11.3: Sprinkler Performance

The performance of sprinkler systems depends on the operation of individual sprinkler heads. The goal of sprinkler irrigation is to apply water uniformly at a rate that does not cause runoff or erosion. The system should meet crop water requirements and attain the highest practical efficiency—and of course must be cost-effective. The discharge, or volume flow rate of water, leaving the nozzle is important and can be described by:

\(q_s = 29.82 C_d D^2 \sqrt{P}\)

where: q_s = discharge through the nozzle (gallons per minute, gpm),

C_d = discharge coefficient for the sprinkler head,

D = inside diameter of the nozzle orifice (inches),

P = pressure of the water at the inlet to the sprinkler device (pounds per square inch, psi); and

29.82 is a unit conversion and geometric constant.

Example 11.1

The discharge from a sprinkler depends on the pressure at the nozzle and the diameter of the nozzle orifice. Would a 20% increase in nozzle diameter produce more flow than a 20% increase in pressure?

Given: A straight bore nozzle is used in a sprinkler. The discharge is 10 gpm.

Solution

Let q_s1 = 10 gpm be the initial flow rate. Use Equation 11.1 to develop a term called the discharge ratio where 2 denotes the new condition and 1 the original condition.

Use Equation 11.1 to develop a term called the discharge ratio where 2 denotes the new condition and 1 the original condition.

\(\dfrac{q_{s2}}{q_{s1}}=\dfrac{(D_2)^2 \sqrt{P_2}}{(D_1)^2\sqrt{P_1}}\)

\(\text{ For a 20% increase in diameter }D_2=1.2 \times D_1 \text{ and } P_2=P_1\)

\(q_{s2}=q_{s1}\left(\dfrac{1.2 \times D_1}{D_1}\right)^2=1.44 \times q_{s1}=14.4 \text{ gpm} \)

\(\text{So, a 20% increase in diameter provides a 44% } \left(\dfrac{14.4-10}{10}\times100\%\right) \text{ increase in flow.}\)

\(\text{For a 20% increase in pressure }P_2=1.2P_1\text{ and } D_2=D_1\)

\( q_{s2}=q_{s1}\sqrt{\dfrac{1.2P_1}{P_1}}=1.1q_{s1}=11\text{ gpm}\)

So, a 20% increase in pressure only changes the discharge by 10%. Changing the nozzle size increases flow more than an equal percentage change of pressure.

The value of the discharge coefficient is about 0.96 but depends on the design of the nozzle and sprinkler head. The inside diameter of nozzles is customarily referred to as the nozzle size. Performance for a range of nozzle sizes and pressures is summarized in Table 11.1 for straight bore nozzles. Some manufacturers produce nozzles sized by the diameter in 64ths of an inch; others may use 128ths of an inch. For example, a nozzle diameter of one-quarter inch is referred to as a size of 16 (Table 11.1) or 32 depending on which system is used. Table 11.1 represents the typical discharge for a broad range of sprinkler nozzles. The discharge from a specific design of nozzle and sprinkler may vary from data presented in Table 11.1. Data from the relevant manufacturer should be used for specific systems. The total discharge from a sprinkler head with two nozzle outlets is the sum of the discharge from each nozzle for that pressure. The discharge for pressures between those listed in Table 11.1 can be determined by interpolation.

The second important characteristic of sprinkler performance is the diameter of coverage (also referred to as wetted diameter) as illustrated in Figures 11.3 and 11.4. The diameter of coverage is the maximum diameter wetted by the sprinkler at a rate that is significant for the intended use of the sprinkler. For example, the diameter of coverage for agricultural sprinklers is usually determined to be the maximum radial distance where the water application rate equals 0.01 inches per hour. Usually, the wetted diameter is measured in an indoor laboratory with no wind. The diameter of coverage is affected by the design of the sprinkler body and nozzle. Representative diameters of coverage are given in Table 11.2 for impact sprinklers with straight bore nozzles. The data are for sprinklers where the water jet exits from the sprinkler head at an angle of 23° above the horizon for the range nozzle. The diameter may vary for other designs and should be determined from data by the manufacturer. The diameter of coverage also depends on the height of the device above the crop or the ground surface; therefore, the intended usage of the device is important. The straightening vanes shown in Figure 11.2 are used to reduce turbulence in the sprinkler barrel; thus, producing a larger diameter of coverage. Straightening vanes increase the diameter of coverage from 5% to as much as 20% depending on the design of the sprinkler head and the specific nozzle. Nozzles are designed to operate within a specified pressure range. When used outside that range the performance changes in an undesirable way. The patterns shown in Figure 11.5 illustrate the impact of pressure on the distribution of water. When the pressure is within the proper range, the pattern is nearly elliptical with distance from the sprinkler. When the pressure is too high the water jet breaks up into a high percentage of small drops. In some cases, the jet atomizes into very small drops.

