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Math problem set Grade 12 Math

Coyle Valley Irrigation District: Acre-Feet and Conveyance

A grade 12 problem set on a fictional irrigation district, chaining acre-feet, gallons, MGD, and cfs while accounting for canal conveyance losses and crop water.

Objectives

  1. Students will convert an irrigation delivery in acre-feet to gallons, MGD, and cfs.
  2. Students will account for canal conveyance efficiency when finding river diversions.
  3. Students will choose the quantity that best describes canal performance for a decision maker.

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.
Diversion
Taking water out of a river or stream and sending it somewhere else, such as into a canal or pipeline, to be used by farms or cities.
Water footprint
All the water it takes to make the things we use and eat, counting water used far away. A hamburger's water footprint includes the water that grew the cattle's feed.

Also: conveyance efficiency

Teacher overview

The fictional Coyle Valley Irrigation District diverts water from the Coyle River, carries it through open canals, and delivers what survives the trip to farm turnouts. This set has students account for the water lost along the way, then express the same delivery in the several units a district actually uses: acre-feet for the season, MGD for average flow, and cfs for a canal gauge. A common error is treating the delivered volume as the diverted volume; because the canals lose water, the district must always divert more than it delivers.

Coyle Valley Irrigation District: Acre-Feet and Conveyance — Grade 12 Math
Name: ____________________________ Date: ______________

Problems

All figures describe the fictional Coyle Valley Irrigation District. Over a 180-day irrigation season, the district delivers 12,000 acre-feet to farms, running canals with a conveyance efficiency of 82 percent (18 percent is lost to seepage and evaporation). Use: 1 acre-foot = 325,851 gallons = 43,560 cubic feet; 1 MGD = 694 gpm = 1.547 cfs. A pound of beef takes roughly 1,800 gallons of water, most of it rainwater used by the pasture and feed crops cattle eat; a pound of wheat takes roughly 220 gallons (Water Footprint Network global averages).

  1. Convert the 12,000 acre-feet delivered into gallons.

  2. Because the canals are only 82 percent efficient, how many acre-feet must the district divert from the river to deliver 12,000 acre-feet? Round to the nearest acre-foot.

  3. How many acre-feet are lost to seepage and evaporation in the canals over the season?

  4. Convert the delivered volume into an average flow over the 180-day season, in MGD. Round to the nearest tenth.

  5. Convert the average flow from problem 4 into cubic feet per second (cfs). Round to the nearest tenth.

  6. One farm uses 500 acre-feet of the delivery to grow wheat. At roughly 220 gallons of water per pound of wheat, about how many pounds of wheat could that water support?

  7. Using the water-footprint figures, how many times more water does a pound of beef take than a pound of wheat?

  8. The board wants one number that describes how tightly the canals hold water, comparable from year to year. Should they report total acre-feet diverted, acre-feet lost, or the conveyance efficiency percent? Justify your choice.

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: 3,910,212,000 gal.
    12,000 acre-feet × 325,851 gal/acre-foot = 3,910,212,000 gallons, or about 3.91 billion gallons.

  2. Answer: 14,634 acre-feet.
    Delivered = diverted × efficiency, so diverted = 12,000 ÷ 0.82 = 14,634.1, which rounds to 14,634 acre-feet. The district must pull more from the river than it delivers.

  3. Answer: 2,634 acre-feet.
    Loss = diverted − delivered = 14,634 − 12,000 = 2,634 acre-feet lost to the canals over the season.

  4. Answer: 21.7 MGD.
    Delivered gallons ÷ days = 3,910,212,000 ÷ 180 = 21,723,400 gallons per day, which is 21.7 MGD.

  5. Answer: 33.6 cfs.
    21.7 MGD × 1.547 cfs/MGD = 33.57, which rounds to 33.6 cfs. Using the unrounded 21.72 MGD gives the same 33.6 cfs.

  6. Answer: 740,570 lb.
    500 acre-feet × 325,851 gal/acre-foot = 162,925,500 gallons. At 220 gallons per pound: 162,925,500 ÷ 220 = 740,570.45, which rounds to 740,570 pounds of wheat, about 0.74 million pounds.

  7. Answer: about 8 times.
    1,800 gallons per pound of beef ÷ 220 gallons per pound of wheat = 8.18, or about 8. Beef takes about 8 times as much water per pound as wheat.

  8. Answer: conveyance efficiency, a percent.
    Conveyance efficiency is a ratio, so it does not grow or shrink just because the district moved more or less water in a given year. That makes it comparable across seasons and against other districts, while total acre-feet diverted or lost both rise and fall with the size of the delivery.

Differentiation

Support

Provide a filled-in unit-conversion chart showing acre-feet stepping to gallons, then to gallons per day, then to MGD, and pre-compute problem 1 so students can chain from there. Allow a calculator throughout and accept answers kept to one extra decimal place.

Extension

Ask students to find what conveyance efficiency the district would need to reach in order to cut its river diversion to 13,500 acre-feet while still delivering 12,000 acre-feet, and to comment on whether lining the canals to reach that efficiency is likely worth the cost.

ELL supports

Pre-teach "divert," "delivery," "conveyance," and "seepage" with a simple canal diagram showing water entering, some leaking out, and the rest reaching a farm. Provide the conversion chart from the Support note and sentence frames for the justification in problem 8.