Part 4b, Sprinkler Irrigation, Small Systems, Design Example
By Ed Butts, PE, CPI
We have now had four articles in this series on irrigation fundamentals and concepts. Previous installments have discussed irrigation basics beginning with terms and definitions; soil-water-plant relationships, water quality considerations, and application efficiency; determining required flow rate, volume, and distribution uniformity.
Last month began a two-part subseries on sprinkler irrigation techniques and design. We’ll wrap up this topic by going over a design example.
Our example will illustrate the procedure for designing an irrigation system. Note that each step is deliberate and detailed. This is atypical of the actual process as there are generally several shortcuts taken. However, I am approaching this example as a step-by-step design to better show the proper procedure.
Design an irrigation system for 40 acres of onions (refer to Figure 1) with the following conditions:
Soil: Type 3: light (fine) sandy loam up to 6 feet of depth with 6.2% slope: AWC range: 1.5-2.0 inches/foot
Maximum application rate: <0.80 inch/hr (using Table 1 in WWJ May issue)
Soil water-holding (AWC) capacity: ~1.75 inches/ft of soil as midrange value (refer to Table 1 in WWJ April issue)
Environmental conditions: Maximum prevailing wind is across field at 6 mph
Water source quantity and quality: 150-foot well producing 450 GPM Firm Q at 105 feet PWL; water quality is acceptable (no salts)
Elevation to last sprinkler from well: +14 feet
Crop: Dry onions
Applied area: 40 acres (1320 feet × 1320 feet)
Total growing season: Six to seven months (April to October)
Effective root depth: 1-2 feet
Seasonal water requirements (Crop ET): ~28 inches
Crop kC for various growth stages: initial: 0.50; crop development: 0.75; mid-season: 1.05; late season: 0.85
Peak crop ET: 0.26 inches (July)
Design Step No. 1:
This initial procedure is where actual selection of the irrigation method is conducted. After considering the aspects of source and soils data, selecting the method of irrigation is performed to enable completing the design.
For this example, after a review and discussion of the capital, labor, operating costs, and also the advantages and disadvantages of the three logical methods—hand-lines, wheelline, and a hard hose traveler, the client has opted to purchase a wheelline to operate using conventional impact sprinklers with higher pressures between 50 to 75 psi. It has the lowest capital investment cost of the mechanized methods, reasonable power costs, and acceptable labor requirements for a 40-acre field.
Design Step No. 2:
This should involve a water balance determination. This allows the designer and client to review the projected yearly water use and includes factors for the crop’s evapotranspiration (ET), normal precipitation as an offset to irrigation, and the gross irrigation requirement, after including the irrigation efficiency.
Although not guaranteed to be totally accurate or actually needed for a design, this type of analysis is helpful as it allows the client to understand the projected volume of water they will need for a year’s crop production.
This is especially valid if the water is purchased from a cooperative or district since it provides a method for yearly budgeting of water costs. It can also assist in determining basin or reservoir sizes for irrigation systems requiring storage volume to compensate for undersized or inadequate source capacity.
Even though the water balance assumes that 8.4 inches of rainfall will offset a portion of the required irrigation demand, for irrigation system planning and design purposes, I recommend disregarding the potential precipitation and using the crop ET value divided by the irrigation efficiency and peak CU as the determiners.
For this example, the estimated yearly water volume would be: 28 inches (Crop ET) × 27,150 gals/ac-in × 40 acres = 30,408,000 gals/0.70 (for 70% irrigation or application efficiency) = 43,440,000 gallons and peak CU of 0.26 inches/day be used for the design.
Design Step No. 3:
A crop with a shallow root zone demands careful attention to the available water-holding capacity and the amount of water available to the crop between irrigation applications. For onions, since we know the root depth is 2 feet and maximum consumptive use of the crop to be 0.26 inches/day, along with the soil’s water-holding capacity of 1.75 inches per foot of soil, we must use these values to determine the irrigation frequency:
As a safety factor for soil water loss through drainage, to ensure that some water is left in the soil to prevent plant stress and to accommodate system downtime and possible equipment failure, a 20% safety factor is recommended. However, this will vary with the soil type, water-holding capacity, and crop root depth:
Design irrigation rotation: 13.46 days × 0.80 = 10.76 days. Round down to a 10-day rotation schedule.
Design Step No. 4:
Since the maximum allowable soil intake rate is another fixed value and we know a wheelline will be used with impact sprinklers at high pressure or 50-75 psi, we can now apply this value to select the nozzles using an initial assumed spacing of 40 feet × 50 feet (from 1320 feet/50 feet = 26.4) = 28 sets and moves.
Verify number of sets per day: 28 total sets/10-day rotation = 2.8/day. Use 3 per day (8 hrs/set and move).
