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Worksheet Grade 8 Science

Birchford Creek Runoff: The Rational Method and Paving

Grade 8 students use the rational method and runoff coefficients to compare peak stormwater runoff before and after paving a fictional meadow site.

Objectives

  1. Students will calculate peak stormwater runoff using the rational method Q = C x i x A.
  2. Students will find the slope (i x A) of the proportional relationship between C and Q and use it to predict runoff for new surfaces.

Vocabulary

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

Teacher overview

When land is paved, rain that once soaked into the ground runs off instead, and the peak flow into a creek climbs. This worksheet has students use the rational method, a standard stormwater formula, to compare runoff from a meadow and a parking lot on the same land. The site and its numbers belong to a fictional town, while the runoff coefficients are the standard values engineers use.

Birchford Creek Runoff: The Rational Method and Paving — Grade 8 Science
Name: ____________________________ Date: ______________

Student Worksheet

Birchford (a fictional town) plans to pave a 5-acre meadow to build a parking lot. Engineers estimate peak runoff with the rational method: Q = C × i × A, where Q is peak runoff in cubic feet per second, C is the runoff coefficient (a decimal), i is rainfall intensity in inches per hour, and A is drainage area in acres. For the design storm, i = 2 inches per hour. Use C = 0.2 for the meadow and C = 0.9 for pavement.

  1. Write the rational method formula and state what each of the three letters on the right side stands for.
  2. Before development, the 5-acre site is meadow with C = 0.2. With i = 2 inches per hour, calculate the peak runoff Q in cubic feet per second.
  3. After development, the same 5 acres becomes pavement with C = 0.9. Calculate the new peak runoff Q.
  4. How many times greater is the paved runoff than the meadow runoff?
  5. With i and A fixed at 2 inches per hour and 5 acres, Q depends only on C, so Q is proportional to C. If you graphed Q against C, what would the slope of that line be?
  6. Using your slope from item 5, predict Q for a gravel lot with C = 0.5. Then check your prediction by putting C = 0.5 into the full formula.
  7. Explain why paving a watershed increases the peak runoff even though the same amount of rain falls on the land.
  8. A retention pond downstream can safely handle up to 6 cubic feet per second. After paving, from item 3, does the runoff exceed the pond's limit? By how much?
  9. To keep runoff at or below 6 cubic feet per second on the paved lot, engineers want to lower the effective C. What value of C would give exactly 6 cubic feet per second? Solve 6 = C × 2 × 5.
  10. Explain how a rain garden or permeable pavement lowers the runoff coefficient C for a paved area.

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: Q = C × i × A, where C is the runoff coefficient, i is rainfall intensity, and A is drainage area.
    Q is the peak runoff being solved for.
  2. Answer: 2.0 cfs.
    Q = 0.2 × 2 × 5 = 2.0 cubic feet per second.
  3. Answer: 9.0 cfs.
    Q = 0.9 × 2 × 5 = 9.0 cubic feet per second.
  4. Answer: 4.5 times.
    9.0 ÷ 2.0 = 4.5, so the paved runoff is 4.5 times the meadow runoff.
  5. Answer: 10.
    With i × A = 2 × 5 = 10, Q = 10 × C, so the slope is 10 cubic feet per second per unit of C.
  6. Answer: 5.0 cfs.
    Slope method: 10 × 0.5 = 5.0. Full formula check: 0.5 × 2 × 5 = 5.0 cubic feet per second, which matches.
  7. Answer: Pavement blocks rain from soaking in, so more of it runs off at once.
    A higher runoff coefficient means a larger share of the rain becomes fast surface flow. Accept any answer describing less soaking in and more runoff.
  8. Answer: Yes, by 3.0 cfs.
    9.0 cubic feet per second is greater than the 6 cubic feet per second limit: 9.0 − 6 = 3.0 over the limit.
  9. Answer: 0.6.
    Solve 6 = C × 2 × 5, so 6 = 10C and C = 0.6.
  10. Answer: They let some rain soak in or pause, so less becomes runoff.
    A rain garden or permeable surface captures and infiltrates part of the rain, which lowers the fraction that runs off and therefore lowers C. Accept any answer describing infiltration or storage reducing runoff.

Differentiation

Support

Provide the formula with i and A already filled in (Q = C × 10) so students focus on the coefficient. Work item 2 together as a model, then let students try item 3 on their own. Supply a number line showing C from 0 to 1 with sample surfaces labeled.

Extension

Ask students to build a short table of Q for five surfaces with coefficients 0.2, 0.4, 0.6, 0.8, and 0.9, then graph the points and confirm the slope they found in item 5. Have them explain what the y-intercept of the line means for a perfect surface where no water runs off.

ELL supports

Pre-teach "runoff," "coefficient," and "peak" with a picture of rain hitting grass versus rain hitting pavement. Provide the sentence frame "Paving increases runoff because ___" for items 7 and 10. Allow students to answer the calculation items with the setup and result rather than full sentences.