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13.2: Center Pivot Characteristics

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    Sprinkler Discharge

    Since center pivot laterals rotate around the field, the delivery of water along the lateral is much different than for other lateral-based systems. The area that is irrigated by an individual sprinkler increases with distance from the pivot base (Figure 13.4). The goal in irrigation is to apply the same depth of water to all parts of the field; therefore, the discharge from a sprinkler must be larger near the distal end of the lateral than close to the pivot point. The required discharge is given by:

    \(q_s=\dfrac{2\pi RSC_g}{43560} \) (13.1)

    where: qs = the discharge from an individual sprinkler (gpm),

    R = the distance of the sprinkler head or spray nozzle from the pivot base (ft),

    S = the local spacing between successive sprinklers along the lateral (ft),

    Cg = the gross system capacity required for the irrigation system (gpm/ac) = Q/A

    Figure 13.4. Diagram of the area associated with a sprinkler along a center pivot lateral.

    diagramAreaSprinklerA.jpegdiagramAreaSprinklerB.jpeg

    The discharge from the sprinkler increases linearly with the distance from the pivot, i.e., a sprinkler 1,000 feet from the pivot will require twice as much discharge as a sprinkler at 500 feet. The discharge also depends on the spacing between sprinklers and the gross system capacity. The system capacity is determined by the crop, climate, and soils as described in Chapters 4 and 5, and does not vary by location along the pivot. The system capacity (Cg) must be determined from the field requirements and should not be determined arbitrarily.

    Originally, pivots were manufactured with a constant spacing of about 32 feet between sprinklers. Spacing sprinklers closer together at the distal end allows lower operating pressures to be used while maintaining excellent uniformity. Today pivot laterals are manufactured with sprinkler outlets spaced at 7.5 to 10 feet. Near the pivot base sprinklers are not placed in every available outlet. Somewhere along the lateral the discharge required from a sprinkler becomes too large if outlets are skipped. Then the spacing must be reduced. This generally allows for using the same size of sprinkler device along a major portion of the lateral. Equation 13.1 has been solved in terms of discharge per unit length along the lateral (i.e., qs /S) for a range of conditions for pivots (Table 13.1).

    Table 13.1. Sprinkler discharge requirement per unit length along the lateral (qs/S), gpm/ft.
    Distance from Pivot (ft) Gross System Capacity: 4 gpm/ac Gross System Capacity: 5 gpm/ac Gross System Capacity: 6 gpm/ac Gross System Capacity: 7 gpm/ac Gross System Capacity: 8 gpm/ac Gross System Capacity: 9 gpm/ac Gross System Capacity: 10 gpm/ac
    100 0.06 0.07 0.09 0.10 0.12 0.13 0.14
    200 0.12 0.14 0.17 0.20 0.23 0.26 0.29
    300 0.17 0.22 0.26 0.30 0.35 0.39 0.43
    400 0.23 0.29 0.35 0.40 0.46 0.52 0.58
    500 0.29 0.36 0.43 0.50 0.58 0.65 0.72
    600 0.35 0.43 0.52 0.61 0.69 0.78 0.87
    700 0.40 0.50 0.61 0.71 0.81 0.91 1.01
    800 0.46 0.58 0.69 0.81 0.92 1.04 1.15
    900 0.52 0.65 0.78 0.91 1.04 1.17 1.30
    1000 0.58 0.72 0.87 1.01 1.15 1.30 1.44
    11000 0.63 0.79 0.95 1.11 1.27 1.43 1.59
    12000 0.69 0.87 1.04 1.21 1.38 1.56 1.73
    13000 0.75 0.94 1.13 1.31 1.50 1.69 1.88
    14000 0.81 1.01 1.21 1.41 1.62 1.82 2.02
    15000 0.87 1.08 1.30 1.51 1.73 1.95 2.16
    16000 0.92 1.15 1.38 1.62 1.85 2.08 2.31
    17000 0.98 1.23 1.47 1.72 1.96 2.21 2.45
    18000 1.04 1.30 1.56 1.82 2.08 2.34 2.60
    19000 1.10 1.37 1.64 1.92 2.19 2.47 2.74
    2000 1.15 1.44 1.73 2.02 2.31 2.60 2.88
    21000 1.21 1.51 1.82 2.12 2.42 2.73 3.03
    22000 1.27 1.59 1.90 2.22 2.54 2.86 3.17
    23000 1.33 1.66 1.99 2.32 2.65 2.99 3.32
    24000 1.38 1.73 2.08 2.42 2.77 3.12 3.46
    25000 1.44 1.80 2.16 2.52 2.88 3.25 3.61
    26000 1.50 1.88 2.25 2.63 3.00 3.38 3.75

