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Worksheet Grade 7 Engineering & Design

Torrenhill Pump Station: Comparing Three Upgrade Options

A grade 7 worksheet that screens three pump station upgrades against capacity, lot size, downtime, and cost limits, then compares their weekly energy use.

Objectives

  1. Students will screen three design options against four stated limits.
  2. Students will compute weekly energy use from a rate given per ten thousand gallons.
  3. Students will express one option's energy saving as a percent of another's use.

Vocabulary

Pump station
A pump station is a building full of powerful pumps that push water through pipes or lift it uphill. Pumps give water the extra push that gravity alone cannot provide.

Also: capacity, downtime, variable speed drive, constraint, unit cost

Teacher overview

The fictional village of Torrenhill has an undersized pump station on a small corner lot, and its board has three upgrade proposals to choose among. This worksheet walks students through the screening a design team actually performs: check each option against every stated limit, find the one option left standing, and only then compare the energy the choice will use. The misconception to watch for is that the strongest option must be the best one. Students who notice the largest capacity and the shortest shutdown on the third proposal often recommend it before checking the lot line and the price, which are the two places that proposal fails. The closing items ask students to say what would have to change for the rejected proposal to become buildable, which turns a screening exercise into a design conversation.

Torrenhill Pump Station: Comparing Three Upgrade Options — Grade 7 Engineering & Design
Name: ____________________________ Date: ______________

Student Worksheet

Suppose you are advising the board of the fictional village of Torrenhill. Use these figures for every question.

The pump station sits on a corner lot measuring 30 feet by 40 feet. The board wrote four requirements:

  • The station must deliver at least 900 gpm.
  • The new building must fit on the lot.
  • Construction may shut the station down for no more than 10 days.
  • The project must cost 180,000 dollars or less.

The three proposals are:

Option What it does Capacity Building footprint Shutdown Cost Energy per 10,000 gallons pumped
1 Rebuild the two pumps that are there 800 gpm 900 square feet 6 days 95,000 dollars 18 kWh
2 Add a third pump and variable speed drives 1,050 gpm 1,150 square feet 9 days 162,000 dollars 13 kWh
3 Build a new station beside the old one 1,400 gpm 1,600 square feet 3 days 240,000 dollars 12 kWh

  1. What is the area of the corner lot in square feet?

  2. Using your answer to question 1, which options have a footprint that fits on the lot?

  3. Which options deliver at least 900 gpm?

  4. Which options cost 180,000 dollars or less?

  5. Which options shut the station down for 10 days or fewer?

  6. Which single option meets all four requirements?

  7. The station pumps 1,200,000 gallons in a typical week. How many 10,000-gallon units is that?

  8. Using your answer to question 7, how many kWh would Option 2 use in that week?

  9. Using your answer to question 7, how many kWh would Option 1 use in that week?

  10. How many fewer kWh does Option 2 use than Option 1 in that week?

  11. What percent less energy is that than Option 1 uses? Round to the nearest whole percent.

  12. Option 2 costs 162,000 dollars and delivers 1,050 gpm. What is its cost per gpm of capacity, to the nearest dollar?

  13. Option 3 has the most capacity and the shortest shutdown. Which two of the board's four requirements does it fail?

  14. Describe one change to Option 3 that would bring it inside both of the requirements you named in question 13. Then state how the board could check, before construction starts, that your change really worked.

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: 1,200 square feet.
    30 feet times 40 feet equals 1,200 square feet.

  2. Answer: Options 1 and 2.
    Option 1 needs 900 square feet and Option 2 needs 1,150 square feet, both at or under 1,200. Option 3 needs 1,600 square feet, which does not fit.

  3. Answer: Options 2 and 3.
    Option 2 delivers 1,050 gpm and Option 3 delivers 1,400 gpm, both at or above the 900 gpm requirement. Option 1 delivers 800 gpm, which falls short.

  4. Answer: Options 1 and 2.
    Option 1 costs 95,000 dollars and Option 2 costs 162,000 dollars, both within the 180,000-dollar limit. Option 3 costs 240,000 dollars, which is over by 60,000 dollars.

  5. Answer: All three options.
    The shutdowns are 6 days, 9 days, and 3 days, and all three are 10 days or fewer. This requirement does not separate the options.

  6. Answer: Option 2.
    Option 2 is the only option that appears in the answers to questions 2, 3, 4, and 5. Option 1 fails on capacity and Option 3 fails on footprint and cost.

  7. Answer: 120 units.
    1,200,000 divided by 10,000 equals 120.

  8. Answer: 1,560 kWh.
    120 units times 13 kWh per unit equals 1,560 kWh.

  9. Answer: 2,160 kWh.
    120 units times 18 kWh per unit equals 2,160 kWh.

  10. Answer: 600 kWh.
    2,160 minus 1,560 equals 600 kWh.

  11. Answer: 28 percent.
    600 divided by 2,160 equals 0.2778, which is 28 percent to the nearest whole percent.

  12. Answer: 154 dollars per gpm.
    162,000 divided by 1,050 equals 154.29, which rounds to 154 dollars for each gpm of capacity.

  13. Answer: The lot size and the cost limit.
    Option 3 needs 1,600 square feet on a lot of 1,200, and it costs 240,000 dollars against a limit of 180,000. It passes on capacity and on shutdown days.

  14. Answer: A workable change plus a check before construction.
    Accept any change that addresses both the footprint and the cost. Common correct answers include dropping the new station's capacity to about 900 to 1,000 gpm so a smaller, cheaper building fits within 1,200 square feet and 180,000 dollars, or installing the new pumps inside the existing building instead of building beside it. For the check, accept a site plan drawn to scale on the 1,200-square-foot lot, a revised contractor quote, or a written cost estimate reviewed before bidding. Do not accept a change that fixes only one of the two failures, such as buying the neighboring parcel, which fixes the lot but adds to the cost.

Differentiation

Support

Give these students a screening grid for questions 2 through 6 with the four requirements written into the rows and the three options across the columns, so their task is to write pass or fail in each cell. Provide the multiplication for question 1 already set up. For questions 8 and 9, supply the 120-unit figure from question 7 so an error there does not cascade through the energy questions.

Extension

Have students find how many weeks it would take for Option 2's energy saving to equal the extra cost of Option 2 over Option 1, given a stated price per kWh the class agrees on. Ask them to write two sentences on why the fictional board might still choose the more expensive option even if that payback turns out to be long.

ELL supports

Pre-teach capacity, footprint, and shutdown with a labeled plan view showing the lot line, the existing building, and the space a new one would need. Provide the frames "Option ____ fails because ____ is over the limit of ____" and "Option ____ uses ____ kWh in that week." Allow questions 2 through 6 to be answered by circling option numbers rather than writing them out in sentences.

Extensions

Ask students to rewrite the four requirements as the fictional board would print them in a request for proposals, keeping every number and unit but adding one sentence that says how each requirement will be verified. Discuss why a requirement nobody can check turns into an argument later, and which of the four is hardest to verify before the work is finished.