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Lesson plan Grade 12 Careers & CTE

Verrant Gorge Dam: Instrument Readings and Safety Decisions

Students act as dam safety technicians, computing average rates of change in seepage and piezometer data and weighing three surveillance responses against criteria.

Objectives

  1. Students will calculate the average rate of change of seepage flow and piezometer head over stated intervals.
  2. Students will project a future reading from a recent rate of change and find when a stated threshold is reached.
  3. Students will evaluate three surveillance responses against prioritized criteria including safety, cost, and reliability.

Vocabulary

Penstock
The huge pipe that carries water from a reservoir down to the turbines in a hydropower plant. Falling water rushes through it with enormous force.

Also: piezometer, seepage, measuring weir, surveillance plan, average rate of change

Teacher overview

Every embankment dam passes some water through its structure, and the technicians who monitor one have to judge which changes in that seepage matter. In this lesson students read eight weeks of instrument data from the fictional Verrant Gorge Dam, calculate how fast seepage and internal water pressure are climbing, project when an action threshold would be crossed, and then weigh what the operator should do about it. The misconception the lesson corrects is the belief that seepage through an earth embankment is itself a sign of failure, when clear seepage collected at a measuring weir is expected behavior and what concerns a dam safety engineer is a rising rate, a change in the water's clarity, or a pressure reading that no longer tracks the reservoir level. Students who hold that belief will treat the week 0 reading as an emergency instead of a baseline.

Procedure

Hook (6 min). Project a cross-section of an embankment dam showing the reservoir, the impervious core, the drainage zone, and a measuring weir at the toe. Ask students whether water passing through the embankment means the dam is failing, and record their answers. Explain that the fictional Verrant Gorge Dam has been monitored this way since it was built and that the numbers they will work with come from its routine surveillance record.

Instrumentation briefing (10 min). Describe the two instruments in the data set. A measuring weir at the toe of the dam collects seepage in a channel and reports it as a flow in gallons per minute. A piezometer, identified in the record as P-3, reports the height of the water surface inside the embankment as a head in feet. Correct the hook misconception directly, then state the two things that make a dam safety engineer act: a rate of increase that does not match reservoir level, and seepage that carries soil particles. Introduce the surveillance plan's action threshold of 90 gpm at the weir.

Modeled calculation (9 min). Work one average rate of change aloud using an interval from a different structure so the model is instruction rather than a keyed answer. Write the difference in readings above the difference in weeks and read the result aloud with its full unit, gallons per minute per week, so students hear that the quantity is a rate of a rate. Ask a student to explain what a negative value would mean here.

Student handout (18 min). Distribute the handout and have students work in pairs. Circulate and check that item 2 uses the week 4 and week 8 readings rather than all five, since averaging across the whole record is the most common error and it hides the acceleration the lesson is about.

Response evaluation and debrief (7 min). Present three responses the operator could authorize: increase inspection frequency to daily and keep generating, lower the reservoir by ten feet over the coming week, or mobilize a contractor to install additional toe drainage. Have each pair rank the three against four criteria you post on the board, which are downstream public safety, cost, reliability of the fix, and generation lost while the reservoir is down. Collect item 6 as an exit ticket, and if fewer than three quarters of the class finds a threshold date inside three weeks, review the projection before the next class.

Verrant Gorge Dam: Instrument Readings and Safety Decisions — Grade 12 Careers & CTE
Name: ____________________________ Date: ______________

Student Handout

You are a dam safety technician at the fictional Verrant Gorge Dam. The table below holds eight weeks of surveillance readings. Seepage is measured at the toe weir in gallons per minute. Piezometer P-3 reports head in feet. Show your work and label every unit.

Week Seepage at toe weir (gpm) Piezometer P-3 head (ft)
0 42 118
2 45 not read
4 51 121
6 60 not read
8 74 129
  1. Calculate the average rate of change in seepage from week 0 to week 8, in gallons per minute per week.
  2. Calculate the average rate of change in seepage from week 4 to week 8, in gallons per minute per week.
  3. Comparing your answers to items 1 and 2, which interval shows the faster increase in seepage? Name the interval.
  4. Calculate the average rate of change in piezometer P-3 head from week 0 to week 8, in feet per week. Round to one decimal place.
  5. If seepage continues to rise at the week 4 to week 8 rate, what would the weir read at week 12?
  6. The surveillance plan sets an action threshold of 90 gpm at the weir. At the week 4 to week 8 rate, how many weeks after week 8 would the threshold be reached? Round to one decimal place.
  7. Convert the week 8 seepage reading to cubic feet per second, using 448.8 gallons per minute per cubic foot per second. Round to two decimal places.
  8. The penstock intake sits 168 feet below the reservoir surface. Calculate the water pressure at the intake in pounds per square inch, using pressure (psi) = head (ft) x 0.433. Round to one decimal place.

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: 4.0 gpm per week. The change is 74 gpm minus 42 gpm = 32 gpm across 8 weeks minus 0 weeks = 8 weeks. Dividing, 32 / 8 = 4.0 gallons per minute per week.
  2. Answer: 5.75 gpm per week. The change is 74 gpm minus 51 gpm = 23 gpm across 8 weeks minus 4 weeks = 4 weeks. Dividing, 23 / 4 = 5.75 gallons per minute per week.
  3. Answer: Weeks 4 through 8. The recent interval is climbing at 5.75 gallons per minute per week against 4.0 for the record as a whole, so seepage is accelerating rather than rising steadily. That difference is exactly what an eight-week average would conceal.
  4. Answer: 1.4 feet per week. The change is 129 ft minus 118 ft = 11 ft across 8 weeks. Dividing, 11 / 8 = 1.375, which rounds to 1.4 feet per week.
  5. Answer: 97 gpm. Four more weeks at 5.75 gallons per minute per week adds 4 x 5.75 = 23 gpm to the week 8 reading, and 74 + 23 = 97 gallons per minute.
  6. Answer: 2.8 weeks. The remaining distance to the threshold is 90 gpm minus 74 gpm = 16 gpm, and 16 / 5.75 = 2.783, which rounds to 2.8 weeks after week 8.
  7. Answer: 0.16 cfs. Flow = 74 gpm / 448.8 gpm per cfs = 0.1649, which rounds to 0.16 cubic feet per second. Written this way the seepage is a small flow, which is why the trend rather than the size of the number is what matters.
  8. Answer: 72.7 psi. Pressure = 168 ft x 0.433 psi per foot = 72.744, which rounds to 72.7 pounds per square inch.

Differentiation

Support

Give students the two subtraction steps for item 1 already set up so the structure of an average rate of change is visible before they build item 2 themselves. Provide a number line marked in weeks with the seepage readings plotted, which makes the acceleration in item 3 visible before it is calculated. Students who complete items 1 through 4 have met the first objective.

Extension

Ask students to fit a line to the five seepage readings, compare the slope of that line with both rates they calculated, and explain which is the better basis for a decision. Students can also research how a state dam safety program classifies dams by hazard potential and what inspection frequency each class requires, then explain how the classification would change the response they recommended.

ELL supports

Pre-teach piezometer, seepage, weir, head, threshold, and penstock with a labeled cross-section that shows where each instrument sits in the structure. Provide the table with the two calculated intervals shaded in different colors so students can see which rows belong to each calculation, and allow item 3 to be answered with the interval alone.

Extensions

Have students locate the national inventory record for a dam near their school, identify its height, storage, and hazard classification, and describe what surveillance a structure of that size would receive. Students can also interview a hydroelectric operator about how generation schedules are set and what happens to those schedules when a surveillance reading crosses a threshold.