    Area Irrigated

    The area irrigated with a center pivot depends on the radius irrigated with the main lateral and the radius gain when the end gun is turned on. Typically, a center pivot is positioned into a square land area similar to that shown in Figure 13.5. The end gun can only be operated when the spray pattern stays within the field boundary. In the example in Figure 13.5 the end gun operates over an angle (ß) of 42° in each corner.

    Figure 13.5. Diagram of the effect of end-gun operation on the area irrigated (adapted from Martin et al., 2017).

    diagramEffectEndGun.png

    Usually the end gun discharges water only about half of the time that the main system operates. The time that the end gun operates depends on the radius of the main system and the gain from the end gun.

    The amount of area irrigated with a pivot placed in the center of a square tract of land with the end gun operating in all four corners is computed with the following equation (von Bernuth, 1983):

    \(A_t=\dfrac{\pi{R_l}^2+\left[\pi-4\cos^{-1}\left(\dfrac{R_l}{R_l+R_{eg}} \right) \right]}{43560} \) (13.2)

    where: At = the total irrigated area (ac),

    Rl = the radius irrigated with the main system lateral (ft),

    Reg = the radius gain from using the end gun (ft), and inverse cosine is evaluated in radians.

    Increasing the radius gain from the end gun does not ensure more irrigated area since the angle of the section that can be irrigated with the end gun decreases. The maximum irrigated area will, in fact, occur when the radius gain from the end gun is about 21% of the length of the main pivot lateral. Usually, however, the availability of end gun nozzle sizes, discharge requirement of the end gun, and available system pressure dictate the radius gain from the end gun. Solutions to Equation 13.2 have been developed in Table 13.2. The values in this table apply when all four corners are irrigated. Sometimes a road along the property reduces the angle of operation of the end gun in the corner of the field. Table 13.2 also assumes that the entire area wetted by the end gun is planted to the irrigated crop. This may not be done in some cases if the depth of application tapers off near the end of the radius of coverage of the end gun. This will reduce the values from Table 13.2 slightly, but usually not by a significant amount. The values in Table 13.2 should be adequate for planning and management.

    Table 13.2. Total irrigated area for different lengths of the main system and the end gun coverage.
    Radius Irrigated with Main Lateral (ft)

    Gain of Wetted Radius from End Gun Operation

    0 ft

    Gain of Wetted Radius from End Gun Operation

    50 ft

    Gain of Wetted Radius from End Gun Operation

    75 ft

    Gain of Wetted Radius from End Gun Operation

    100 ft

    Gain of Wetted Radius from End Gun Operation

    125 ft

    Gain of Wetted Radius from End Gun Operation

    150 ft

    Gain of Wetted Radius from End Gun Operation

    200 ft

    Gain of Wetted Radius from End Gun Operation

    Maximum Area[a]

    800 46 49 50 51 51 51 - 51
    900 58 62 63 64 65 65 - 65
    1000 72 77 78 79 80 80 80 80
    11000 87 92 94 95 96 97 97 97
    12000 104 109 111 113 114 115 116 115
    13000 122 128 130 132 133 134 135 135
    14000 141 148 151 152 154 155 157 157
    15000 162 170 172 175 176 178 180 180
    16000 185 193 196 198 200 202 204 205
    17000 208 217 220 223 225 227 230 231
    18000 234 243 246 249 252 254 257 259
    19000 260 270 274 277 280 282 286 289
    20000 288 299 303 306 300 312 316 320
    21000 318 329 333 337 340 343 348 353
    22000 349 361 365 369 373 376 381 387
    23000 382 394 399 403 307 376 415 423
    24000 415 428 434 438 442 410 451 461
    25000 451 464 470 475 479 482 489 500
    26000 488 502 507 512 517 521 528 541
    [a] Maximum area occurs when the radius gain is 21% of the main lateral length.