Figure 11.4. Diameter of coverage for a sprinkler.

Table 11.1. Discharge (gpm) for straight bore nozzles of various sizes operating at a range of pressures.

Nozzle Size	Nozzle Pressure (psi)
in	64th in	25	30	35	40	45	50	55	60	65	70	75	80	85	90	95	100
3/32	6	1.2	1.4	1.5	1.6	1.7	1.8	1.9
7/64	7	1.7	1.9	2.0	2.2	2.3	2.4	2.6
1/8	8	2.2	2.5	2.7	2.9	3.0	3.2	3.4	3.5	3.6	3.8	3.9	4.0
9/64	9	2.8	3.1	3.4	3.6	3.8	4.0	4.2	4.4	4.6	4.8	5.0	5.1
5/32	10	3.5	3.9	4.2	4.5	4.7	5.0	5.2	5.5	5.7	5.9	6.1	6.3
11/64	11	4.3	4.7	5.1	5.4	5.7	6.0	6.3	6.6	6.9	7.2	7.4	7.6
3/16	12	5.1	5.6	6.0	6.4	6.8	7.2	7.5	7.9	8.2	8.5	8.8	9.1
13/64	13	6.0	6.5	7.1	7.6	8.0	8.4	8.9	9.2	9.6	10.0	10.3	10.7
7/32	14	6.9	7.6	8.2	8.8	9.3	9.8	10.3	10.7	11.2	11.6	12.0	12.4
15/64	15	7.9	8.7	9.4	10.1	10.7	11.2	11.8	12.3	12.8	13.3	13.8 1	14.2
1/4	16	9.0	9.9	10.7	11.4	12.1	12.8	13.3	14.0	14.6	15.1	15.7	16.2
17/64	17	10.0	11.2	12.1	12.9	13.7	14.4	15.1	15.8	16.5	17.1	17.7	18.3
9/32	18	11.0	12.5	13.5	14.5	15.4	16.2	17.0	17.7	18.5	19.2	19.8	20.5
5/16	20	14.0	15.5	16.7	17.9	19.0	20.0	21.0	21.9	22.8	23.6	24.5	25.3
11/32	22	17.0	19	20	22	23	24	26	27	28	29	30	31	32	32	33	34
3/8	24	20.0	22	24	26	27	29	30	32	33	34	35	36	33	39	40	41
13/32	26	23.0	26	28	30	32	34	35	37	38	40	41	43	40	45	47	48
7/16	28	27.0	30	33	35	37	39	41	43	45	46	48	50	47	53	54	55
15/32	30	31.0	35	38	40	43	45	47	49	51	53	54	57	54	60	62	64
½	32	33.0	37	40	43	45	48	50	52	54	57	58	60	62	64	66	68
17/32	34	38.0	42	45	48	51	54	57	59	62	64	66	68	70	72	74	76
9/16	36	42.0	47	51	54	57	60	64	66	69	72	74	76	79	81	83	86
5/8	40	52.0	58	62	67	71	75	78	82	85	88	92	94	97	100	103	105
11/16	44	63.0	70	76	81	84	90	95	99	103	106	110	114	117	121	124	127

Figure 11.5. Sprinkler distribution as affected by operating pressure.

Table 11.2. Diameter of coverage (ft) for impact sprinklers with straight bore nozzles.^_[a]

