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Worksheet Grade 12 Careers & CTE

Marchbourne Creek Spill Response: Coordinator Field Math

Grade 12 worksheet using stream velocity, travel time, and the pounds formula to judge how a fertilizer spill affects a fictional town's drinking water intake.

Objectives

  1. Students will calculate stream velocity from discharge and cross-sectional area and use it to find travel time to a downstream intake.
  2. Students will calculate a contaminant concentration in a stream and in a reservoir using the pounds formula.
  3. Students will evaluate three response measures against the physical behavior of a dissolved contaminant.

Vocabulary

Action level
A trigger number in lead and copper testing. If too many homes test above this level, the utility must take steps like improving treatment and telling the public.

Also: discharge, cross-sectional area, travel time, dilution, source water

Teacher overview

When a spill reaches a stream that supplies a drinking water intake, one of the first questions a response coordinator answers is how long the utility has before the contaminant arrives. This worksheet places students in that role after a tanker accident on Marchbourne Creek upstream of the fictional town of Foxcote, and works through velocity, travel time, in-stream concentration, and reservoir dilution before asking which response measure would actually help. The error to watch for is the assumption that a larger stream always dilutes a spill to safety, since the concentration depends on the mass released and the volume of water passing during the release rather than on the size of the stream alone.

Marchbourne Creek Spill Response: Coordinator Field Math — Grade 12 Careers & CTE
Name: ____________________________ Date: ______________

Student Worksheet

A tanker carrying liquid fertilizer overturns on a bridge over Marchbourne Creek, 3.2 miles upstream of the drinking water intake serving the fictional town of Foxcote. Responders estimate that 900 pounds of nitrogen entered the creek during a release lasting one hour. At the accident site the creek is flowing at 38 cfs, with an average width of 22 feet and an average depth of 1.8 feet. Foxcote's utility has set an internal action level of 12 mg/L of nitrogen at the intake for this event. The intake reservoir holds 46 million gallons. Use 5,280 feet per mile, 448.8 gallons per minute per cubic foot per second, 1.547 cubic feet per second per MGD, and 8.34 pounds per gallon. Show your work and label every unit.

  1. Calculate the creek's cross-sectional area at the accident site, in square feet.
  2. Using Q = A x V, calculate the creek's average velocity in feet per second. Round to two decimal places.
  3. Calculate how long the leading edge of the spill takes to travel 3.2 miles to the intake, in hours. Round to one decimal place.
  4. Convert the creek's discharge of 38 cfs to million gallons per day. Round to one decimal place.
  5. Convert the creek's discharge of 38 cfs to gallons per minute.
  6. Calculate how many gallons of creek water passed the accident site during the one-hour release.
  7. Express your answer to item 6 in million gallons. Round to two decimal places.
  8. Calculate the average nitrogen concentration in the creek water that passed during the release, using concentration (mg/L) = pounds / (million gallons x 8.34). Round to one decimal place.
  9. Calculate the dilution factor needed to bring the concentration from item 8 down to the utility's 12 mg/L action level. Round to one decimal place.
  10. If the entire 900 pounds of nitrogen mixes completely into the 46 million gallons held in the intake reservoir, calculate the resulting concentration in mg/L. Round to one decimal place.
  11. Compare your answer to item 10 with the utility's action level. Would the fully mixed reservoir concentration stay below the action level? Answer yes or no.
  12. The response team can close the intake for eight hours, place a floating boom across the creek mouth, or increase the coagulant dose at the treatment plant. Nitrogen from this fertilizer is fully dissolved in the water. Which measure keeps the most concentrated dissolved nitrogen out of the treatment plant?

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: 39.6 square feet. Area = 22 feet wide x 1.8 feet deep = 39.6 square feet.
  2. Answer: 0.96 ft/s. Rearranging Q = A x V gives V = 38 cubic feet per second / 39.6 square feet = 0.9596, which rounds to 0.96 feet per second.
  3. Answer: 4.9 hours. The distance is 3.2 miles x 5,280 feet per mile = 16,896 feet. Time = 16,896 feet / 0.96 feet per second = 17,600 seconds, and 17,600 / 3,600 seconds per hour = 4.89, which rounds to 4.9 hours.
  4. Answer: 24.6 MGD. Flow = 38 cfs / 1.547 cfs per MGD = 24.56, which rounds to 24.6 million gallons per day.
  5. Answer: 17,054.4 gpm. Flow = 38 cfs x 448.8 gpm per cfs = 17,054.4 gallons per minute.
  6. Answer: 1,023,264 gallons. Volume = 17,054.4 gallons per minute x 60 minutes = 1,023,264 gallons.
  7. Answer: 1.02; that is 1.02 million gallons. Dividing, 1,023,264 gallons / 1,000,000 = 1.023264, which rounds to 1.02 million gallons.
  8. Answer: 105.5 mg/L. Concentration = 900 pounds / (1.023264 million gallons x 8.34 pounds per gallon). The denominator is 8.534, and 900 / 8.534 = 105.46, which rounds to 105.5 milligrams per liter.
  9. Answer: 8.8. Dilution factor = 105.5 mg/L / 12 mg/L = 8.79, which rounds to 8.8. The slug has to be diluted to roughly nine times its original volume before its concentration reaches the action level.
  10. Answer: 2.3 mg/L. Concentration = 900 pounds / (46 million gallons x 8.34 pounds per gallon). The denominator is 383.64, and 900 / 383.64 = 2.346, which rounds to 2.3 milligrams per liter.
  11. Answer: Yes. At 2.3 mg/L the fully mixed reservoir sits well under the 12 mg/L action level, which is why holding the intake closed until the slug passes and then relying on reservoir mixing is a workable strategy here.
  12. Answer: Closing the intake for eight hours. The travel time from item 3 is under five hours, so an eight-hour closure keeps the most concentrated water out of the plant entirely. A floating boom holds back material that floats on the surface and does nothing for a contaminant already dissolved through the water column, and coagulant removes particles rather than dissolved nitrogen, so neither of the other measures keeps the dissolved nitrogen out of the plant.

Differentiation

Support

Provide a labeled sketch of the creek cross-section for item 1 and give the mile-to-foot conversion already worked for item 3. Supply the pounds formula rearranged for concentration on a reference card, and complete item 8 with the class before students attempt item 10 on their own. Students who complete items 1 through 8 have met the first two objectives.

Extension

Ask students to calculate how much longer the intake would have to stay closed if the creek were flowing at half the discharge given here, and explain why a low-flow spill is the harder case. Students can also design a sampling plan that states where and how often they would collect samples between the bridge and the intake, and what result would justify reopening.

ELL supports

Pre-teach discharge, cross-section, velocity, travel time, dilution, and action level with a plan-view diagram showing the bridge, the creek, the intake, and the reservoir with the distance labeled. Provide a units checklist students can tick as they complete each conversion, and allow items 11 and 12 to be answered with a choice plus one supporting number.

Extensions

Have students locate the source water assessment their own utility has published and identify the roads, rail lines, or facilities listed as potential contamination sources upstream of the intake. Students can also invite a county emergency management official to describe how a spill notification actually reaches a water utility and how quickly an intake can be closed.