LOS CONFLICTOS EN LA EMPRESA 1. Resultados de aprendizaje

• Center pivots are used on about half of the sprinkler-irrigated lands in the USA.

• Center pivots are also found in many other countries.

• Typical lateral length is 1,320 ft (400 m), or ¼ mile.

• The lateral is often about 10 ft above the ground.

• Typically, 120-ft pipe span per tower (usual range: 90 to 250 ft), often with one- horsepower electric motors (geared down).

• At 120 ft per tower, a 1,320-ft lateral has about 11 towers; with 1-HP motors, that comes to about 10 HP just for moving the pivot around in a circle.

• The cost for a ¼ mile center pivot is typically about $45,000 (about $354/ac or $875/ha), plus about $25,000 for a corner system.

• For a ½ mile lateral, the cost may be about $75,000 (with out corner system).

• In the state of Nebraska, there are said to be 50,000 installed center pivots, about 10 to 15% of which have corner systems.

• The state of Texas has over 10,000 center pivots.

• Center pivots are easily (and commonly) automated, and can have much lower labor costs than periodic-move sprinkler systems.

• Center pivot maintenance costs can be high because it is a large and fairly complex machine, operating under "field" (sun, wind, dust, dirt) conditions.

• The typical maximum complete rotation is 20 hrs or so, but some (120-acre pivots) can go around in only about 6 hrs.

• Running a pivot around at relatively high speeds makes the mechanical parts wear out faster, and may also increase evaporation losses.

• IPS 6" lateral pipe is common (about 6-5/8 inches OD); lateral pipe is generally 6 to 8 inches, but can be up to 10 inches for 2,640-ft laterals.

• Long pivot laterals will usually have two different pipe sizes.

• Typical lateral inflow rates are 45 - 65 lps (700 to 1,000 gpm).

• At 55 lps with a 6-inch pipe, the entrance velocity is a bit high at 3 m/s.

• Typical lateral operating pressures are 140 - 500 kPa (20 to 70 psi).

• The end tower sets the rotation speed; micro switches and or cables keep other towers aligned.

• Without a corner system or end gun (see below), /4 = 79% of the square area is irrigated. An end-gun will irrigate additional 5% of the total area. Whereas a corner pivot can irrigate additional 12% of the total area. Thus total area irrigated comes out 96% (79% + 5% + 12% = 96%) leaving rest of the area un-irrigated.

• For a 1,320-ft lateral (without an end gun), the irrigated area is 126 acres.

• For design purposes, usually ignore soil WHC (WaZ); but, refill root zone at each irrigation (even if daily).

• Center pivots can operate on very undulating topography.

• Many farmers like extra capacity in the center pivot so they can shut off during windy times of the day, and still complete the irrigations in time.

• Some center-pivot irrigated fields have half the circle in one crop, and the other half in another crop (or fallow) - it can be difficult to make the pivot to stop at exactly the right position when some sections of the circle are irrigated differently than others.

• Center pivots on rolling terrain usually have pressure regulators at each sprinkler; otherwise, there is too much pressure variation among sprinklers, and the application uniformity is low.

• Some engineers claim that center pivots can haveup to about 90% application efficiency. A stationary sprinkle system applies water at constant rate, while the water application rate at a point varies continuously with time during application by any moving sprinkle system. As the system approaches a point, the application rate starts from zero, increases to a maximum, and then decreases to zero again as the moving system passes over the location. The water application under a center-pivot lateral is even more complicated. The application rate varies along the lateral from a low value near the pivot to higher values at the outer end (Figure 2). This variation in the application rates is essential due to two reasons: i) area of the circular irrigated field increases with square of the radius, ii) time of water application at a point decreases with increasing distance from the pivot as shown in the above figure. Thus instantaneous application rate patterns are different at different locations along the lateral. Since the application rate is the highest near the end of a center-pivot system and runoff may occur at this location if it exceeds the soil intake rate.

Figure 7.2 Measured water application rates and application times along a center- pivot lateral.