Nozzle Size	Nozzle Pressure (psi)
in	64th in	25	30	35	40	45	50	55	60	65	70	75	80	85	90	95	100
3/32	6	64	66	69	69	70	71	72
7/64	7	65	67	69	70	71	72	73
1/8	8	78	79	80	81	82	83	84	85	86	86	87	87
9/64	9	80	81	82	83	84	85	86	87	88	89	90	91
5/32	10	82	85	87	88	89	90	91	92	93	94	95	96
11/64	11	83	88	90	92	93	95	96	97	98	99	100	101
3/16	12	85	91	94	96	98	100	101	102	103	104	105	106
13/64	13	91	97	100	103	105	107	109	111	113	114	116	117
7/32	14	92	99	102	105	108	110	113	115	117	118	120	122
15/64	15	93	100	104	107	110	112	115	117	119	121	123	125
1/4	16	94	102	105	109	112	115	118	120	122	124	127	129
17/64	17	95	103	107	110	114	117	119	122	125	127	129	131
9/32	18	96	104	108	112	116	119	122	125	127	130	132	134
5/16	20	121	124	127	130	133	122	140	143	145	127	149	151
11/32	22	122	128	134	138	142	140	150	154	158	162	164	166	170	172	174	176
3/8	24	124	130	136	142	146	150	154	158	162	166	168	172	174	178	180	182
13/32	26	128	136	144	150	154	158	162	166	168	172	174	178	180	184	186	188
7/16	28	132	138	158	154	158	162	166	172	174	178	180	184	186	190	192	194
15/32	30	132	144	154	160	164	168	172	176	180	182	186	188	192	194	196	198
1/2	32	132	146	156	166	170	174	178	182	186	188	192	194	198	200	202	204
17/32	34	132	146	158	166	176	180	184	188	192	196	198	202	204	208	210	212
9/16	36	132	146	158	172	180	188	192	194	198	202	204	208	210	212	216	218
5/8	40	132	146	158	172	184	190	198	202	204	208	210	214	216	220	222	224
11/16	44	132	146	158	172	184	194	200	208	212	216	218	220	224	226	230	232
^[a] For a brass impact sprinkler where the exit angle of the range nozzle is 23° above the horizontal

Small drops decelerate very quickly in the air and fall to the soil close to the sprinkler, giving a reduced diameter of coverage and higher application rate. When pressure is too low, the water jet does not breakup sufficiently and the sprinkler primarily wets an annular area located near the end of the diameter of coverage. Areas at the center of the circle receive little water. The diameter of coverage is also reduced with low pressures because the velocities of the droplets leaving the sprinkler are smaller. The net effect of low pressure is that a doughnut shaped pattern results with a dry area in the middle of the pattern near the sprinkler. Either too much or too little pressure will produce a poor distribution of water. The acceptable operating range for specific sprinklers is provided by the manufacturer and should be followed. Straightening vanes reduce droplet breakup, which can lead to a doughnut shaped pattern. Usually, the minimum operating pressure of sprinklers with vanes is higher than those without vanes to prevent the doughnut shaped pattern. Sprinkler systems require that the water pattern from one sprinkler overlap with adjacent sprinklers. When the sprinklers are properly designed and located, the overlap pattern will be like that shown in Figures 11.3 and 11.6. The depth of water applied to a point is the sum of water from all sprinklers reaching that point. In Figure 11.6 the total depth would be d₁ + d₂ for the point shown. Some irrigators attempt to reduce costs by extending the spacing between laterals or between sprinklers on a lateral. When that is done, the overlap is inadequate and poor uniformity results. The upper portion of Figure 11.6 shows the water pattern where sprinklers are spaced a distance S_L between sprinklers. The depth of application is relatively uniform. When the spacing is increased to 1.5 x S_L, the depth of application between the sprinklers decreases.

Figure 11.6. Illustration of the effect of sprinkler spacing on uniformity of water application.

The lower and middle portions of Figure 11.6 show the three-dimensional distribution of water between sprinklers along and between laterals. The middle figure shows the distribution when sprinklers are spaced 40 ft apart along the lateral and 60 ft between laterals. The bottom figure shows the distribution when the spacing is increased to 50 ft along and 70 ft between laterals. The system was designed to apply 3 inches of water during a 10-hour application time with an operating pressure of 50 psi. The required sprinkler discharge for the 40 ft x 60 ft spacing is 7.48 gpm and 10.9 gpm for the 50 ft x 70 ft spacing. The diameter of coverage for the two spacings was 106 and 112 ft, respectively. The wider spacing leads to a poorer distribution with a peak depth centered in the representative area. Overlap requirements have been developed for sprinkler systems. The recommendations depend on the wind speed and direction. Consider a plan view of the wetted pattern of a single sprinkler as shown in Figure 11.7. The pattern for calm conditions will be circular. As the wind speed increases the pattern is displaced downwind giving the elongated pattern. Note that the wetted pattern is not only displaced downwind, but also is narrower perpendicular to the direction of wind travel. This occurs because the wind blowing perpendicular to the water jet causes droplets to travel a curved path, originally perpendicular to the wind but later in a more downwind direction. The perpendicular wind may also cause the jet to breakup into a distribution with a higher percentage of smaller drops which do not travel as far. The narrowing of the wetted pattern perpendicular to the wind direction has an important impact on sprinkler spacings and on the orientation of the lateral relative to the predominant wind during the irrigation season. The diagram in Figure 11.8 shows the effect of wind on two orientations of laterals relative to the wind direction. With no wind the individual sprinkler pattern is circular, and the laterals appear to have adequate overlap.

