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Worksheet Grade 6 Engineering & Design

Tarrowgate Vessing Creek Manhole Seal Retrofit Worksheet

Eleven items where students measure storm water leaking into a fictional sewer, size a manhole sealing project, and check whether the plant stays within capacity.

Objectives

  1. Students will find the extra wet-weather flow entering a sewer system and the share it represents per manhole.
  2. Students will apply a stated percent removal to find how much flow a sealing project takes out.
  3. Students will compare a treated flow with a plant's rated capacity and state the remaining margin.

Vocabulary

Manhole
A manhole is the round, metal-covered opening you see in streets and sidewalks that lets crews climb down into the sewer pipes below for inspection and repair. Manholes are placed at regular intervals along sewer lines to provide access.

Also: inflow, insert seal, capacity, wet weather

Teacher overview

Tarrowgate is a fictional town, and every flow, price, and capacity on this worksheet was invented for it. Its sanitary sewers are supposed to carry only wastewater, yet on heavy rain days the treatment plant receives far more than usual because storm water pours in through cracked manhole covers along Vessing Creek. Engineers call that extra water inflow, and one common fix is a rubber insert seal that sits under the cover. This worksheet has students measure the problem, size the sealing project, and check whether sealing lets the town avoid building a larger plant.

Tarrowgate Vessing Creek Manhole Seal Retrofit Worksheet — Grade 6 Engineering & Design
Name: ____________________________ Date: ______________

Student Worksheet

Every number below belongs to the fictional Tarrowgate scenario.

  1. On a dry day the plant receives 900,000 gallons. On a heavy rain day it receives 1,500,000 gallons. How many extra gallons arrive on the rain day?
  2. Crews found 40 leaking manholes. Using item 1, what is the average extra flow from one manhole on a rain day?
  3. A rubber insert seal for one manhole costs $180. What do seals for all 40 manholes cost?
  4. Engineers expect the seals to stop 70 percent of the extra flow. How many gallons would that keep out on a rain day?
  5. Using item 4, how many gallons would the plant receive on a heavy rain day after the seals are in place?
  6. The plant can treat 1,200,000 gallons in one day. Using item 5, how many gallons of room would be left on a rain day?
  7. Treating water costs the town $1.10 for every 1,000 gallons. What does it cost to treat the extra water from item 4?
  8. Tarrowgate expects 30 heavy rain days a year. Using item 7, how much would the seals save in one year?
  9. Using items 3 and 7, how many heavy rain days of saving equal the cost of the seals? Round up to a whole day.
  10. What percent of the plant's 1,200,000-gallon capacity is the rain-day flow you found in item 5?
  11. Tarrowgate also thought about building a bigger plant. Use items 5 and 6 to explain why the seals let the town keep the plant it already has.

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: 600,000 gallons. The rain day brings 1,500,000 gallons and the dry day brings 900,000 gallons, so 1,500,000 - 900,000 = 600,000 extra gallons.
  2. Answer: 15,000 gallons. The extra flow is 600,000 gallons spread over 40 manholes, so 600,000 / 40 = 15,000 gallons each.
  3. Answer: $7,200. Forty seals at 180 dollars each give 40 x 180 = 7,200 dollars.
  4. Answer: 420,000 gallons. Seventy percent of the extra flow is 600,000 x 0.70 = 420,000 gallons kept out.
  5. Answer: 1,080,000 gallons. The rain-day flow was 1,500,000 gallons, and 1,500,000 - 420,000 = 1,080,000 gallons.
  6. Answer: 120,000 gallons. The plant can take 1,200,000 gallons, so 1,200,000 - 1,080,000 = 120,000 gallons of room.
  7. Answer: $462. The 420,000 gallons make 420 groups of 1,000 gallons, so 420 x 1.10 = 462 dollars.
  8. Answer: $13,860. At 462 dollars for each of 30 rain days, 462 x 30 = 13,860 dollars a year.
  9. Answer: 16 days. The seals cost 7,200 dollars and each rain day saves 462 dollars, so 7,200 / 462 = 15.58, which rounds up to 16 rain days.
  10. Answer: 90 percent. The new rain-day flow is 1,080,000 gallons out of 1,200,000 gallons of capacity, and 1,080,000 / 1,200,000 = 0.90.
  11. Answer: After sealing, the heaviest day brings 1,080,000 gallons, which is under the plant's 1,200,000-gallon capacity with 120,000 gallons to spare. Because the flow now fits, the town does not have to pay for more treatment capacity. Accept any answer that compares the sealed rain-day flow with the plant capacity and notes the remaining margin.

Differentiation

Support

Give these students a printed bar diagram of the fictional flows, with the dry-day bar and the rain-day bar drawn to scale and the difference already shaded, so item 1 can be read from the picture before the subtraction is written. Provide the reminder that 70 percent means 0.70 beside item 4.

Extension

Ask students to find the percent of the extra flow the seals would have to stop in order to bring the fictional rain-day flow down to exactly 1,000,000 gallons, then to say whether that is more or less than the 70 percent the engineers expect.

ELL supports

Provide a cutaway drawing of a manhole with the cover, the insert seal, and the pipe labeled, and an arrow showing rain entering through the cracked cover. Allow students to answer item 11 with two numbers and an arrow on that drawing rather than in sentences.

Extensions

Have students find a manhole cover near the school, viewing it from a sidewalk without stepping into the street or touching the cover, and sketch what they see, noting whether the cover has holes in it. Ask them to write two sentences about how a cover with holes would behave in a storm compared with a solid, sealed one.