Referring to Table 1 in the WWJ July issue, the closest fit to this application at 50 psi nozzle pressure is to use a ¼-inch nozzle at 50 psi. This is equal to 13 GPM per sprinkler (although a 5/16-inch nozzle at 40 psi is closer, this falls outside of the desired pressure range and may compromise wind resistance and coverage; double nozzle sprinklers with equivalent capacity could also be used to improve the coverage next to the sprinkler). Thus, the corrected application rate is:
Now, we can determine the required number of operating hours per set:
Peak CU = 0.26 inches/day/0.70 (irr. eff.) = 0.37 inches/day × 10-day rotation = 3.71 inches of gross water application required
3.71 inches (10-day max. CU)/0.625 inches/hr (application rate) = 5.936 hours. Operate each set for 6 hours < 8 hours
Next, verify that the source is adequate. From the raw data, the maximum source capacity is equal to 450 GPM
Design Step No. 5:
The system hydraulics to determine the required head would be the final step.
Calculating the friction loss in a lateral is somewhat complicated and there are numerous slide rule calculators, nomographs, and websites that can easily conduct this calculation. But for those who wish to be able to find the solution manually, the following equation can be used for an end- or center-feed wheelline, hand-move, or solid-set lateral (a center feed line would simply use one-half the length and number of sprinklers):
Lateral line head loss (in psi):
Q = Total lateral flow in GPM
C = Pipe type Hazen-Williams friction coefficient (aluminum = 120, plastic = 150)
S = Nominal pipe or tube size (inches)
L = Total lateral length (feet)
NS = Number of sprinklers per lateral
For this example, using 32 sprinklers on the 1280-foot wheelline at 13 GPM each with a 4-inch aluminum line (C= 120):
Since the recommended maximum lateral line loss is 20% of the line pressure (50 psi × 0.20 = 10 psi), use of a 4-inch lateral line will result in a seriously inequitable distribution and inadequate coverage. Therefore, we would move up to a larger 5-inch line to lower the pressure drop. The only value that will change from the previous calculation is to upsize from a 4-inch to a 5-inch line (S value):
FL = 4.552 × 9.998 × 0.00039 × 1280 feet × 0.36654 = 8.32 psi
This value is within the allowable pressure drop of 10 psi although flow control nozzles (FCN) can also be used to ensure even better distribution of sprinkler flow rates across the line. However, this design will be used as the variance and is not felt to be significant. The remaining friction loss is in the mainline from the well to the farthest hydrant.
In order to limit a buried PVC pipeline velocity to a recommended value of 5 feet per second (5 FPS), a 6-inch PVC mainline is selected (V = 4.73 FPS). Since the well is located in the center of the field, the mainline friction loss is roughly equal to one-half the distance. Therefore, using friction loss charts, the pressure loss equals:
FL in 6-inch PVC mainline:
hf = (1320 feet/2/100 feet/c) × 0.55 psi/c at 416 GPM (C=140) = 3.63 psi
Converting the two pressure drop and operating pressure values to feet of head for the pump design yields:
8.32 psi (wheelline ΔP) + 3.63 psi (mainline ΔP) = 11.95 psi × 2.31 feet/psi = 27.60 feet of head
(+) 55 psi of sprinkler operating pressure = 55 psi × 2.31 feet per psi = 127.05 feet of head
Adding this value to the well lift of 105 feet and elevation gain of 14 feet from the well to the last sprinkler equals the pump’s required total dynamic head (TDH):
TDH = 27.60 feet (hf) + 127 feet (55 psi) + 14 feet (elev.) + 105 feet (PWL) = 273.6 feet TDH
Estimating the required pump horsepower with an estimated pump efficiency at a low of 75% (0.75) yields:
Referring to Figure 1, The well pump will be a 40 HP submersible or vertical turbine pump set at approximately 135 feet. A 1280-foot-long end-feed 5-inch wheelline with 64-inch-diameter wheels will be equipped with 32¼-inch single-nozzle sprinklers on a 40-foot lateral line spacing and travel between sets on 50-foot mainline spacings.
The mainline will consist of a 6-inch Class 160 psi buried pipeline with hydrant risers at 150-foot spacings; 50-foot swing pipes will be used to offset the 150-foot distances between hydrants in order to connect the wheelline at 50-foot intervals. This results in an application rate of 0.625 inches/hour, well below the maximum permissible application rate of 0.80 inches/hour.
Each set will operate for six hours for a gross application of 3.75 inches of water. Twenty-eight (28) individual sets are required to traverse the field. At three sets per day, this will require approximately 10 days to cover the field.
After the final set (28th set), the wheelline will deadhead back across the field to the 1st set and resume irrigation at the location of the 1st set to replenish the water used during the previous 10 days. This cycle will continue with adjustments in frequency and operational hours to coincide with the crop’s intake rate.
This is obviously a simplistic approach to an irrigation system design where each element seemingly fell into line. This is usually rare in actual practice, but gives you an idea as to what goes into a system design and layout.
This concludes this month’s Engineering Your Business on small sprinkler irrigation system design. Next month, we will delve into larger impact sprinkler systems, including the Big-Gun type.
Until then, work safe and smart.
Ed Butts, PE, CPI, is the chief engineer at 4B Engineering & Consulting, Salem, Oregon. He has more than 40 years of experience in the water well business, specializing in engineering and business management. He can be reached at firstname.lastname@example.org.