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Worksheet Grade 12 Careers & CTE

Redlaw Flats Irrigation District: A Ditch Rider's Delivery Math

Grade 12 worksheet converting canal flow among cfs, gpm, MGD, and acre-feet per day, then sizing farm water orders and delivery times for a fictional district.

Objectives

  1. Students will convert a canal flow rate among cubic feet per second, gallons per minute, MGD, and acre-feet per day.
  2. Students will calculate a farm water order in acre-feet from an application depth and a field area.
  3. Students will determine delivery time and the headgate release needed to cover canal seepage losses.

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.
Headgate
The gate at the entrance of an irrigation canal or ditch that opens and closes to control how much water flows toward the fields.

Also: acre-inch, lateral, ditch rider, application depth, seepage loss

Teacher overview

A ditch rider works for an irrigation district, setting gates along a canal so that each farm receives the water it ordered on the day it was scheduled. The job runs on two units that are easy to confuse, because orders are written as volumes in acre-feet while gates are set as rates in cubic feet per second. This worksheet follows one delivery week on Lateral 7 of the fictional Redlaw Flats Irrigation District, moving from the flow in the canal to two farm orders, the hours needed to fill them, and the extra release required to cover seepage. The error to watch for is treating an acre-inch and an acre-foot as interchangeable, which puts every volume answer off by a factor of twelve.

Redlaw Flats Irrigation District: A Ditch Rider's Delivery Math — Grade 12 Careers & CTE
Name: ____________________________ Date: ______________

Student Worksheet

Lateral 7 of the fictional Redlaw Flats Irrigation District carries 14 cfs when its headgate is fully open. Use 448.8 gallons per minute per cubic foot per second, 1.547 cubic feet per second per MGD, 325,851 gallons per acre-foot, and 43,560 cubic feet per acre-foot. There are 86,400 seconds in a day. Show your work and label every unit.

  1. Convert the Lateral 7 flow of 14 cfs to gallons per minute.
  2. Convert the same flow to million gallons per day. Round to two decimal places.
  3. Convert the same flow to acre-feet per day. Round to one decimal place.
  4. The Harrowfield place has 160 acres of alfalfa and has ordered an application depth of 4.5 inches. Calculate the order volume in acre-feet.
  5. Convert the Harrowfield order to gallons.
  6. Convert the Harrowfield order to cubic feet.
  7. Using the flow in cubic feet per second and your answer to item 6, calculate how many hours of continuous delivery the Harrowfield order requires. Round to one decimal place.
  8. The Ostler place has 80 acres and has ordered an application depth of 3.0 inches. Calculate that order volume in acre-feet.
  9. The district plans to deliver both orders back to back on Lateral 7. Using your answer to item 3, calculate how many days of continuous delivery the combined orders require. Round to one decimal place.
  10. The unlined canal between the headgate and the Harrowfield turnout loses 8 percent of what is released to seepage. Calculate how many acre-feet must be released at the headgate so that 60 acre-feet arrives at the turnout. Round to one decimal place.
  11. A center pivot on a neighboring 132-acre field applies 0.28 inches on each pass. Calculate the volume applied in one pass, in acre-feet. Round to two decimal places.
  12. Explain in two or three sentences why the district writes farm orders in acre-feet but writes gate settings in cubic feet per second.

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: 6,283.2 gpm. Flow = 14 cfs x 448.8 gpm per cfs = 6,283.2 gallons per minute.
  2. Answer: 9.05 MGD. Flow = 14 cfs / 1.547 cfs per MGD = 9.0498, which rounds to 9.05 million gallons per day.
  3. Answer: 27.8 acre-feet per day. In one day the canal carries 14 cubic feet per second x 86,400 seconds = 1,209,600 cubic feet. Dividing, 1,209,600 / 43,560 = 27.77, which rounds to 27.8 acre-feet per day.
  4. Answer: 60 acre-feet. An application depth of 4.5 inches is 4.5 / 12 = 0.375 feet. Volume = 0.375 ft x 160 acres = 60 acre-feet. Students who use 4.5 directly will report 720, which is twelve times too large.
  5. Answer: 19,551,060 gallons. Volume = 60 acre-feet x 325,851 gallons per acre-foot = 19,551,060 gallons.
  6. Answer: 2,613,600 cubic feet. Volume = 60 acre-feet x 43,560 cubic feet per acre-foot = 2,613,600 cubic feet.
  7. Answer: 51.9 hours. Time in seconds = 2,613,600 cubic feet / 14 cubic feet per second = 186,685.7 seconds. Converting, 186,685.7 / 3,600 seconds per hour = 51.857, which rounds to 51.9 hours, or a little over two days of continuous delivery.
  8. Answer: 20 acre-feet. An application depth of 3.0 inches is 3.0 / 12 = 0.25 feet. Volume = 0.25 ft x 80 acres = 20 acre-feet.
  9. Answer: 2.9 days. The combined order is 60 + 20 = 80 acre-feet. Dividing, 80 acre-feet / 27.8 acre-feet per day = 2.878, which rounds to 2.9 days.
  10. Answer: 65.2 acre-feet. If 8 percent is lost, then 92 percent of the release arrives, so the release = 60 acre-feet / 0.92 = 65.217, which rounds to 65.2 acre-feet. Adding 8 percent to 60 instead gives 64.8, which is the common error and leaves the farm short.
  11. Answer: 3.08 acre-feet. An application of 0.28 inches is 0.28 / 12 = 0.023333 feet. Volume = 0.023333 ft x 132 acres = 3.08 acre-feet per pass.
  12. Answer: An acre-foot is a volume and a cubic foot per second is a rate. A farm orders a total amount of water for its crop, which is a volume, while a ditch rider can only control how fast water moves past a gate at any moment, which is a rate. The two are connected by time, since a flow rate held for a stated number of hours delivers a particular volume.

Differentiation

Support

Give students a conversion card listing every constant used here with its unit, and complete item 1 together before students continue. For items 4, 8, and 11, provide the inches-to-feet step already worked so students perform only the multiplication by acreage. Students who complete items 1 through 8 have met the first two objectives.

Extension

Ask students to build a delivery schedule that fills both orders inside a five-day window while the canal also carries a third order of their own design, then state what gate setting each day would require. Students can also calculate what lining the canal would save over a season if seepage dropped from 8 percent to 2 percent.

ELL supports

Pre-teach lateral, headgate, turnout, application depth, and seepage using a simple plan-view diagram of the canal with the two farms marked. Provide a two-column reference sheet that pairs each unit with the word rate or volume, which supports the reasoning item 12 asks for. Allow students to answer item 12 with a labeled sketch and a single sentence.

Extensions

Have students find the published water order form or delivery schedule for a real irrigation district and identify which units appear on it. Students can also compare the application depths used for two different crops in their region and calculate how many acre-feet a season of irrigation would require for each.