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Math problem set Grade 11 Careers & CTE

Ferrisholt Stormwater Fees: An ERU and Runoff Problem Set

A grade 11 careers problem set in which students work as a stormwater program specialist, billing a shopping center by impervious area and checking its peak runoff.

Objectives

  1. Students will convert a parcel's impervious area into equivalent residential units and compute the resulting stormwater bill.
  2. Students will calculate peak runoff with the rational method before and after a site retrofit.
  3. Students will explain why a stormwater utility bills on impervious area rather than lot size or metered water use.

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.

Also: equivalent residential unit, runoff coefficient, rational method, stormwater credit

Teacher overview

A stormwater program specialist spends much of the year translating maps into bills. In the fictional city of Ferrisholt, the drainage system is paid for by a stormwater utility fee rather than by property taxes, so every parcel is charged according to how much hard surface it drains. This set follows one specialist through a single commercial property, from measuring roof and pavement to certifying a credit for a detention retrofit. The misconception worth correcting early is the assumption that the fee scales with lot size or with metered water use; only impervious area enters the calculation, so a large wooded parcel can pay less than a small paved one.

Ferrisholt Stormwater Fees: An ERU and Runoff Problem Set — Grade 11 Careers & CTE
Name: ____________________________ Date: ______________

Problems

The fictional city of Ferrisholt charges every parcel a monthly stormwater fee. One equivalent residential unit, or ERU, is defined as 2,800 square feet of impervious area, the citywide median for a single-family home. Single-family homes pay a flat 1.0 ERU. Every other parcel pays ERUs equal to its impervious area divided by 2,800, rounded to the nearest tenth. The monthly rate is $6.25 per ERU. For peak runoff, use the rational method: Q equals C times i times A, where Q is peak flow in cubic feet per second, C is the runoff coefficient, i is rainfall intensity in inches per hour, and A is drainage area in acres.

  1. Northgate Plaza, a shopping center in Ferrisholt, has 96,000 square feet of roof and 148,000 square feet of paved parking and drive lanes. Find its total impervious area in square feet.
  2. Using your answer from problem 1, find the plaza's ERU count. Round to the nearest tenth.
  3. Find the plaza's monthly stormwater bill at $6.25 per ERU. Round to the nearest cent.
  4. Find the plaza's annual stormwater bill by multiplying its ERU count from problem 2 by the monthly rate and then by 12 months.
  5. The plaza's owner builds a detention basin and two bioretention cells. The utility certifies them for a 30 percent credit. Find the plaza's annual bill after the credit is applied to your answer from problem 4.
  6. Find the annual savings the credit produces, in dollars.
  7. The detention basin and bioretention cells cost $24,000 to build. Using your answer from problem 6, find how many years of savings it takes to pay back that cost. Round to the nearest tenth of a year.
  8. Northgate Plaza drains 8.4 acres. Before the retrofit its runoff coefficient was 0.86. Ferrisholt's design storm has an intensity of 3.2 inches per hour. Find the peak runoff in cubic feet per second, rounded to the nearest tenth.
  9. After the retrofit the site's runoff coefficient drops to 0.74. Using the same drainage area and design storm, find the new peak runoff in cubic feet per second, rounded to the nearest tenth.
  10. A property owner argues that the fee should be based on lot size instead of impervious area. Explain, in two or three sentences, why the specialist bills on impervious area, and name one quantity the fee deliberately ignores.

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: 244,000 square feet.
    96,000 square feet of roof plus 148,000 square feet of pavement equals 244,000 square feet of impervious area.
  2. Answer: 87.1 ERU.
    244,000 divided by 2,800 equals 87.142857, which rounds to 87.1 ERU.
  3. Answer: $544.38.
    87.1 ERU times $6.25 per ERU equals $544.375, which rounds to $544.38 per month.
  4. Answer: $6,532.50.
    87.1 ERU times $6.25 per ERU times 12 months equals 87.1 times 75, or $6,532.50 per year.
  5. Answer: $4,572.75.
    A 30 percent credit leaves 70 percent of the bill: $6,532.50 times 0.70 equals $4,572.75.
  6. Answer: $1,959.75.
    $6,532.50 minus $4,572.75 equals $1,959.75 of savings each year.
  7. Answer: 12.2 years.
    $24,000 divided by $1,959.75 per year equals 12.246, which rounds to 12.2 years.
  8. Answer: 23.1 cfs.
    Q equals 0.86 times 3.2 inches per hour times 8.4 acres. First 0.86 times 3.2 equals 2.752, then 2.752 times 8.4 equals 23.1168, which rounds to 23.1 cubic feet per second.
  9. Answer: 19.9 cfs.
    Q equals 0.74 times 3.2 times 8.4. First 0.74 times 3.2 equals 2.368, then 2.368 times 8.4 equals 19.8912, which rounds to 19.9 cubic feet per second.
  10. Answer: The fee is charged on impervious area because hard surfaces are what generate the runoff the drainage system has to carry.
    A wooded or lawn-covered acre soaks up most of the rain that falls on it, while an acre of roof and pavement sends nearly all of it to the storm drain, so impervious area is the closest available measure of the demand a parcel places on the system. The fee deliberately ignores metered water use, which measures what a parcel draws from the drinking water system rather than what it discharges to the storm sewer. Lot size is ignored for the same reason: two parcels of equal size can put very different volumes into the pipes.

Differentiation

Support

Give students the impervious total from problem 1 already computed so they can begin the fictional plaza's ERU calculation without stalling, and provide a worked example of the rational method using a different runoff coefficient and drainage area before problem 8.

Extension

Ask students to find the runoff coefficient the fictional plaza would need in order to hold its peak runoff at or below 18 cubic feet per second for the same design storm, then judge whether that value is realistic for a site that must keep its parking lot.

ELL supports

Pre-teach "impervious," "runoff coefficient," "credit," and "equivalent residential unit" with a labeled aerial sketch of the fictional plaza showing roof, pavement, and landscaped areas shaded differently. Allow students to answer problem 10 with a labeled diagram plus two sentences rather than a full paragraph.

Extensions

Have students take a satellite image of a large parcel near the school, estimate its roof and pavement areas by counting grid squares, and compute what that parcel would pay each year under the fictional Ferrisholt rate structure. Ask them to list the measurement decisions that would most change their estimate.