Figure 11.7. Plan view of the effect of wind on the distribution of water from a sprinkler.

Figure 11.8. Effect of wind direction on overlap of sprinkler distribution pattern.

When the laterals are oriented parallel to wind travel, the wind causes the wetted pattern from a sprinkler to narrow into a tighter pattern along the lateral. A dry zone may result between the laterals because of insufficient overlap. To adjust for this problem, more laterals would be needed with a smaller spacing between laterals. This leads to a more expensive system.When the laterals are oriented perpendicular to the wind as shown in Figure 11.8, the pattern of an individual sprinkler is still narrower due to the wind; however, now the spacing of sprinklers along the lateral is smaller than the spacing between laterals. Therefore, more overlap occurs and better uniformity results. At the same time, this is a more economical system because it is more efficient to install more sprinklers along a lateral, rather than install more laterals. The major point is that laterals should be laid out perpendicular to the pervading wind when possible. The spacing of sprinklers and laterals depends upon wind conditions. Recommendations for maximum spacing of sprinklers along the lateral and between laterals is given in Table 11.3. The rate of application from a sprinkler system is a major consideration. The representative areas for the rectangular and triangular sprinkler orientations shown in Figure 11.3 are used to compute the rate water is applied. One-fourth of the discharge from a sprinkler is applied into the rectangular area. Thus, the total water applied into the rectangular area is the sum of one-fourth of the flow from four sprinklers equaling the discharge from one sprinkler. Water from a sprinkler may be applied beyond the representative area; however, an adjacent sprinkler applies water into the area which offsets the overthrow from the original sprinkler. Therefore, the effective water discharge into the area is the discharge from one sprinkler. Thus, the application rate—volume per unit area per unit time—for sprinklers positioned in a rectangular spacing is given by:

\(A_r=\dfrac{96.3q_s}{S_L S_m} \) (11.2)

where: A_r = the rate of water application (in/hr),

q_s = the sprinkler discharge rate (gpm),

S_L = spacing of sprinklers along the lateral (ft),

S_m = spacing of laterals along the mainline (ft), and

96.3 is for unit conversion.

Table 11.3. Maximum spacing of sprinklers

Average Wind Speed (mph)	Maximum Spacing Between Sprinklers on the Lateral	Maximum Spacing Between Laterals Along the Mainline
0–3 (Rectangular Spacing)	50% of diameter	60% of diameter
4–7 (Rectangular Spacing)	45% of diameter	60% of diameter
8–12 (Rectangular Spacing)	40% of diameter	60% of diameter
0–3 (Square Spacing)	55% of diameter	-
4–7 (Square Spacing)	50% of diameter	-
8–12 (Square Spacing)	45% of diameter	-
0–3 (Equilateral Triangle Spacing)	60% of diameter	0.866> sprinkler spacing
4–7 (Equilateral Triangle Spacing)	55% of diameter	0.866> sprinkler spacing
8–12 (Equilateral Triangle Spacing)	50% of diameter	0.866> sprinkler spacing

Example 11.2

Adequate overlap is necessary with sprinkler systems to ensure that the water application is reasonably uniform. Will the layout described below provide acceptable uniformity?

Given: Impact sprinklers with two nozzles (23° exit angle for range nozzle) are spaced 40 ft apart along a lateral. Laterals are spaced at intervals of 60 ft along the mainline. The nozzle sizes are 11/64 in x 3/32 in and the operating pressure is 50 psi. Wind in the area usually averages 5 mph

Solution

The diameter of coverage for the range nozzle (11/64 in) is 95 ft, from Table 11.2.

From Table 11.3 the maximum sprinkler spacing along the lateral is 45% of the diameter of coverage.

Maximum spacing along lateral = 0.45 x 95 = 43 ft

The maximum spacing between laterals is 60% of the diameter of coverage.

Maximum spacing between laterals = 0.60 x 95 = 57 ft

So, this layout just fails the criteria for the spacing between laterals in Table 11.3 and uniformity may be less than desired.

A straightening vane for the nozzle would probably provide adequate coverage.

