Water for Schools
Menu

Worksheet Grade 11 Science

Ellingham's Peak Day: Per-Capita Demand and a Conservation Target

A grade 11 worksheet on per-capita demand, peaking factors, and how two ordinary conservation measures change a growing town's projected peak-day water use.

Objectives

  1. Students will calculate per-capita demand and a maximum-day peaking factor from a utility's production records.
  2. Students will quantify the water two conservation measures would free up and express it as a change in per-capita demand.
  3. Students will project demand five years forward and compare it with a treatment plant's rated capacity.

Vocabulary

Acre-foot
The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.

Also: per-capita demand, peaking factor, maximum day, rated capacity

Teacher overview

The town of Ellingham draws its whole supply from a single river intake, and its treatment plant is sized for the busiest day of the year rather than for the yearly average. This worksheet has students calculate Ellingham's per-capita demand and its maximum-day peaking factor, quantify the water that efficient showerheads and a leak-repair campaign would free up, and carry those results forward through five years of population growth. One misconception is worth addressing before students start: many assume a utility's reported per-capita figure should match the 80 to 100 gallons per person per day commonly cited for water use at home, and they read anything higher as waste. A system-wide figure also carries schools, businesses, industry, and water lost from the pipes, so the two numbers count different things and should not be compared directly.

Ellingham's Peak Day: Per-Capita Demand and a Conservation Target — Grade 11 Science
Name: ____________________________ Date: ______________

Student Worksheet

All items describe Ellingham, a fictional town. Use these production records in every item.

Quantity Value
Population served 20,000 people
Average-day production 2,600,000 gallons per day
Maximum-day production 4,420,000 gallons per day
Treatment plant rated capacity 5,000,000 gallons per day
Households served 7,600
Projected population growth 1.6 percent per year
  1. Ellingham produced an average of 2,600,000 gallons per day for 20,000 people. Calculate the average-day per-capita demand in gallons per person per day.
  2. Ellingham's maximum-day production was 4,420,000 gallons and its average-day production was 2,600,000 gallons. Calculate the maximum-day peaking factor, which is maximum-day production divided by average-day production.
  3. Using the average-day production of 2,600,000 gallons per day, calculate Ellingham's total production for a 365-day year, in gallons.
  4. One acre-foot equals 325,851 gallons. Convert your item 3 answer to acre-feet, rounded to the nearest tenth.
  5. Per-person water use at home in the United States is commonly cited at 80 to 100 gallons per day. Ellingham's system figure from item 1 is higher. Explain what a system-wide per-capita number includes that a residential figure does not.
  6. Each of Ellingham's 20,000 residents takes one shower a day, averaging 7.5 minutes. A standard showerhead flows at 2.5 gallons per minute, and a WaterSense-labeled model uses 2.0 gallons per minute. Calculate the gallons per day the town would save if every shower used the labeled model.
  7. Ellingham's utility plans to repair leaks in 1,200 homes. Household leaks waste an average of about 9,400 gallons per year. Calculate the total gallons per year those repairs would save.
  8. Convert your item 7 answer to gallons per day using a 365-day year, then add the savings from item 6. Report the combined savings in gallons per day, rounded to the nearest gallon.
  9. Subtract the combined savings from item 8 from the average-day production of 2,600,000 gallons per day, then divide by 20,000 people. Report the reduced per-capita demand in gallons per person per day, rounded to the nearest tenth.
  10. Ellingham's population of 20,000 is projected to grow 1.6 percent per year. Calculate the projected population five years from now, rounded to the nearest person.
  11. Using your item 10 population and the reduced per-capita demand of 124.7 gallons per person per day, calculate the projected average-day demand in five years, rounded to the nearest ten thousand gallons per day.
  12. Assume the peaking factor from item 2 stays the same. Using your item 11 answer, calculate the projected maximum-day demand five years from now, in gallons per day.
  13. Compare your item 12 answer with the plant's rated capacity of 5,000,000 gallons per day. What percent of rated capacity is the projected maximum day, rounded to the nearest tenth of a percent?
  14. Engineers size a treatment plant on the maximum day rather than the average day. Explain why, and state what would happen in Ellingham on a hot July afternoon if the plant had been built for the average day instead.

