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Worksheet Grade 6 Engineering & Design

Foxglen Road Culvert Capacity and Peak Flow Worksheet

Nine items where students test three fictional replacement culverts against a required peak flow and a project budget, then check a safety margin.

Objectives

  1. Students will identify which culvert options meet a stated peak-flow requirement.
  2. Students will check culvert options against a fixed project budget.
  3. Students will calculate the percent of a culvert's rated capacity that a required peak flow represents.

Vocabulary

Key words: culvert, peak flow, capacity, constraint

Teacher overview

Foxglen Road (a fictional road used for this worksheet) carries an aging culvert, a pipe that channels stormwater under the road, that engineers must replace with a properly sized option. This worksheet has students compare three replacement culverts against the road's required peak stormwater flow and a fixed project budget, then check the chosen design's margin against an even heavier storm, the same criteria-and-constraints reasoning a real culvert replacement requires.

Foxglen Road Culvert Capacity and Peak Flow Worksheet — Grade 6 Engineering & Design
Name: ____________________________ Date: ______________

Student Worksheet

All flow rates and costs on this worksheet are fictional, invented for the Foxglen Road scenario. During a heavy storm, engineers expect a peak flow of 480 gallons per minute at this crossing. The project budget is $2,200. Three replacement culverts are available:

Culvert Maximum capacity (gallons per minute) Cost
Pipe A (12 inch) 300 $1,200
Pipe B (18 inch) 520 $1,900
Pipe C (24 inch) 700 $2,600
  1. Which pipe or pipes have a maximum capacity greater than or equal to the required 480 gallons-per-minute peak flow?
  2. Of the pipe or pipes that meet the flow requirement in problem 1, which one costs less?
  3. Does Pipe B fit within the $2,200 budget? By how many dollars is it under or over?
  4. Does Pipe C fit within the $2,200 budget? By how many dollars is it under or over?
  5. Based on problems 1 through 4, which single pipe should Foxglen Road choose, and why?
  6. Pipe B's capacity is 520 gallons per minute, and the required peak flow is 480 gallons per minute. By how many gallons per minute does Pipe B's capacity exceed the requirement?
  7. What percent of Pipe B's 520 gallons-per-minute capacity does the required 480 gallons-per-minute peak flow represent? Round to the nearest whole percent.
  8. If an even heavier storm produced a peak flow of 550 gallons per minute, would Pipe B still have enough capacity? Explain, using the numbers.
  9. Pipe A costs $1,200, the least expensive option. Using Pipe A's flow capacity as evidence, explain why the lowest-cost option is not always the right engineering choice.

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: Pipes B and C. Pipe B (520 gpm) and Pipe C (700 gpm) both meet or exceed 480 gpm; Pipe A (300 gpm) does not.
  2. Answer: Pipe B. Pipe B costs $1,900, less than Pipe C's $2,600.
  3. Answer: Under by $300. $2,200 minus $1,900 equals $300 under budget.
  4. Answer: Over by $400. $2,600 minus $2,200 equals $400 over budget.
  5. Answer: Pipe B. It is the only option that both meets the 480 gpm flow requirement and fits within the $2,200 budget; Pipe A fails the flow requirement, and Pipe C exceeds the budget.
  6. Answer: 40 gallons per minute. 520 minus 480 equals 40 gpm.
  7. Answer: 92 percent. 480 divided by 520 equals 0.9231, which rounds to 92 percent.
  8. Answer: No. A 550 gallons-per-minute peak flow would exceed Pipe B's 520 gallons-per-minute capacity by 30 gallons per minute, so Pipe B would be undersized for that heavier storm.
  9. Answer: Pipe A's 300 gallons-per-minute capacity is well below the required 480 gallons-per-minute peak flow, so it would not carry the storm's water even though it costs the least; an engineer must first check that a design meets its required constraints, such as flow capacity, before comparing cost.

Differentiation

Support

Provide a printed comparison table with the flow-requirement column and budget column already highlighted, and let students check off each pipe as "meets" or "fails" for each requirement before calculating any dollar or percent figures.

Extension

Ask students to find the minimum flow capacity, in whole gallons per minute, that a fourth replacement pipe would need in order to leave at least a 100 gallons-per-minute safety margin above the 480 gallons-per-minute peak flow.

ELL supports

Provide a simple cross-section diagram of a culvert pipe under a road with water flowing through it, labeled with the words "capacity" and "peak flow." Allow students to show comparisons using a simple table of checkmarks and numbers rather than full sentences.

Extensions

Have students research, using a teacher-provided map or photo, whether their own school or neighborhood has a visible culvert or storm drain, and describe in writing what they think happens to that pipe's capacity during an unusually heavy storm.