Worksheet Grade 9 Science
Copperfield Commons: Stormwater Runoff and the Rational Method
A grade 9 worksheet using the rational method to show how paving a fictional site raises peak stormwater runoff into a creek, and how green infrastructure lowers it.
Objectives
- Students will use the rational method to calculate peak stormwater runoff before and after land development.
- Students will explain how increasing the runoff coefficient raises peak flow and how green infrastructure reduces it.
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.
- 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: runoff coefficient, peak flow, rational method
Teacher overview
Engineers estimate how much stormwater will rush off a site during a design storm using the rational method, Q = C x i x A. The runoff coefficient C describes how much rain runs off instead of soaking in: a meadow lets most rain infiltrate, while pavement and rooftops send almost all of it downhill. This worksheet follows a fictional development, Copperfield Commons, to show how the same storm produces a much larger peak flow into Cranewood Creek after the land is paved, and how green infrastructure can pull that peak back down. Watch for students who forget that C has no units and that A is measured in acres.
Student Worksheet
Use these facts about Copperfield Commons, a fictional 8-acre development in the town of Millbrook, for every item. Keep units attached and show your work.
- Rational method: peak runoff Q (cfs) = C x i (in/hr) x A (acres).
- Site area A = 8 acres.
- Runoff coefficient before development (meadow and lawn): C = 0.2.
- Runoff coefficient after development, uncontrolled (pavement and roofs): C = 0.9.
- Design storm rainfall intensity: i = 3 in/hr.
- Roof runoff: gallons = roof area (sq ft) x rainfall (in) x 0.623.
- Before development, the site is meadow and lawn. Calculate the peak runoff Q in cfs using C = 0.2.
- After development with no controls, calculate the peak runoff Q in cfs using C = 0.9.
- How much did the peak runoff increase, in cfs, from before development to after development?
- By what factor did the peak runoff increase? Divide your after-development answer by your before-development answer.
- Convert the uncontrolled after-development peak of 21.6 cfs to gallons per minute, using 1 cfs = 448.8 gpm. Round to the nearest whole gpm.
- Using the runoff coefficient, explain why replacing meadow with pavement and rooftops raises the peak flow that reaches Cranewood Creek during a storm.
- Suppose the developer adds rain gardens and permeable pavement that lower the site's overall runoff coefficient to C = 0.55. Calculate the new peak runoff Q in cfs.
- How much peak runoff, in cfs, does the green-infrastructure design remove compared with the uncontrolled case in item 2?
- One building at Copperfield Commons has a roof of 6,000 sq ft. Using the roof-runoff formula, how many gallons run off that roof during a storm that drops 1.5 inches of rain?
- Explain why directing that rooftop runoff into a cistern or a rain garden reduces the peak flow reaching the creek, and connect your answer to the 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
- Answer: 4.8 cfs. Q = 0.2 x 3 x 8 = 4.8 cfs.
- Answer: 21.6 cfs. Q = 0.9 x 3 x 8 = 21.6 cfs.
- Answer: 16.8 cfs. 21.6 - 4.8 = 16.8 cfs of additional peak runoff.
- Answer: 4.5 times. 21.6 / 4.8 = 4.5, which matches the ratio of the coefficients, 0.9 / 0.2 = 4.5.
- Answer: 9,694 gpm. 21.6 cfs x 448.8 gpm/cfs = 9,694.08, which rounds to 9,694 gpm.
- Answer: Meadow has a low runoff coefficient because most rain soaks into the soil. Pavement and rooftops are impervious, so they have a high runoff coefficient, and nearly all the rain runs off instead of infiltrating. In the rational method, a larger C multiplies the same rainfall and area into a larger peak flow, so more water reaches the creek faster.
- Answer: 13.2 cfs. Q = 0.55 x 3 x 8 = 13.2 cfs.
- Answer: 8.4 cfs. 21.6 - 13.2 = 8.4 cfs removed compared with the uncontrolled case.
- Answer: 5,607 gallons. 6,000 sq ft x 1.5 in x 0.623 = 9,000 x 0.623 = 5,607 gallons.
- Answer: Capturing rooftop runoff in a cistern or rain garden holds back water that would otherwise run straight to the creek, and it lets some of that water soak into the ground. In effect it lowers the site's overall runoff coefficient, so the rational method predicts a smaller peak flow reaching Cranewood Creek.
Differentiation
Support
Provide a filled-in reference showing the rational method with each variable labeled and one worked example using a 4-acre site, so students can match the structure before working the 8-acre site. Allow a calculator and let students check items 1 and 2 with a partner before item 3.
Extension
Ask students to find the runoff coefficient that green infrastructure would need in order to bring the developed site's peak flow back down to its original before-development level, and to comment on whether that target is realistic for a paved development.
ELL supports
Pre-teach "impervious" (water cannot pass through) and "infiltrate" (soak into the ground) with paired images of a puddle on pavement and rain soaking into soil. Provide the sentence frame "Pavement has a ___ runoff coefficient, so the peak flow ___."
Extensions
Have students map the impervious surfaces around the school, such as the roof, parking lot, and walkways, estimate each area, and use the rational method with a local design-storm intensity from the public-works department to predict the peak runoff their campus sends to the nearest storm drain.