Worksheet Grade 11 Science
Larkfield Commons Runoff: Rational Method and Bioretention Sizing
A grade 11 stormwater worksheet where students use the rational method to compare pre- and post-development runoff and size a bioretention cell for a fictional site.
Objectives
- Students will apply the rational method to compare peak runoff before and after development.
- Students will size a bioretention cell to capture the first flush of runoff from an impervious area.
Vocabulary
- Impervious surface
- An impervious surface is any hard surface, like a road, roof, or parking lot, that rain cannot soak through. The more impervious surface a town has, the more stormwater rushes off it.
- First flush
- First flush is the very first bit of runoff at the start of a rainstorm, which often carries the most pollution because it washes off everything that built up on streets and roofs during the dry period before the rain. Later rainfall in the same storm is usually cleaner.
Also: rational method, runoff coefficient, bioretention, peak flow
Teacher overview
When a field is paved over, the same rainstorm produces a much sharper, faster flood downstream because water can no longer soak into the ground. This worksheet uses the rational method, Q = C x i x A, to put numbers on that change for a fictional redevelopment, then has students size a bioretention cell that catches the dirtiest first flush of runoff. Students should come away seeing green infrastructure as a piece of hydraulic engineering with a size that can be calculated.
Student Worksheet
Larkfield Commons is a fictional 5-acre site being redeveloped from open meadow into stores and parking. Use these stated values. In the rational method Q = C x i x A, the peak runoff Q comes out in cfs when the rainfall intensity i is in inches per hour and the area A is in acres, and C is the unitless runoff coefficient. The design storm intensity is 2.4 inches per hour. Before development the whole site behaves like meadow with C = 0.2. After development the whole site behaves like pavement and roofs with C = 0.85. One acre equals 43,560 square feet, and one cubic foot holds 7.48 gallons.
Find the peak runoff Q before development. Use C = 0.2, i = 2.4, A = 5.
Find the peak runoff Q after development. Use C = 0.85, i = 2.4, A = 5.
How much does the peak runoff increase from before to after development, in cfs?
After development, runoff from 3 of the 5 paved acres (roofs and pavement) drains to the bioretention cell. Convert 3 acres to square feet.
The town requires capturing the first 1 inch of runoff from that 3-acre drainage area. Using the rule that runoff gallons = area (sq ft) x rainfall (inches) x 0.623, find the first-flush volume in gallons.
Convert your first-flush volume from item 5 into cubic feet.
A bioretention cell will hold that first-flush volume. If the cell provides 1.5 feet of effective storage depth (ponding plus the void space in its soil media), what footprint area, in square feet, does the cell need?
Explain, in terms of infiltration, why the after-development peak runoff in item 2 is so much larger than the before-development peak in item 1.
Explain how a bioretention cell lowers both the peak runoff and the pollutant load leaving the site.
The town rule also says the after-development peak must not exceed the before-development peak from item 1. Does capturing the first flush by itself meet that rule for the full design storm? Explain what else the site would need.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
Answer: 2.4 cfs. Q = C x i x A = 0.2 x 2.4 x 5 = 2.4 cfs.
Answer: 10.2 cfs. Q = 0.85 x 2.4 x 5 = 10.2 cfs.
Answer: 7.8 cfs. The peak rises from 2.4 to 10.2 cfs, an increase of 10.2 - 2.4 = 7.8 cfs; the new peak is more than four times the original.
Answer: 130,680 sq ft. 3 acres x 43,560 square feet per acre = 130,680 square feet.
Answer: about 81,400 gallons. 130,680 sq ft x 1 inch x 0.623 = 81,413.6, which rounds to about 81,400 gallons.
Answer: about 10,880 cu ft. 81,413.6 gallons / 7.48 gallons per cubic foot = 10,884 cubic feet, about 10,880 cubic feet.
Answer: about 7,260 sq ft. Footprint = volume / depth = 10,884 cubic feet / 1.5 feet = 7,256 square feet, about 7,260 square feet.
Answer: Before development, meadow soil let most of the rain soak in, so only a small fraction ran off (C = 0.2). After development, roofs and pavement block infiltration, so most of the rain runs off quickly (C = 0.85), producing a much higher and faster peak.
Answer: The cell holds runoff and lets it soak slowly into the ground and its plants, so less water rushes downstream at once, lowering the peak. As the water filters through soil and roots, sediment, oil, and nutrients are trapped, lowering the pollutant load.
Answer: No. Capturing the first inch controls water quality and small storms, but the full design storm produces far more runoff than the first flush, so the peak from item 2 would still exceed the item 1 target. The site would also need detention storage that releases water slowly to bring the peak back down to the pre-development rate.
Differentiation
Support
Provide the rational-method formula with each variable already labeled and the units written beside it, and work one example (a 1-acre lawn) together before item 1. Give the acre-to-square-foot and gallon-to-cubic-foot conversions on a reference card so students focus on setting up each step.
Extension
Suppose the site must release the design storm at no more than 2.4 cfs. Have students design the detention needed in item 10, estimate the extra storage volume required, and explain why detention and bioretention solve two different parts of the stormwater problem.
ELL supports
Pre-teach "runoff," "impervious," "infiltration," "first flush," and "bioretention" with paired images of a meadow and a parking lot in the same rainstorm. Allow items 8, 9, and 10 to be answered with a labeled diagram and a short sentence rather than a full paragraph.