Keller and Bliesner (1988) derived water-application rate profiles along different points along the lateral of a center-pivot system as shown in Figure 8.8. The rate is maximum near the end of the lateral and it decreases inward as explained earlier. Water application rate for an elliptical profile is given by:

xj aj xj aj aj e e j I T I T T Q dR I 4 4 60 /      (7.1)

Where,

Ij = average application rate required at radial distance rj, mm/hr (in/hr) d = gross depth of water required per irrigation, mm (in)

Taj = application time at radial distance rj, min

Ixj = peak application rate at radial distance rj, mm/hr (in/hr)

Qe = ratio of water effectively discharged through sprinklers to total system discharge,

Re = effective portion of water discharged from sprinklers, most of which reaches the soil-plant surface in decimal

Figure 7.3 Water application rates at different points along a center-pivot lateral (Source: Keller and Bliesner, 1990)

Thus average application rate is a function of the radial distance rj from the pivot and it is proportional to the length of circular travel path at rj divided by the width of the application profile. It is given by:

T d . wj r π 2 Ij  j pi (7.2)

Combining the above equations gives:

2 e e b j j L O R Q K wj r π 2 I   (7.3) Where

Ij = average application rate at radius rj, mm/hr (in/hr) rj = radial distance from pivot to point under study, m (ft) dpi = average peak gross infiltration required per day, mm (in.) wj = width of stationary application patterns at rj, m (ft) T = average daily operating time, hr

K = conversion constant 1146 for metric units 30.6 for English units) L = radius of the irrigated field, m (ft)

Corner Systems

• Corner systems are expensive, and they don't irrigate the whole corner.

• Corner systems on center pivots have buried cables so that sprinklers in the corner extension arm turn on and off individually (or in groups) as the arm swings out and then back in again.

• The cables are buried about 5 ft (1.5 m) below the surface to prevent damage during tillage operations (such as chiseling or "ripping").

• The end tower on the main part of the lateral has an antenna facing downward to detect the signal from the buried cable, and to know when to begin to swing the extension arm outward.

Figure 7.4 A view of center-pivot system with a corner system

• Usually, groups of sprinklers are controlled by separate valves in the extension arm because the application rate and uniformity would differ too greatly from the desired values if all the corner system sprinklers turned on (and off) simultaneously.

• There may be a control box at both the pivot point (center of field) and at the joint where the extension arm connects to the main lateral; either box can be used to program and control the pivot (e.g. to shut it down).

• Application uniformity in the corners is not as high as in the main circle area.

End Guns

Some pivots have an end gun that turns on in the corners, in which all other sprinklers shut off via individual solenoid-actuated valves. The pivot stops in the corner while the end gun runs for a few minutes. Others just slow down in the corners, turning on an end gun, but leaving the other sprinklers running (at lower discharges); in these cases, a pressure transducer might be used at the end of the lateral to indicate when the gun turns on (resulting in a pressure drop), thus knowing when to slow the pivot. The figure below shows an example of the approximate corner areas than might be irrigated by an end gun.

Figure 7.5 (a). Area irrigated by the main system and end gun.

The end-guns turn on when the lateral is in pointing toward a corner area (which is when they should turn on) by angle measurements at the pivot point. In other cases, an end gun on a center pivot lateral might be set to run all of the time (i.e. all the way around the circle), effectively increasing the diameter of the irrigated area, but not dealing with un-irrigated corner areas.

Safety Switches

• Most center pivots have one or more safety switches.

• Some have switches to shut the whole machine off if any tower gets too far out of alignment.

• Some also have safety switches to shut them off if the temperatures gets below freezing (ice builds up and gets heavy, possibly collapsing the structure) - typically shuts off at 32°F and turns back on at 40°F.

• With drop-down sprayer sprinklers, ice build-up is not so problematic.

• Some have safety switches connected to timers: if a tower has not moved in a specified number of minutes, the system shuts down.

There may also be safety switches associated with the chemical injection equipment at the lateral inlet location.

Figure 7.6 A view collapsed center pivot system

Drop Down Sprinkler

 Almost all new center pivots have drop-down, low-pressure (20 - 25 psi) sprinklers.

 Many older center pivots, which formerly had above-lateral impact sprinklers (50 - 60 psi) have been retrofitted with drop-down, low-pressure sprinklers. These features help reduce energy (pumping) costs and reduce evaporation and wind drift.

 Center pivot laterals sometimes have manual flush valves (gate or butterfly) at the end to periodically wash sediments out of the pipe. Some of the drop-down tubes are polyethylene, others are PVC, and still others are galvanized steel.

