons / 325,851 gallons per acre-foot = 1.3773, which rounds to 1.38 acre-feet.

  7. Answer: 4,170 pounds.
    500 gallons x 8.34 pounds per gallon = 4,170 pounds.

  8. Answer: 8,000 mg/L.
    0.8 percent x 10,000 mg/L per percent = 8,000 mg/L.

  9. Answer: 120 mg/L.
    In fresh water, a liter weighs about 1 kilogram, so 1 mg/L is approximately equal to 1 ppm and 120 ppm equals 120 mg/L. In seawater or brine, above about 7,000 mg/L of dissolved solids, the two units differ enough that a density correction is needed.

  10. Answer: 814,627,500 gallons.
    2,500 acre-feet x 325,851 gallons per acre-foot = 814,627,500 gallons, about 815 million gallons.

  11. Answer: 1.30 MGD.
    900 gpm / 694 gpm per MGD = 1.2968, which rounds to 1.30 MGD.

  12. Answer: Cancelling units confirms the result is in the unit you wanted.
    When the factors are set up so the unwanted units divide out, only the target unit is left. In item 1, gpm per MGD times MGD leaves gpm; if a student had divided by 694 instead, the leftover units would not be gpm, signaling the error before the number is reported.

Differentiation

Support

Provide the conversion factors on a printed strip and model item 1 with the units written out and cancelled. Let students use that worked item as a template for the rest, and accept answers that keep one extra decimal place.

Extension

Ask students to chain two conversions in a single setup, for example converting 12 cfs directly to MGD in one line by multiplying by the correct factors so the units cancel, and to explain why the chained answer matches the two-step result.

ELL supports

Give a bilingual glossary card for "flow," "volume," "strength," and "per," and a color code that marks which factor multiplies and which divides. Allow item 12 to be answered with a labeled worked example instead of a paragraph.

Extensions

Have students collect the flow units their local utility publishes in its annual water quality report, then convert each reported figure into the other flow units so they can compare the plant's capacity across the units operators actually use.