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Worksheet Grade 11 Engineering & Design

Aldous Commons Runoff: A Rational-Method Detention Sizing Worksheet

A grade 11 worksheet using the rational method to compare peak runoff before and after developing the fictional Aldous Commons site, then size a detention volume.

Objectives

  1. Students will apply the rational method to find peak runoff before and after a site is developed.
  2. Students will compute a composite runoff coefficient and size a detention volume for the increase in flow.

Vocabulary

Key words: rational method, runoff coefficient, peak flow, detention, impervious

Teacher overview

When a grassy lot becomes a parking lot, rain that once soaked in now runs off, and the peak flow leaving the site rises sharply. Engineers estimate that peak flow with the rational method, Q = C × i × A, where C is a runoff coefficient, i is rainfall intensity, and A is drainage area. This worksheet uses a fictional site, Aldous Commons, to compare runoff before and after development and then size a detention basin to hold the difference. A common error is using one runoff coefficient for a mixed site; when a site has both pavement and lawn, you must combine their coefficients by area into a composite value first.

Aldous Commons Runoff: A Rational-Method Detention Sizing Worksheet — Grade 11 Engineering & Design
Name: ____________________________ Date: ______________

Student Worksheet

Use these facts about the fictional Aldous Commons site for every item:

  • The site is 4 acres. Before development it is all lawn.
  • Lawn has a runoff coefficient of about 0.2. Pavement and roof have a coefficient of about 0.9.
  • After development, 2.5 acres are pavement and roof, and 1.5 acres stay lawn.
  • The design storm intensity is 2.0 inches per hour.
  • With area in acres and intensity in inches per hour, the rational method gives Q in cubic feet per second (cfs). One cfs equals 448.8 gpm. One cubic foot holds 7.48 gallons.
  1. Find the pre-development peak flow, using the lawn coefficient for the whole 4-acre site.
  2. After development, find the peak flow from the 2.5 acres of pavement and roof alone.
  3. After development, find the peak flow from the 1.5 acres of lawn alone.
  4. Add items 2 and 3 to find the total post-development peak flow.
  5. Find the composite runoff coefficient for the developed site, weighting each coefficient by its area and dividing by the total 4 acres.
  6. Find the increase in peak flow caused by developing the site, using item 4 minus item 1.
  7. Convert the increase in peak flow from cfs to gpm.
  8. A detention basin must hold the extra runoff over a 30-minute storm. Find that volume in cubic feet, multiplying the increase in cfs by 1,800 seconds.
  9. Convert the detention volume from cubic feet to gallons.
  10. Explain which land-cover change drove most of the increase in peak flow, and name one green-infrastructure measure that would lower the developed site's runoff coefficient.

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: 1.6 cfs. Q = C × i × A = 0.2 × 2.0 × 4 = 1.6 cubic feet per second.
  2. Answer: 4.5 cfs. Pavement and roof: Q = 0.9 × 2.0 × 2.5 = 4.5 cubic feet per second.
  3. Answer: 0.6 cfs. Lawn: Q = 0.2 × 2.0 × 1.5 = 0.6 cubic feet per second.
  4. Answer: 5.1 cfs. Total post-development peak flow = 4.5 + 0.6 = 5.1 cubic feet per second.
  5. Answer: 0.64. Composite C = (2.5 × 0.9 + 1.5 × 0.2) ÷ 4 = (2.25 + 0.30) ÷ 4 = 2.55 ÷ 4 = 0.6375, about 0.64.
  6. Answer: 3.5 cfs. Increase = post minus pre = 5.1 − 1.6 = 3.5 cubic feet per second.
  7. Answer: 1,570.8 gpm. 3.5 cfs × 448.8 gpm per cfs = 1,570.8 gallons per minute.
  8. Answer: 6,300 cu ft. Volume = 3.5 cubic feet per second × 1,800 seconds = 6,300 cubic feet.
  9. Answer: 47,124 gal. 6,300 cubic feet × 7.48 gallons per cubic foot = 47,124 gallons.
  10. Answer: Paving 2.5 acres. Converting lawn to pavement and roof, which raised the coefficient on more than half the site from 0.2 to 0.9, drove almost all of the increase. Permeable pavement, a rain garden, a green roof, or added lawn area would each lower the composite runoff coefficient by letting more rain soak in.

Differentiation

Support

Provide the rational-method formula and the three conversions on a reference strip, and pre-fill the area and intensity values in each item so students focus on choosing the correct coefficient and carrying units.

Extension

Ask students to find the runoff coefficient the developed site would need in order to keep its peak flow at the pre-development rate they found in item 1, then judge whether that coefficient is achievable with green infrastructure on a 4-acre site.

ELL supports

Pre-teach "runoff," "coefficient," "intensity," and "detention" with a picture pairing bare pavement (fast runoff) and lawn (slow soaking). Allow item 10 to be answered with a labeled sketch of one green-infrastructure measure plus a short caption.