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Worksheet Grade 9 Social Studies & Civics

Loamside's Data Center Water Agreement: A Capacity Worksheet

A grade 9 worksheet in which students convert plant capacity units, test a fictional town's remaining growth room, and price a data center's water contract.

Objectives

  1. Students will convert between million gallons per day and gallons per minute using a standard operator conversion.
  2. Students will calculate the unused capacity of a treatment plant under average and peak demand.
  3. Students will evaluate who gains and who bears risk under a large industrial water agreement.

Vocabulary

Key words: permitted capacity, peak day demand, unit conversion, host agreement, operating budget

Teacher overview

A water system is permitted for a maximum daily production, and every large new customer takes a share of the room between what the system makes today and that permit. This worksheet places students in the fictional town of Loamside, where a data center company has offered to pay for a large, steady block of that room. Students convert the plant's capacity into the units an operator actually reads off a flow meter, subtract the proposed demand, and find how many years of ordinary town growth the agreement would consume. The misconception to watch for is the belief that a plant running below its permit has spare capacity to sell; peak day demand, not average demand, is what fills a permit, so a system with a comfortable average can still run out of room on the hottest week of the year.

Loamside's Data Center Water Agreement: A Capacity Worksheet — Grade 9 Social Studies & Civics
Name: ____________________________ Date: ______________

Student Worksheet

Use the following information about the fictional town of Loamside for every item. The town, the company, and all figures below were invented for this worksheet.

  • The Loamside Water Authority serves about 12,400 residents from one treatment plant.
  • The plant's permitted capacity is 3.5 MGD, which means 3.5 million gallons per day.
  • The plant currently produces an average of 1.9 MGD.
  • One million gallons per day equals 694 gallons per minute.
  • Grindley Data Works has proposed a data center that would use 0.6 MGD on an average day and 0.9 MGD on the hottest days, because its cooling towers evaporate more water in heat.
  • On the hottest days, Loamside's other customers together use 2.4 MGD.
  • Residential and business demand in Loamside is projected to grow by 0.04 MGD each year.
  • Grindley Data Works has offered to pay the Loamside Water Authority $0.0042 per gallon of water delivered.
  • The Loamside Water Authority's annual operating budget is $2,300,000.
  1. Convert the plant's permitted capacity of 3.5 MGD to gallons per minute. Round to the nearest whole gallon per minute.
  2. Convert the plant's current average production of 1.9 MGD to gallons per minute. Round to the nearest whole gallon per minute.
  3. How much of the permitted capacity is unused today, in MGD?
  4. On an average day the data center would use 0.6 MGD. What percent of the plant's permitted capacity is that? Round to the nearest tenth of a percent.
  5. Add the data center's average use of 0.6 MGD to the plant's current average production of 1.9 MGD. How much unused permitted capacity would remain, in MGD?
  6. On a hottest day the data center would use 0.9 MGD and the town's other customers would use 2.4 MGD. What is the total demand on that day, in MGD?
  7. Compare your answer to item 6 with the permitted capacity of 3.5 MGD. How much margin is left, in MGD?
  8. Let y be a number of years. Starting from your hottest-day total in item 6 and adding 0.04 MGD of growth each year, write an equation stating that demand reaches the 3.5 MGD permit, then solve it for y.
  9. At an average use of 0.6 MGD, how much would Grindley Data Works pay the Loamside Water Authority over 365 days at $0.0042 per gallon?
  10. What percent of the Loamside Water Authority's $2,300,000 annual operating budget would the payment in item 9 cover? Round to the nearest tenth of a percent.
  11. Using your answers to items 7 and 8, describe one condition Loamside should write into the agreement to protect its existing customers. Explain what problem the condition prevents.
  12. The company says the payment will hold down water bills for every household in Loamside. A resident says the agreement uses up the town's room to grow. Explain, using two specific numbers from your work, how both statements can be true at once.

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: 2,429 gpm.
    Multiply 3.5 MGD by 694 gallons per minute per MGD. The product is 2,429 gallons per minute exactly.
  2. Answer: 1,319 gpm.
    Multiply 1.9 MGD by 694, which gives 1,318.6 gallons per minute, and round to 1,319.
  3. Answer: 1.6 MGD.
    Subtract the current average of 1.9 MGD from the permitted 3.5 MGD, which leaves 1.6 MGD unused on an average day.
  4. Answer: 17.1 percent.
    Divide 0.6 by 3.5 to get 0.1714, which is 17.14 percent and rounds to 17.1 percent of the permit.
  5. Answer: 1.0 MGD.
    The new average production would be 1.9 plus 0.6, which is 2.5 MGD. Subtracting 2.5 from the 3.5 MGD permit leaves 1.0 MGD.
  6. Answer: 3.3 MGD.
    Add the data center's hottest-day use of 0.9 MGD to the other customers' 2.4 MGD, which totals 3.3 MGD.
  7. Answer: 0.2 MGD.
    Subtract the 3.3 MGD hottest-day total from the 3.5 MGD permit, which leaves a margin of 0.2 MGD.
  8. Answer: 5 years.
    The equation is 3.3 plus 0.04y equals 3.5. Subtracting 3.3 from both sides gives 0.04y equals 0.2, and dividing by 0.04 gives y equals 5.
  9. Answer: $919,800.
    An average of 0.6 MGD is 600,000 gallons per day, and 600,000 times 365 days is 219,000,000 gallons. Multiplying 219,000,000 by $0.0042 per gallon gives $919,800.
  10. Answer: 40.0 percent.
    Divide $919,800 by the $2,300,000 operating budget to get 0.3999, which rounds to 40.0 percent.
  11. Answer: A condition that reduces the data center's draw on peak days, such as a mandatory cutback whenever town demand passes a stated level. Item 7 shows only 0.2 MGD of margin on the hottest day, and item 8 shows ordinary growth erases that margin in about 5 years, so without a peak-day clause Loamside would have to enlarge or repermit the plant to serve its own new homes. Accept other specific conditions, including a minimum payment that funds plant expansion or a fixed end date for the agreement.
  12. Answer: The payment of $919,800 covers about 40.0 percent of the authority's operating budget, which is real money that can hold rates down for the town's roughly 12,400 residents. At the same time the agreement consumes the peak-day margin, leaving 0.2 MGD and about 5 years of growth room, so the town trades lower bills now for a costly plant expansion later. Both statements describe the same agreement measured over different time spans.

Differentiation

Support

Give students a conversion box showing one worked example, such as 2.0 MGD converted to 1,388 gallons per minute, before item 1, and provide a partially filled capacity table for the fictional town of Loamside with items 3 and 5 already entered. Allow calculators throughout and let students skip the rounding rule on the first attempt.

Extension

Ask students to find the largest average daily use, in MGD, that Grindley Data Works could be allowed in Loamside while still leaving 10 years of growth room on the hottest day. Assume the data center's hottest-day use stays 1.5 times its average use, as in the proposal. They must show the inequality they solved and state the payment that use would generate at $0.0042 per gallon.

ELL supports

Pre-teach "permitted capacity," "peak day," and "operating budget" with a simple bar diagram of the fictional Loamside plant showing the permit as the full bar, current production as a shaded portion, and the proposed data center as a second shaded block. Provide sentence frames for items 11 and 12: "Loamside should require ___ because the margin is only ___," and "The payment helps because ___, while the agreement costs the town ___."

Extensions

Students look up the permitted capacity and average daily production of their own local water system, using only the utility's published annual water quality report, and calculate the unused capacity the same way they did for the fictional town of Loamside. A second option is to write the one-page staff recommendation the Loamside Water Authority's manager would submit to the town board, citing at least four of the computed values.