 The steel drop-down tubes have the advantage of rigidity and do not sway nearly as much as polyethylene hoses (which usually have weights at bottom) under windy conditions.

Figure 7.7 System with sprinkler heads below the lateral

II. System Capacity

• The general center pivot design equation for system capacity is based on Eq.

5.4 from the textbook:

pa f d s TE k k U R fT k d R fT Ad K Q 1 2 1 2 '    (7.4)

Where, K is 2.78 for metric units and 453 for English units kl is (10,000 m2/ha)/(2.78 TI) = 1,145 for metric units kl is (43,560 ft2/acre)/(453 %) 30.6 for English units kf is the peak period evaporation factor (Table 14.1) A is area (ha or acre) d is gross daily application depth (mm or inch) d' is defined in the equation below (mm or inch) f is frequency in days per irrigation.

T is operating time (hrs/day) R is the effective radius (m or ft) Ud is the peak-use ET rate of the crop (mm/day or inch/day) Qsis the system capacity (lps or gpm).

• The gross application depth, d, is equal to dn/Epa, where Epa is the design application efficiency, based on uniformity and percent area (pa) adequately irrigated.

• The operating time, T, is generally 20-22 hrs/day during the peak-use period.

• R is the effective radius, based on the wetted area from the center pivot.

• The effective radius is about 400 m for many center pivots.

• R « L + 0.4w, where L is the physical length of the lateral pipe, and w is the wetted diameter of the end sprinkler.

• This assumes that approximately 0.8 of the sprinkler radius beyond the lateral pipe is effective for crop production.

• Note that, for center pivots, Qs is proportional to Ud, and d and f are generally not used, which is similar to drip irrigation design.

• Usually, for center pivot design, f = 1 day. So, if you use f > 1 day, you must also increase d or d' to accommodate f number of days.

III. Gross Application Depth

If a center pivot is operated such that the water holding capacity of the soil is essentially ignored, and water is applied frequently enough to satisfy peak- use crop water requirements, then use dn/f = Ud, and

e e pa d f pa d f s O R DE U k E U k d'   (7.5)

where d' is the gross daily application depth (mm/day or inches/day); and kfis a peak- use period evaporation factor, which accounts for increased soil and foliage evaporation due to high frequency (daily) irrigation.

When LR > 0.1, the LR can be factored into the equation as:

pa d f e e pa d f E LR U k O R DE LR U k d ) 1 ( 9 . 0 ) 1 ( 9 . 0 '     (7.6)

Which is the same as Eq. 14.1b from the textbook, except that DEpa, Re and Oeare all as fractions (not percent).

Values of kf can be selected for the peak period from Table 14.1 of the textbook for varying values of frequency, f.

Values for non-peak periods can be computed as described in the textbook on page 314:

Where, kf and PT are for the peak-use period (Table 14.1), and k'f and PT are the frequency coefficient and transpiration percentage (PT) for the non-peak period.

ET T

PT  (7.8)

• PT and PT' can be thought of as the basal crop coefficient (Kcb), or perhaps Kcb - 0.1 (relative to alfalfa, as per the note in Table 14.1).

• It represents the transpiration of the crop relative to an alfalfa reference.

IV. Water Application along the Pivot Lateral

• A major design difficulty with a center pivot is maintaining the application rate so that it is less than the intake rate of the soil.

• This is especially critical near the end of the lateral where application rates are the highest.

• As one moves along the center pivot lateral, the area irrigated by each unit length of the lateral (each 1 ft or 1 m of length) at distance r from the pivot point can be calculated as:

r r

r

a( 0.5)2 ( 0.5)2 2 (7.9) This is equal to the circumference at the radial distance r.

• The portion of Qs(called q) which is applied to the unit strip at distance r is:

2 2 2 2 R r R r A a Q q s      (7.10) 2 2 R rQ q s (7.11) where q can be in units of lps per m, or gpm per ft

This gives the amount of water which should be discharging from a specific unit length of lateral at a radial distance r from the pivot point.

The q value at the end of the lateral (r = R) per ft or m is: Use q to select the nozzle size, where qnozzle= q Se

UNIFORMITY OF A CENTER PIVOT