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Worksheet Grade 10 Science

Yarrowton Orchard Irrigation: Tracking Soil Water and Crop Use

Grade 10 students run a seven-day soil water balance for an apple orchard, decide when to irrigate, and compare the water a drip and a sprinkler system would need.

Objectives

  1. Students will calculate crop evapotranspiration from reference values and a crop coefficient.
  2. Students will use available water and allowable depletion to decide when an orchard must be irrigated.
  3. Students will compare the gross water two irrigation systems need to deliver the same net depth.

Vocabulary

Evapotranspiration
Evapotranspiration is the total amount of water that leaves the land and goes into the air, both from wet surfaces and from plants. Scientists combine evaporation and transpiration into one word.
Irrigation efficiency
The share of irrigation water that crops actually use compared with the amount taken from the river or well. Higher efficiency means less waste.
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: crop coefficient, available water, allowable depletion

Teacher overview

Irrigation scheduling begins as an accounting problem. The soil holds a limited depth of water that plant roots can actually use, the atmosphere draws on that store every day through evapotranspiration, and rain and irrigation are the only additions. The depth of water applied is not the depth the crop receives, and ignoring irrigation efficiency leaves a sprinkler system nearly a third short of what the root zone needed. The fictional Yarrowton Orchard, a 40-acre apple block in the Umberly Valley, gives students a full week of data to work through.

Yarrowton Orchard Irrigation: Tracking Soil Water and Crop Use — Grade 10 Science
Name: ____________________________ Date: ______________

Student Worksheet

Suppose Yarrowton Orchard grows 40 acres of mature apple trees. The soil is a silt loam that holds 2.0 inches of available water per foot of soil, and the root zone is 3 feet deep. The orchard manager irrigates before the soil loses more than 50 percent of that available water. Crop evapotranspiration equals reference evapotranspiration times the crop coefficient, and the crop coefficient for these trees in midsummer is 0.95. The reference values measured last week were 0.28, 0.30, 0.26, 0.31, 0.33, 0.29, and 0.27 inches per day. Use 1 acre-foot = 325,851 gallons and 12 inches = 1 foot.

  1. The soil holds 2.0 inches of available water per foot, and the root zone is 3 feet deep. Calculate the total available water in the root zone, in inches.
  2. The manager irrigates once the soil has lost 50 percent of the total available water you found in item 1. Calculate the allowable depletion, in inches.
  3. The seven reference values for last week were 0.28, 0.30, 0.26, 0.31, 0.33, 0.29, and 0.27 inches per day. Calculate the total reference evapotranspiration for the week.
  4. Using your weekly total from item 3 and a crop coefficient of 0.95, calculate the crop evapotranspiration for the week, in inches.
  5. Using a weekly crop evapotranspiration of 1.94 inches over 7 days, calculate the average daily crop evapotranspiration. Round to the nearest hundredth of an inch.
  6. The soil starts full. Using an allowable depletion of 3.0 inches and an average crop use of 0.277 inches per day, calculate how many days pass before the manager must irrigate. Round to the nearest tenth.
  7. A storm drops 0.60 inch of rain, and 80 percent of it soaks in and stays in the root zone. Using the same daily crop use of 0.277 inches per day, calculate how many extra days that rain buys before irrigation is needed. Round to the nearest tenth.
  8. The manager must replace 3.0 inches of water across all 40 acres. Calculate that net irrigation volume in acre-feet, using 12 inches equals 1 foot.
  9. Convert your answer from item 8 to gallons, using 1 acre-foot = 325,851 gallons.
  10. The orchard's drip system is 90 percent efficient, so only that share of the applied water reaches the root zone. Using a net requirement of 3,258,510 gallons, calculate the gross gallons the drip system must deliver.
  11. A neighbor uses a sprinkler system that is 70 percent efficient. Using the same net requirement of 3,258,510 gallons, calculate the gross gallons that sprinkler system must deliver.
  12. Using your answers from items 10 and 11, calculate the percent less water the drip system delivers compared with the sprinkler system. Round to the nearest tenth.
  13. The drip system must apply 3,620,567 gallons over 40 hours of run time. Calculate the flow rate the system needs, in gallons per minute.
  14. Some growers irrigate on a fixed calendar, such as every Tuesday and Friday. Explain two ways the soil water balance in this worksheet gives a better answer than a calendar, and name the measurement a grower would need to keep it running.

