Worksheet Grade 12 Math

Glenmarr Hydroelectric Station: Storage and Power Output

A grade 12 worksheet using unit analysis to convert reservoir storage and turbine flow and compute a fictional dam's power output.

Grade: Grade 12
Subject: Math
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Items 1 through 7 carry units through chained conversions among acre-feet, gallons, cubic feet, cubic feet per second, gallons per minute, and million gallons per day.

All materials for HSN-Q.A.1 →

HSN-Q.A.3 Common Core Math

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

How this material aligns: Item 8 asks students to choose a level of accuracy for the reported power output that matches the limited precision of the gauge readings and the efficiency constant that feed the calculation.

All materials for HSN-Q.A.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will convert reservoir storage and river flow across acre-feet, gallons, cubic feet, cfs, gpm, and MGD.
Students will compute a dam's power output and report it at a precision matched to its inputs.

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: net head, cubic feet per second, significant figures

Teacher overview

Glenmarr Hydroelectric Station is a fictional dam whose reservoir stores water measured in acre-feet while its turbines pass a flow measured in cubic feet per second. Moving between those two units, and then to the units an electric utility uses, is exactly the dimensional-analysis discipline an operator-certification exam rewards. This worksheet has students convert storage and flow, estimate the station's power output from a stated relationship, and then judge how precisely that output should be reported. A common error is treating a volume unit such as acre-feet as if it were a flow rate; storage answers a "how much" question, while cfs answers a "how fast" question.

Glenmarr Hydroelectric Station: Storage and Power Output — Grade 12 Math

Name: ____________________________ Date: ______________

Student Worksheet

Glenmarr Hydroelectric Station (a fictional facility) has a usable reservoir storage of 12,000 acre-feet, a turbine flow of 1,500 cubic feet per second (cfs), and a net head of 220 feet. Use these relationships:

1 acre-foot = 325,851 gallons = 43,560 cubic feet.
1 cfs = 448.8 gallons per minute (gpm).
1 million gallons per day (MGD) = 1.547 cfs.
For this station, power in kilowatts = flow (cfs) x net head (ft) x 0.072. The 0.072 already includes an assumed turbine-and-generator efficiency.

Convert the reservoir's usable storage of 12,000 acre-feet to gallons.
Convert the same 12,000 acre-feet of storage to cubic feet.
Convert the turbine flow of 1,500 cfs to gallons per minute.
Convert the turbine flow of 1,500 cfs to million gallons per day. Round to the nearest tenth.
Find the station's power output in kilowatts, using the stated relationship with flow 1,500 cfs and net head 220 feet.
If the station generates at that output for a full 24 hours, find the energy produced in kilowatt-hours.
If the turbines drew down the full usable storage at 1,500 cfs with no inflow, how many hours would that take? Use your cubic-foot answer from item 2 and note that 1,500 cfs moves 1,500 cubic feet each second.
The flow gauge reads to the nearest 10 cfs and the head gauge to the nearest foot. Explain how many significant figures are reasonable to report for the power output in item 5, and restate that answer at that precision.
During a drought the net head falls from 220 feet to 200 feet while the flow stays at 1,500 cfs. Find the new power output, and state the percent decrease from item 5. Round the percent to the nearest whole number.
Explain why reservoir managers report storage in acre-feet but report the turbine flow in cubic feet per second, rather than using one unit for both.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Answer: 3,910,212,000 gallons.
12,000 acre-feet x 325,851 gallons per acre-foot = 3,910,212,000 gallons, or about 3.91 billion gallons.
Answer: 522,720,000 cubic feet.
12,000 acre-feet x 43,560 cubic feet per acre-foot = 522,720,000 cubic feet.
Answer: 673,200 gpm.
1,500 cfs x 448.8 gpm per cfs = 673,200 gallons per minute.
Answer: 969.6 MGD.
1,500 cfs / 1.547 cfs per MGD = 969.62, which rounds to 969.6 MGD.
Answer: 23,760 kW.
Power = flow x head x 0.072 = 1,500 x 220 x 0.072. First 1,500 x 220 = 330,000, then 330,000 x 0.072 = 23,760 kilowatts.
Answer: 570,240 kWh.
Energy = power x time = 23,760 kW x 24 hours = 570,240 kilowatt-hours.
Answer: 96.8 hours.
Time = volume / flow = 522,720,000 cubic feet / 1,500 cubic feet per second = 348,480 seconds. Dividing by 3,600 seconds per hour gives 96.8 hours, or about 4.0 days.
Answer: 2 significant figures.
Both gauge readings carry three significant figures (1,500 to the nearest 10 cfs, 220 to the nearest foot), but the 0.072 constant carries only two, so reporting 23,760 kW implies more precision than the data support. The product should be reported to two significant figures: about 24,000 kW, or 24 megawatts. Accept 23,800 kW (three significant figures) from a student who reasons from the gauge readings alone.
Answer: 9 percent decrease.
New power = 1,500 x 200 x 0.072 = 21,600 kW. The decrease is 23,760 - 21,600 = 2,160 kW, and 2,160 / 23,760 = 0.0909, which rounds to a 9 percent decrease.
Answer: Storage and flow are different kinds of quantities.
Storage is a volume, a fixed amount of water held behind the dam, and acre-feet is a large unit suited to that amount. Flow is a rate, the volume passing the turbines each second, and cubic feet per second is suited to that rate. Using one unit for both would blur the difference between how much water is stored and how fast it moves.

Differentiation

Support

Give students a conversion-factor sheet listing each relationship as a labeled arrow, and pre-compute item 2 so they can begin item 7 from a known cubic-foot value. Allow calculator use throughout and accept answers written in scientific notation.

Extension

Ask students to research the stated efficiency constant: given that the theoretical constant for cfs and feet is about 0.0846 at full efficiency, what turbine-and-generator efficiency does the station's 0.072 constant imply? Have them show the division that produces the percentage.

ELL supports

Provide a cross-section diagram of a dam labeling the reservoir, the net head, the penstock, and the turbine, glossing each term. Offer a sentence frame for item 10: "Storage is a ___ because ___, while flow is a ___ because ___."

Extensions

Have students compare the station's usable storage in days of full-output generation with the residence time of water in a natural reservoir, and discuss how operators balance generating power now against holding water for a dry season later.