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: 130 gallons per person per day.
    2,600,000 gallons per day / 20,000 people = 130 gallons per person per day.
  2. Answer: 1.70.
    4,420,000 / 2,600,000 = 1.70. The peaking factor has no units because both quantities are gallons per day.
  3. Answer: 949,000,000 gallons.
    2,600,000 gallons per day x 365 days = 949,000,000 gallons for the year.
  4. Answer: 2,912.4 acre-feet.
    949,000,000 gallons / 325,851 gallons per acre-foot = 2,912.37, which rounds to 2,912.4 acre-feet.
  5. Answer: It includes all the non-residential water the system delivers.
    A system-wide per-capita figure divides every gallon produced by the residential population, so it also carries water used by schools, stores, restaurants, industry, and firefighting, plus water lost through leaks in the mains before it reaches any customer. A residential figure counts only what households use, so the system number is expected to be larger.
  6. Answer: 75,000 gallons per day.
    Standard: 7.5 minutes x 2.5 gallons per minute = 18.75 gallons per shower; 18.75 x 20,000 = 375,000 gallons per day. Labeled: 7.5 x 2.0 = 15 gallons per shower; 15 x 20,000 = 300,000 gallons per day. Savings = 375,000 - 300,000 = 75,000 gallons per day.
  7. Answer: 11,280,000 gallons per year.
    1,200 homes x 9,400 gallons per year = 11,280,000 gallons per year.
  8. Answer: 105,904 gallons per day.
    11,280,000 / 365 = 30,904.1 gallons per day from leak repair. 30,904 + 75,000 = 105,904 gallons per day combined.
  9. Answer: 124.7 gallons per person per day.
    2,600,000 - 105,904 = 2,494,096 gallons per day. 2,494,096 / 20,000 = 124.70 gallons per person per day.
  10. Answer: 21,652 people.
    20,000 x 1.016^5 = 20,000 x 1.08260 = 21,652.0, so about 21,652 people.
  11. Answer: 2,700,000 gallons per day.
    21,652 people x 124.7 gallons per person per day = 2,700,004 gallons per day, which rounds to 2,700,000 gallons per day.
  12. Answer: 4,590,000 gallons per day.
    2,700,000 x 1.70 = 4,590,000 gallons per day on the projected maximum day.
  13. Answer: 91.8 percent.
    4,590,000 / 5,000,000 = 0.918, or 91.8 percent of rated capacity.
  14. Answer: Because the plant must meet demand on the worst day, not an average one.
    Averages hide the summer peak: Ellingham's busiest day runs 1.70 times its average day, so a plant built for 2,600,000 gallons per day would fall roughly 1,820,000 gallons short on the peak day. Storage would drain, pressure would drop across the system, and the utility would have to impose restrictions or risk losing pressure that protects the mains from contamination.

Differentiation

Support

Give students a worked example of a peaking factor for a different community before item 2, and provide item 10 with the growth factor 1.016^5 already evaluated as 1.08260 so the projection reduces to a single multiplication. A unit-labeled template for items 6 through 9, with blanks for gallons per shower, gallons per day, and gallons per year, keeps the conversions in order.

Extension

Have students calculate what per-capita demand Ellingham would need to reach for the projected maximum day in five years to stay at or below 85 percent of rated capacity, then decide whether the two measures in this worksheet could plausibly get there or whether the utility would need additional programs.

ELL supports

Pre-teach per-capita, peaking factor, maximum day, and rated capacity with a two-column glossary that pairs each term with the arithmetic that produces it. Provide sentence frames for items 5 and 14, such as "A system figure is larger because it also counts ___" and "The plant is built for the maximum day because ___."

Extensions

Ask students to find their own utility's published average-day and maximum-day production in its annual report or consumer confidence report, compute the local peaking factor, and compare it with Ellingham's. Communities with heavy summer irrigation often run much higher factors than communities where most use is indoors, which gives students a reason to explain a difference rather than only compute one.