For a square spacing S_L and S_m are equal so that the denominator becomes S_L² . The effective water supply into a triangular space is half of the discharge from a sprinkler, i.e., a sprinkler applies water into six triangles surrounding the sprinkler. This yields the application rate of a system with sprinklers oriented in an equilateral triangle spacing as:

\(A_r=\dfrac{111.2q_s}{S^2}\) (11.3)

where S = the spacing of sprinklers in the triangular orientation and all other parameters are as previously defined. The application rate of the sprinkler system is important for two reasons. First, the depth of water applied for a given time is proportional to the application rate:

d_g = A_r T_o (11.4)

where: d_g = the gross depth of water applied per irrigation (in) and

T_o = the actual time of operation (hr).

For example, if the application rate was 0.4 in/hr, then an irrigation that lasted 10 hours would apply 4 in of water. The time of operation (T_o) is the time that water is applied. The quantity of water determined from Equation 11.4 is a gross application and must be reduced by the application efficiency to determine the amount of water provided to the crop. Second, when the application rate of the sprinkler system exceeds the infiltration rate of the soil, water will accumulate on the soil surface. If enough water accumulates, runoff will begin. The maximum application rate that is acceptable for different soils and slopes is summarized in Table 11.4. These are general recommendations and should be adjusted upward for production practices that enhance infiltration, especially where adequate crop residue protects the soil, and downward for practices that reduce infiltration.

Table 11.4. Maximum recommended water application rates for soils (inches/hr).^_[a]

Slope (%)	Coarse Textured Soils (sands, fine sands, and loamy fine sands	Medium Textured Soils (sandy loams, fine sandy loams, and silt loam soils)	Fine Textured Soils (silty clay loams, clay loams, and clayey soils)
Soil Surface Not Protected
0–5	0.50–0.75	0.25–0.50	0.10–0.25
6–8	0.40–0.60	0.20–0.40	0.08–0.20
9–12	0.30–0.45	0.15–0.30	0.06–0.15
13–20	0.35–0.50	0.10–0.20	0.04–0.10
> 20	0.10–0.20	0.05–0.10	0.02–0.05
Turfgrass or Heavy Residue Cover
0–5	0.85–1.30	0.50–0.95	0.15–0.35
6–8	0.70–1.00	0.40–0.75	0.10–0.25
9–12	0.50–0.75	0.30–0.55	0.10–0.20
13–20	0.35–0.50	0.20–0.40	0.05–0.15
> 20	0.15–0.35	0.10–0.20	0.03–0.05
^[a] Based on recommendations of the Rain Bird Corporation and Pair et al., 1983.

Example 11.3

A sprinkler irrigation system is used to irrigate a young row crop with an unprotected soil surface. The sprinkler spacing is 40 ft between sprinklers and 60 ft between the laterals.A pressure of 50 psi is available at the design location along the lateral. Wind in the region averages 5 mph during the irrigation season.The soil texture is silt loam.The sprinklers are brass impact sprinklers with straight bore nozzles and the range nozzle has an exit angle of 23° above horizontal. Determine the smallest nozzle size that is acceptable and the application rate of the system. Is this system acceptable for a silt loam soils with a slope of 2%?

Given: Sprinkler spacing 40 ft x 60 ft
Soil is silt loam
Pa = 50 psi
Wind = 5 mph
Brass impact sprinklers with straight bore and range nozzles at 23o angle.

Solution

1. The maximum spacing of sprinklers along the lateral is 45% of the diameter of coverage fora wind speed of 5 mph in Table 11.3. The maximum spacing between laterals is 60% of the diameter of coverage for that wind speed.
   Since we know the actual spacing of the sprinklers and the lateral spacing, we need to determine the diameter of coverage (dc) needed for this system:
   dc needed = maximum of SL/0.45 and Sm/0.60 or
   dc needed = maximum of 40/0.45 = 89 ft and 60/0.60 = 100 ft.
   The spacing of laterals along the mainline is the most limiting based on the criteria in Table 11.3.
   Thus, a diameter of coverage of 100 feet is needed for sprinklers in this system.
   From Table 11.2, a nozzle size of 3/16 inch will provide a diameter of coverage of 100 feet when operated at a pressure of 50 psi, so the nozzle should provide adequate overlap.
2. From Table 11.1, a 3/16-inch nozzle operated at 50 psi produces a discharge of 7.2 gpm. Using Equation 11.2 the application rate would be:
   \(A_r = \dfrac{96.3q_s}{S_L S_m}=\dfrac{96.3\times 7.2\text{ gpm}}{40\text{ ft}\times60\text{ ft}}=0.29\text{ in/hr}\)
3. The maximum recommended application rate for silt loam soil with little cover is between 0.25
   and 0.5 in/hr (Table 11.4).

Therefore, the 3/16-inch nozzle meets the overlap and application rate limitations.