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: 6.0 inches.
    Multiply the holding capacity by the depth of the root zone: 2.0 inches per foot x 3 feet = 6.0 inches of available water.
  2. Answer: 3.0 inches.
    Take half of the total available water: 6.0 inches x 0.50 = 3.0 inches. Beyond this depletion the trees begin to lose water faster than the roots can supply it.
  3. Answer: 2.04 inches.
    Add the seven daily values: 0.28 + 0.30 + 0.26 + 0.31 + 0.33 + 0.29 + 0.27 = 2.04 inches for the week.
  4. Answer: 1.94 inches.
    Multiply the reference total by the crop coefficient: 2.04 x 0.95 = 1.938 inches, which rounds to 1.94 inches.
  5. Answer: 0.28 in/day.
    Divide the weekly crop use by seven days: 1.94 / 7 = 0.277 inches per day, which rounds to 0.28 inches per day. Keep the unrounded value for the next items.
  6. Answer: 10.8 days.
    Divide the allowable depletion by the daily use: 3.0 / 0.277 = 10.83 days, or about 10.8 days. Students who use the rounded 0.28 will get 10.7 days, which is also acceptable.
  7. Answer: 1.7 days.
    First find the water that actually reaches the root zone: 0.60 inch x 0.80 = 0.48 inch. Then divide by daily use: 0.48 / 0.277 = 1.73 days, or about 1.7 days.
  8. Answer: 10 acre-feet.
    Convert the depth to feet and multiply by area: 3.0 inches / 12 = 0.25 foot, and 0.25 foot x 40 acres = 10 acre-feet. Students may also work in acre-inches: 3.0 x 40 = 120 acre-inches, then divide by 12.
  9. Answer: 3,258,510 gallons.
    Multiply acre-feet by the conversion: 10 x 325,851 = 3,258,510 gallons.
  10. Answer: 3,620,567 gallons.
    Divide the net requirement by the efficiency: 3,258,510 / 0.90 = 3,620,566.7, which rounds to 3,620,567 gallons. Dividing is correct here, because the system must put on more than the crop receives.
  11. Answer: 4,655,014 gallons.
    Divide by the lower efficiency: 3,258,510 / 0.70 = 4,655,014.3, which rounds to 4,655,014 gallons. The same net depth now costs about 1.03 million gallons more.
  12. Answer: 22.2 percent.
    Subtract and divide by the larger figure: 4,655,014 minus 3,620,567 = 1,034,447 gallons saved, and 1,034,447 / 4,655,014 = 0.2222, or 22.2 percent less water. Students may also compare the efficiencies directly, since 1 minus 0.70 / 0.90 gives the same result.
  13. Answer: 1,509 gpm.
    Divide gallons by run time, then by 60 minutes per hour: 3,620,567 / 40 hours = 90,514 gallons per hour, and 90,514 / 60 = 1,508.6, or about 1,509 gallons per minute.
  14. Answer: The balance tracks actual demand, and it accounts for rain.
    A calendar applies the same depth whether the week was hot and windy or cool and cloudy, so it over-irrigates in mild weather and stresses the trees during a heat wave. The balance also credits effective rainfall, as item 7 shows, while a calendar ignores it and pushes water past the root zone. To keep the balance running, a grower needs daily reference evapotranspiration for the area, which usually comes from a regional weather station network, and periodic soil moisture readings to confirm the account is tracking reality.

Differentiation

Support

Give students a partially completed daily table with columns for reference evapotranspiration, crop evapotranspiration, and cumulative depletion, with the first two days filled in. Work one conversion from inches over acres to acre-feet on the board using a smaller block, such as 2.0 inches over 10 acres, before students attempt item 8.

Extension

Have students extend the balance a second week using reference values of 0.34, 0.36, 0.35, 0.38, 0.31, 0.29, and 0.30 inches per day, then determine the exact day the orchard reaches allowable depletion and how the answer would change if the manager set the trigger at 40 percent depletion instead of 50 percent.

ELL supports

Pre-teach "depletion" and "efficiency" with a labeled drawing of the root zone as a container that empties and refills, and post the two formulas in a visible place. Allow students to record items 1 through 7 on the drawing with arrows and short labels, and provide the sentence frame "The orchard must irrigate on day ___ because ___" for item 6.

Extensions

Ask students to prepare a one-page irrigation schedule for the fictional Yarrowton Orchard covering a two-week stretch, showing the trigger depth, the run time in hours, and the flow rate the pump must supply. Require them to state what they would change if a well permit limited the orchard to 1,200 gallons per minute.