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Math problem set Grade 12 Engineering & Design

Verlow Reservoir Drought Supply: Acre-Foot and Demand Problems

A grade 12 problem set where students convert a fictional reservoir's acre-foot storage to gallons, subtract the dead pool, and project days of supply in a drought.

Objectives

  1. Students will convert reservoir storage between acre-feet and gallons and separate usable storage from a dead pool.
  2. Students will define a net depletion rate and use it to project days of remaining supply.
  3. Students will quantify how a stated conservation cut extends a drought supply projection.

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.
Dead pool
A reservoir level so low that water can no longer flow out through the dam on its own. It is the worst-case marker in a long drought.

Also: net depletion, safe supply, conservation stage

Teacher overview

Western utilities account for reservoir water in acre-feet, meaning one acre covered one foot deep, while treatment plants and customer billing use gallons and MGD, so drought planning depends on converting between the two. In this set, students manage the fictional Verlow Reservoir through a dry summer for the town of Casterbrook, computing what the reservoir actually holds, how fast it is falling, and how much time a conservation order buys. A common error in this work is projecting supply from total storage rather than usable storage, because the bottom of a reservoir is a dead pool sitting below the intake, and counting it inflates the projection by months.

Verlow Reservoir Drought Supply: Acre-Foot and Demand Problems — Grade 12 Engineering & Design
Name: ____________________________ Date: ______________

Problems

Use these facts about the fictional Verlow Reservoir and the town of Casterbrook throughout. Full capacity is 8,000 acre-feet, and current storage is 5,200 acre-feet. The bottom 1,300 acre-feet is a dead pool below the intake and cannot be withdrawn. Casterbrook's demand is 3.0 MGD. During drought, stream inflow minus evaporation adds a net 0.8 MGD to the reservoir. One acre-foot equals 325,851 gallons.

  1. What percent of full capacity is the reservoir currently holding?
  2. How many acre-feet of the current storage are actually usable, once the dead pool is excluded?
  3. Convert the usable storage from problem 2 into gallons.
  4. Express Casterbrook's 3.0 MGD demand in acre-feet per day, to the nearest hundredth.
  5. If the drought became severe enough that net inflow stopped entirely, how many days would the usable storage last at 3.0 MGD? Round to the nearest tenth of a day.
  6. Under current drought conditions, define and compute the net depletion rate: demand minus net inflow, in MGD. Then find how many days the usable storage lasts at that rate, to the nearest tenth.
  7. The town council declares a Stage 2 drought, cutting demand by 25 percent while net inflow stays at 0.8 MGD. Find the new net depletion rate and the new days of supply, to the nearest tenth.
  8. How many additional days of supply did the Stage 2 cut buy, compared with problem 6? Round to the nearest whole day.

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: 65 percent. 5,200 ÷ 8,000 = 0.65, or 65 percent of capacity.
  2. Answer: 3,900 acre-feet. 5,200 − 1,300 = 3,900 acre-feet of usable storage.
  3. Answer: 1,270,818,900 gallons. 3,900 acre-feet × 325,851 gallons per acre-foot = 1,270,818,900 gallons.
  4. Answer: 9.21 acre-feet per day. 3,000,000 gallons per day ÷ 325,851 gallons per acre-foot = 9.206, which rounds to 9.21 acre-feet per day.
  5. Answer: 423.6 days. 1,270,818,900 gallons ÷ 3,000,000 gallons per day = 423.6 days. The same result comes from 3,900 acre-feet ÷ 9.2066 acre-feet per day (the unrounded value from item 4); using the rounded 9.21 gives 423.5 days, which should also be accepted.
  6. Answer: 577.6 days. Net depletion = 3.0 − 0.8 = 2.2 MGD, or 2,200,000 gallons per day. 1,270,818,900 ÷ 2,200,000 = 577.6 days.
  7. Answer: 876.4 days. Stage 2 demand = 3.0 × 0.75 = 2.25 MGD. Net depletion = 2.25 − 0.8 = 1.45 MGD, or 1,450,000 gallons per day. 1,270,818,900 ÷ 1,450,000 = 876.4 days.
  8. Answer: 299 days. 876.4 − 577.6 = 298.8, which rounds to about 299 additional days of supply.

Differentiation

Support

Provide the acre-foot conversion and the storage ledger (capacity, current, dead pool) in a pre-drawn diagram of the reservoir so problem 2 becomes a labeled subtraction. Allow students to leave problems 5 through 7 in scientific notation before rounding, and confirm problem 3 as a class before anyone moves on, since every later answer depends on it.

Extension

Ask students to find what percent cut, instead of 25 percent, Casterbrook would need for the fictional reservoir's usable storage to last 1,000 days at the drought inflow of 0.8 MGD. (Working backward: 1,270,818,900 ÷ 1,000 days requires a net depletion of about 1.27 MGD, so demand can be about 2.07 MGD, roughly a 31 percent cut.)

ELL supports

Introduce "acre-foot" with a sketch of a football-field-sized square filled one foot deep, and label the reservoir diagram with "full," "now," "dead pool," and "usable" before assigning the set. Provide a sentence frame for problem 8: "Stage 2 makes the supply last ___ days instead of ___ days, which is ___ more days."