Worksheet Grade 10 Math
Skelbourne Basin Yield: Watershed Area and Reservoir Refill
A grade 10 worksheet on a fictional watershed where students convert square miles to acre-feet of runoff and test whether one reservoir covers town demand.
Objectives
- Students will convert a watershed area and a runoff depth into a runoff volume in acre-feet and gallons.
- Students will compare a reservoir's storage with annual runoff and with daily town demand.
- Students will calculate how long a stated inflow takes to refill a drawn-down reservoir.
Vocabulary
- Watershed
- A watershed is all the land where rain that falls will drain to the same stream, river, or lake. Everyone lives in a watershed, no matter how far from the water they live.
- 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: runoff, basin yield, days of supply
Teacher overview
Skelbourne Basin and Merrin Reservoir are fictional, and every measurement below is set for this worksheet. Students take a watershed area in square miles, a runoff depth in inches, and a storage capacity in acre-feet, then work out whether the reservoir can carry the town through a year. The most common error in this work is multiplying acres by a depth still written in inches, which overstates the volume by a factor of twelve, so watch for answers near 92,160 acre-feet in item 2. A second frequent slip is reporting reservoir storage in acre-feet while reporting demand in gallons and then dividing without converting.
Student Worksheet
Skelbourne Basin, Merrin Reservoir, and the town of Skelbourne are fictional places used for this worksheet. Use these conversions where they are needed: 1 square mile = 640 acres; 1 acre-foot = 325,851 gallons; 1 cubic foot per second = 448.8 gallons per minute; 1 day = 1,440 minutes. Round each answer as the item directs.
Skelbourne Basin drains 18 square miles. Convert that area to acres.
In an average year, 8 inches of the rain and snowmelt landing on the basin runs off into Merrin Reservoir. Using your acreage from item 1, find the annual runoff volume in acre-feet. (Depth must be in feet.)
Convert your item 2 answer to gallons. Report the full number.
Find the basin yield in acre-feet per square mile by dividing the item 2 volume by the 18 square miles of drainage area. Round to the nearest tenth.
Merrin Reservoir holds 4,200 acre-feet when full. What percent of the item 2 annual runoff volume is that? Round to the nearest tenth of a percent.
The town of Skelbourne has 26,000 residents, and the system delivers 90 gallons per resident each day. Find the daily demand in gallons.
Write your item 6 demand in million gallons per day.
Suppose the reservoir is full at 4,200 acre-feet and no water flows in. How many days of demand does that storage cover? Round to the nearest whole day.
In a drought year only 6 inches of runoff reaches the reservoir. Find that runoff volume in acre-feet.
By what percent does the drought-year runoff in item 9 fall below the average-year runoff in item 2?
After the drought the reservoir sits at 1,900 acre-feet, and the inflow averages 15 cubic feet per second. How many days does refilling to 4,200 acre-feet take? Round to the nearest whole day.
Explain in two or three sentences why basin yield per square mile is more useful than total runoff when a planner compares two watersheds of different sizes.
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: 11,520 acres. 18 square miles × 640 acres per square mile = 11,520 acres.
Answer: 7,680 acre-feet. First convert 8 inches to feet: 8 ÷ 12 = 0.6667 feet. Then 11,520 acres × 0.6667 feet = 7,680 acre-feet. Students who skip the inch-to-foot step get 92,160, which is twelve times too large.
Answer: 2,502,535,680 gallons. 7,680 acre-feet × 325,851 gallons per acre-foot = 2,502,535,680 gallons, or about 2.5 billion gallons.
Answer: 426.7 acre-feet per square mile. 7,680 acre-feet ÷ 18 square miles = 426.67, which rounds to 426.7.
Answer: 54.7 percent. 4,200 ÷ 7,680 = 0.546875, and 0.546875 × 100 = 54.7 percent.
Answer: 2,340,000 gallons per day. 26,000 residents × 90 gallons per resident = 2,340,000 gallons each day.
Answer: 2.34 MGD. One million gallons per day is 1,000,000 gallons per day, so 2,340,000 ÷ 1,000,000 = 2.34.
Answer: 585 days. Storage in gallons is 4,200 × 325,851 = 1,368,574,200 gallons. Then 1,368,574,200 ÷ 2,340,000 = 584.9, which rounds to 585 days.
Answer: 5,760 acre-feet. 6 inches is 0.5 feet, and 11,520 acres × 0.5 feet = 5,760 acre-feet.
Answer: 25 percent. The drop is 7,680 − 5,760 = 1,920 acre-feet, and 1,920 ÷ 7,680 = 0.25, or 25 percent.
Answer: 77 days. The reservoir needs 4,200 − 1,900 = 2,300 acre-feet. Inflow is 15 × 448.8 = 6,732 gallons per minute, and 6,732 × 1,440 = 9,694,080 gallons per day. In acre-feet that is 9,694,080 ÷ 325,851 = 29.75 acre-feet per day. Finally 2,300 ÷ 29.75 = 77.3, which rounds to 77 days.
Answer: Yield per square mile states how much water each unit of drainage area sends downstream, so two basins of different sizes can be compared on the same footing. A large basin can produce more total runoff than a small one and still be the drier of the two. A planner sizing a new reservoir needs the rate, not just the total.
Differentiation
Support
Give students a printed conversion ladder that runs square miles to acres to acre-feet to gallons, with one arrow per step and the multiplier written on each arrow. Work item 2 together, and mark the inch-to-foot conversion in a contrasting color so it is not skipped. For item 11, provide the chain in four labeled blanks so students fill in one number at a time.
Extension
Ask students to find the runoff depth, in inches, that would make the annual runoff exactly equal to the reservoir's 4,200 acre-feet of storage, then explain what that depth means for a year in this fictional basin. A second challenge is to find the inflow, in cubic feet per second, that would refill the drawn-down reservoir in 45 days instead of 77.
ELL supports
Provide a labeled cross-section sketch showing the basin, the stream, and the reservoir, with the words watershed, runoff, inflow, and storage placed on the drawing. Pair each vocabulary term with its unit, such as acre-foot for volume and cubic foot per second for flow, on a reference card students keep beside the worksheet.
Extensions
Have students look up the drainage area of a nearby real stream gauge and repeat items 1 through 4 with that area, using that region's typical annual runoff depth, which the teacher supplies. Comparing the resulting yield per square mile against the 426.7 acre-feet per square mile from this fictional basin gives a concrete sense of how wet or dry their own region is. Students can also note that the drainage area cancels out, so only the runoff depth sets the yield per square mile.