Lesson plan Grade 12 Engineering & Design

Sizing a Stormwater Basin for Perch Hollow High: The Rational Method

A 55-minute grade 12 engineering lesson where students use the Rational Method to compare pre- and post-development runoff for a fictional paved lot and size detention.

Grade: Grade 12
Subject: Engineering & Design
Material: Lesson plan
Time: 55 min
Prep: Low prep
Materials: Calculator, Printed site map and runoff-coefficient reference (teacher-provided), Projector with two photos of one lot, grassy and paved, Index cards for the exit ticket

Standards

HS-ETS1-1 NGSS

Analyze a major global challenge to specify qualitative and quantitative criteria and constraints for solutions that account for societal needs and wants.

How this material aligns: The worked example and practice treat the design-storm intensity and drainage area as the quantitative criteria, and the requirement that post-development peak flow not exceed the pre-development peak as the constraint that sizes the detention basin, the criteria-and-constraints reasoning this standard defines.

All materials for HS-ETS1-1 →

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: In guided practice students carry acres, inches per hour, and cubic feet per second through the Rational Method calculation, the unit-consistent multi-step reasoning this standard targets.

All materials for HSN-Q.A.1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-17.

Objectives

Students will calculate peak stormwater runoff for a site using the Rational Method Q = C x i x A.
Students will compare pre- and post-development runoff and estimate the extra volume a detention basin must hold.

Vocabulary

Detention basin: A detention basin is a dug-out area that fills with stormwater during a storm and then slowly drains empty over hours or days. It holds the water back so streets and streams downstream do not flood.
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.

Also: Rational Method, runoff coefficient, peak flow

Teacher overview

When a school paves a grassy lot, rain that once soaked into the ground runs off the new hard surface instead, and the peak flow leaving the site can rise sharply. This lesson has students use the Rational Method, the standard formula stormwater engineers use for small drainage areas, to compare runoff from the fictional Perch Hollow High School lot before and after it is paved, then estimate the extra runoff a detention basin must hold. A common misconception is that a detention basin must store all the runoff from a storm; in fact it is sized to hold the increase caused by development, releasing water slowly so the downstream peak does not rise.

Procedure

Hook (5 min): Project two photos of the same lot, one grassy and one paved. Ask students to predict, with a show of hands, whether paving doubles the runoff, triples it, or leaves it about the same. Record the split without comment; the math will settle it.

Direct instruction (12 min): Introduce the Rational Method: peak runoff Q (in cubic feet per second, cfs) = C x i x A, where C is the runoff coefficient, i is the rainfall intensity in inches per hour, and A is the drainage area in acres. Explain that C reflects how much rain runs off rather than soaking in: a typical value is about 0.9 for pavement and about 0.2 for a lawn. Note that with A in acres and i in inches per hour, Q comes out in cfs by the standard convention.

Worked example (13 min): Work the fictional Perch Hollow lot: 3.0 acres, design-storm intensity 2.5 inches per hour. Pre-development (lawn, C = 0.2): Q = 0.2 x 2.5 x 3.0 = 1.5 cfs. Post-development (paved, C = 0.9): Q = 0.9 x 2.5 x 3.0 = 6.75 cfs. The increase is 6.75 - 1.5 = 5.25 cfs. Convert the post-development flow to gpm as a check: 6.75 cfs x 448.8 = 3,029.4 gpm. Then show a simple detention estimate: if the extra 5.25 cfs runs for a 20-minute storm, the volume is 5.25 x (20 x 60) = 6,300 cubic feet, or about 6,300 x 7.48 = 47,124 gallons the basin must hold.

Guided practice (12 min): In pairs, students work a second fictional lot: 2.0 acres, intensity 3.0 inches per hour, lawn C = 0.2 and pavement C = 0.9. They first find the pre-development (lawn) flow as a warm-up, then answer Question 1 and subtract the two flows to state the increase, checking each other's units.

Question 1. What is the post-development (paved) peak runoff for this lot, in cubic feet per second?

Independent practice (8 min): Each student answers Question 2 on the handout, then states in one sentence what happens to that flow if the intensity doubles.

Question 2. What is the post-development runoff for a 1.5-acre paved plaza (C = 0.9) at 2.0 inches per hour, in cubic feet per second?

Closure / exit ticket (5 min): On an index card, students answer Question 3. Collect and scan for the correct setup (0.9 x 2.0 x 1.0) before dismissal.

Question 3. A 1.0-acre paved lot (C = 0.9) sees a storm of 2.0 inches per hour. What is the peak runoff in cubic feet per second?

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: 5.4 cfs (Question 1, guided practice, post-development flow). Post-development: Q = 0.9 x 3.0 x 2.0 = 5.4 cfs. Pre-development, for the increase comparison: Q = 0.2 x 3.0 x 2.0 = 1.2 cfs. The increase is 5.4 - 1.2 = 4.2 cfs.
Answer: 2.7 cfs (Question 2, independent practice). Q = 0.9 x 2.0 x 1.5 = 2.7 cfs. If the intensity doubles to 4.0 inches per hour, the runoff doubles to 5.4 cfs, because Q is directly proportional to intensity.
Answer: 1.8 cfs (Question 3, exit ticket). Q = 0.9 x 2.0 x 1.0 = 1.8 cfs.

Differentiation

Support

Provide a partially completed calculation frame with the Rational Method written out and one term already filled in for each practice item, so students substitute the remaining values. Give the runoff coefficients on a printed card rather than from memory.

Extension

Ask students to explain, with their own numbers, why raising the runoff coefficient has the same proportional effect on peak flow as raising the rainfall intensity, and to propose one design change (such as permeable pavement) that would lower the site's effective coefficient.

ELL supports

Pre-teach "runoff," "coefficient," "intensity," and "detention" with a labeled diagram of rain hitting a lawn versus pavement. Provide sentence frames for the exit-ticket explanation and allow calculations to be shown as labeled equations.

Extensions

Have students walk the school grounds and estimate the area and surface type of one real drainage area, then apply the Rational Method with a teacher-provided design intensity to estimate its peak runoff, discussing where that water goes and whether the site has any detention already.