    Pressure Distribution

    Nozzle selection and center pivot evaluation require knowledge of the pressure distribution along the pivot lateral. The distribution is unique for pivots since the discharge required of sprinklers increases along the pivot lateral. The pressure at a point along the pivot lateral is given by:

    \(P_R=P_0-\dfrac{P_{lp}R_l f_p}{1000}-0.433Eg \) (13.3)

    where: PR = the pressure at point R along the lateral (psi),

    P0 = the pressure at the inlet to pivot lateral (psi),

    Plp = the pressure loss due to friction in the pivot lateral (psi/1000 ft),

    Eg = the elevation gain from the lateral inlet to point R on the lateral (ft),

    Rl = the distance from the pivot base to the last sprinkler on the main lateral (ft), and

    fp = the pressure distribution factor at fraction distance R/Rl (dimensionless) (Figure 13.6).

    The desired pressure at the inlet to the lateral is selected when the pivot is designed. The actual pressure is determined by the performance of the pump, wear of sprinklers and pressure regulators, and water or pressure loss along the mainline that supplies the pivot. Adding a pressure gauge to the lateral at the inlet is an excellent way to monitor center pivot performance. If the inlet pressure drops much below the design specification, the cause of the problem should be determined and corrected if feasible.

    The pressure loss due to friction along center pivot laterals is computed similarly to that for moved lateral systems. The multiple outlet factor for center pivots does not change with the number of sprinklers along the lateral. The multiple outlet factor for center pivots without an end gun is about 0.54 and 0.56 for systems with an end gun.

    Center pivot laterals are specially made to conduct the water and to provide the strength needed to suspend the lateral above the ground. The lateral diameter is also unique for center pivots and moving lateral systems. The typical lateral is made of galvanized steel pipe with a wall thickness of 0.109 inches. A C value in the HazenWilliams equation (Equation. 8.11) of 140 is typically used to compute friction loss along the pivot. Values for the pressure loss per unit length of center pivot laterals are given in Table 13.3 for typical lateral diameters. Table 13.3 is for laterals that are all one size. As will be illustrated below, 80% of the pressure loss of a pivot lateral occurs in the first half of the lateral. Pressure loss can be reduced by using larger diameter pipe for the initial portion of the lateral rather than one diameter for the whole lateral. The pressure loss for systems with multiple pipe diameters are given in Table 13.4. The pressure distribution factor for center pivots is given in Figure 13.6. The elevation gain in Equation 13.3 is elevation of the point of concern minus the elevation at the pivot base. If the pivot base is higher than the point of concern, then Eg < 0.

    Figure 13.6. Pressure loss distribution factor for center pivot laterals.

    pressureLossDistributionFactor.jpeg

    Table 13.3. Pressure loss in center pivot laterals without end guns, psi/1,000 feet of pipe. Multiply losses by 1.037 for laterals with end guns.

    Hazen Williams Equation C Value = 140 Multiple Outlet Factor for Center Pivots = 0.54

    Flow Rate into Pivot Lateral (gpm)

