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Worksheet Grade 12 Math

Wickham Commons: Green Infrastructure Runoff and Detention

A grade 12 stormwater worksheet using the rational method: composite runoff coefficients, peak flow in cfs and gpm, and detention volume for a redevelopment site.

Objectives

  1. Students will compute a composite runoff coefficient and peak runoff using the rational method Q equals C times i times A.
  2. Students will convert between cfs, gpm, acres, cubic feet, and gallons while estimating detention volume for a redeveloped site.

Vocabulary

Green infrastructure
Green infrastructure uses soil and plants, like rain gardens, green roofs, and street trees, to soak up rainwater where it falls instead of piping it away. It copies the way nature handles rain.

Also: rational method, runoff coefficient, peak flow, detention

Teacher overview

When a paved site is redeveloped with bioretention areas and permeable surfaces, less of each storm runs off and more soaks in. This worksheet uses the fictional Wickham Commons redevelopment to practice the rational method, Q equals C times i times A, the same peak-flow tool a stormwater engineer uses to size pipes and basins. A common misconception to correct is that adding green infrastructure changes how much rain falls; it does not. It lowers the runoff coefficient, so a smaller fraction of the same rainfall leaves the site as runoff.

Wickham Commons: Green Infrastructure Runoff and Detention — Grade 12 Math
Name: ____________________________ Date: ______________

Student Worksheet

Wickham Commons is a fictional 5-acre parcel being redeveloped. Use these design values for every item. Peak runoff uses Q equals C times i times A, which gives flow in cfs when intensity is in inches per hour and area is in acres.

  • Total site area: 5 acres
  • Existing condition: fully paved, runoff coefficient C equals 0.90
  • Design-storm intensity for peak flow: 2.5 inches per hour
  • After redevelopment: 3 acres stay paved (C equals 0.90) and 2 acres become lawn and bioretention (C equals 0.20)
  • Separate design-storm rainfall depth for volume: 1.5 inches
  • Conversions: 1 cfs equals 448.8 gpm; 1 acre equals 43,560 square feet; 1 cubic foot equals 7.48 gallons
  1. Calculate the existing peak runoff in cfs for the fully paved site, using C equals 0.90, i equals 2.5, and A equals 5.
  2. Find the composite (area-weighted) runoff coefficient after redevelopment, combining the 3 paved acres and the 2 bioretention acres.
  3. Calculate the new peak runoff in cfs after redevelopment, using your composite coefficient from item 2.
  4. How much lower, in cfs, is the redeveloped peak runoff than the existing peak runoff?
  5. Express that reduction as a percent of the existing peak runoff. Round to the nearest tenth.
  6. Convert the redeveloped peak runoff from item 3 to gpm, using 1 cfs equals 448.8 gpm. Round to the nearest whole gpm.
  7. Convert the 5-acre site area to square feet, using 1 acre equals 43,560 square feet.
  8. Estimate the redeveloped runoff volume for the 1.5-inch design storm, using volume equals composite C times rainfall depth in feet times area in square feet. Give the answer in cubic feet.
  9. Convert your runoff volume from item 8 to gallons, using 1 cubic foot equals 7.48 gallons. Round to the nearest gallon.
  10. Explain why the bioretention areas lower the site's peak runoff even though the same amount of rain falls on the parcel.

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: 11.25 cfs. Q equals 0.90 times 2.5 times 5, which is 11.25 cfs.
  2. Answer: 0.62. The composite coefficient is (3 times 0.90 plus 2 times 0.20) divided by 5, which is (2.7 plus 0.4) divided by 5, or 3.1 divided by 5, equal to 0.62.
  3. Answer: 7.75 cfs. Q equals 0.62 times 2.5 times 5, which is 7.75 cfs.
  4. Answer: 3.5 cfs. The reduction is 11.25 minus 7.75, which is 3.5 cfs.
  5. Answer: 31.1 percent. The reduction of 3.5 divided by 11.25 is 0.3111, or about 31.1 percent.
  6. Answer: 3,478 gpm. 7.75 cfs times 448.8 gpm per cfs equals 3,478.2, or about 3,478 gpm.
  7. Answer: 217,800 square feet. 5 acres times 43,560 square feet per acre equals 217,800 square feet.
  8. Answer: 16,880 cubic feet. The 1.5-inch depth is 0.125 feet; volume equals 0.62 times 0.125 times 217,800, which is 16,879.5, or about 16,880 cubic feet.
  9. Answer: 126,259 gallons. 16,879.5 cubic feet times 7.48 gallons per cubic foot equals 126,258.7, or about 126,259 gallons.
  10. Answer: Bioretention lowers the runoff coefficient. The same rainfall lands on the site, but the planted, permeable areas let water soak in instead of running off, so a smaller fraction of the rain becomes runoff and the peak flow drops.

Differentiation

Support

Provide the composite-coefficient calculation set up as a table with columns for area and coefficient, so students only fill in the products and the division. Work item 1 together, then let students reuse the pattern in item 3.

Extension

Ask students to find the runoff coefficient the whole 5-acre site would need to cut the existing peak runoff in half, then describe one combination of paved and bioretention acreage that would reach that coefficient.

ELL supports

Pre-teach "runoff," "coefficient," "peak," and "detention" with a labeled cross-section showing rain, a paved surface, and a planted basin. Provide the sentence frame "The coefficient dropped from ___ to ___ because ___" for item 10.

Extensions

Have students look up their own school's site area and estimate its runoff coefficient by sketching paved versus planted areas, then apply the rational method with a rainfall intensity from a local design chart to compare with the fictional Wickham Commons results.