    Outside diameter of pipe=6 in

    Inside diameter of pipe =5.782 in

    Outside diameter of pipe=6 5/8 in

    Inside diameter of pipe =6.407 in

    Outside diameter of pipe=8 in

    Inside diameter of pipe =7.782 in

    Outside diameter of pipe=10 in

    Inside diameter of pipe =9.782 in

    200 0.93 0.57 - -
    300 1.98 1.20 - -
    400 3.38 2.05 - -
    500 5.10 3.10 - -
    600 7.15 4.34 - -
    700 9.51 5.77 3.57 -
    800 12.18 7.39 4.43 -
    900 15.15 9.20 - -
    1000 18.42 11.18 - -
    11000 21.98 13.34 5.18 -
    12000 - 15.67 6.08 2.00
    13000 - 18.17 7.06 2.32
    14000 - 20.85 8.09 2.66
    15000 - - 9.20 3.02
    16000 - - 10.36 3.41
    17000 - - 11.60 3.81
    18000 - - 12.89 4.24
    19000 - - 14.25 4.68
    20000 - - 15.67 5.15
    21000 - - 17.15 5.63
    22000 - - 18.69 6.14
    23000 - - 20.30 6.67
    240000 - - - 7.22
    26000 - - - 8.37
    28000 - - - 9.60
    30000 - - - 10.91
    32000 - - - 12.29
    34000 - - - 13.75
    Table 13.4a. Pressure loss in center pivot laterals with two diameters of pipe, 8 in and 6 in, psi/1,000 feet. Values are for laterals without end guns. Multiply by 1.037 for systems with an end gun.
    Flow Rate (gpm) Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe: 1.0 Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe: 0.9 Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe: 0.8 Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe: 0.7 Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe: 0.6 Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe: 0.5 Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe: 0.4 Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe: 0.3 Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe: 0.2 Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe: 0.1 Fraction of Lateral That Is 8-inch O.D. Galvanized Steel Pipe: 0.0
    900 3.6 3.6 3.7 3.9 4.2 4.7 5.4 6.2 7.1 8.1 9.2
    1000 4.3 4.4 4.5 4.7 5.1 5.8 6.6 7.6 8.7 9.9 11.2
    11000 5.2 5.2 5.3 5.6 6.1 6.9 7.8 9.0 10.4 11.8 13.3
    12000 6.1 6.1 6.2 6.6 7.2 8.1 9.2 10.6 12.2 13.9 15.7
    13000 7.1 7.1 7.2 7.6 8.3 9.4 10.7 12.3 14.1 16.1 18.2
    14000 8.1 8.1 8.3 8.8 9.6 10.7 12.3 14.1 16.2 18.5 20.8
    15000 9.2 9.2 9.4 10.0 10.9 12.2 13.9 16.0 18.4 21.0 23.7
    16000 10.4 10.4 10.6 11.2 12.5 13.7 15.7 18.0 20.7 23.7 26.7
    17000 11.6 11.6 11.9 12.6 13.7 15.4 17.6 20.2 23.2 26.5 29.9
    18000 12.9 12.9 13.2 14.0 15.2 17.1 19.5 22.4 25.8 29.4 33.2
    Table 13.4b. Pressure loss in center pivot laterals with two diameters of pipe, 10 in and 8 in, psi/1,000 feet. Values are for laterals without end guns. Multiply by 1.037 for systems with an end gun.
    Flow Rate (gpm) Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe: 1.0 Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe: 0.9 Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe: 0.8 Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe: 0.7 Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe: 0.6 Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe: 0.5 Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe: 0.4 Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe: 0.3 Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe: 0.2 Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe: 0.1 Fraction of Lateral That Is 10-inch O.D. Galvanized Steel Pipe: 0.0
    19000 4.7 4.7 4.8 5.2 5.8 6.7 7.8 9.2 10.8 12.5 14.2
    20000 5.1 5.2 5.3 5.7 6.4 7.3 8.6 10.1 11.8 13.7 15.7
    21000 5.6 5.7 5.8 6.2 7.0 8.0 9.4 11.1 12.9 15.0 17.1
    22000 6.1 6.2 6.4 6.8 7.6 8.7 10.2 12.0 14.1 16.4 18.7
    23000 6.7 6.7 6.9 7.4 8.2 9.5 11.1 13.1 15.3 17.0 20.3
    24000 7.2 6.9 7.5 8.0 8.9 10.3 12.0 14.2 16.6 19.2 22.0
    25000 7.8 7.8 8.1 8.6 9.6 11.1 13.0 15.3 17.9 20.7 23.7
    26000 8.4 8.4 8.7 9.3 9.6 11.9 13.9 16.4 19.2 22.3 25.5
    27000 9.0 9.0 9.3 10.0 10.3 12.8 15.0 17.6 20.6 23.9 27.3
    28000 9.6 9.6 9.9 10.6 11.9 13.7 16.0 18.8 22.1 25.6 29.2
    29000 10.2 10.3 10.6 11.4 12.7 14.6 17.1 20.1 23.5 27.3 31.2
    3000 10.9 11.0 11.3 12.1 13.5 15.5 18.2 21.4 25.1 29.0 32.2

    Variation of pressure as the pivot rotates around the field affects the uniformity of water application. It is useful to monitor the pressure of the outer end of the pivot as it rotates around the field. The critical points will be the highest and lowest elevations of the outer half of the pivot lateral. If the pressure varies more than 20% of the design pressure for the end of the lateral, consideration should be given to the use of pressure compensating nozzles or pressure regulators. Lower pressures than expected at the highest elevations may be a sign that the pump is not operating as originally designed or that there are leaks in the system.


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