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LATERAL DISTRIBUTION OF NH3 AS AFFECTED BY MANIFOLD CONFIGURATION M. D. Schrock, R. K. Taylor, D. L. Oard, J. D. Anderson

ABSTRACT. The lateral distribution uniformity produced by several commercially available anhydrous ammonia (NH3 ) manifold configurations was determined using a dynamic water absorption technique. For a conventional cast manifold, top and bottom inlet configurations were compared, as were open versus restricted manifold outlet barbs. Coefficient of variation for lateral distribution (lateral CVs) ranged from 15 to 20% for the top inlet and from 8 to 10% for the bottom inlet. For the conventional manifold, the use of open [(5.6 mm ID (0.22 in. ID)] versus restrictor–type hose barbs [2.4 mm ID (0.09 in. ID)] had little influence on lateral distribution. The Continental vertical dam manifold produced lateral CVs ranging from 10 to 13%. For both manifolds, the influence of unequal discharge hose lengths was reduced as manifold pressure increased. Keywords. Ammonia, Nitrogen, Fertilizer application.

A

nhydrous ammonia (NH3) is the least costly and most popular form of nitrogen fertilizer for agricultural crops in North America. It is highly concentrated (82% by mass), which reduces requirements for transportation and material handling in comparison to other forms of nitrogen. Like nearly all other forms of commercial nitrogen fertilizer, NH3 commonly is produced from natural gas, and it represents a major energy input into crop production (Smil, 1991). Ammonia usually is delivered to the field as a liquified gas at pressures ranging from 520 kPag at 4°C to 1720 kPag at 43°C (75 psig at 39°F to 250 psig at 110°F) (VanWylen and Sonntag, 1985). Commonly, the equilibrium pressure of NH3 is used to convey the liquid to a regulator, although positive–displacement pumps sometimes are used for application in low ambient temperatures. The regulator meters NH3 and reduces its pressure, which results in the formation of a large volume of vapor. Downstream of the regulator, both liquid and vapor phases exist, and should be divided by the manifold into equal streams for each knife. Problems with poor lateral distribution of NH3 are well documented. Kerkman and Colvin (1997) tested farmers’ applicators and found lateral CVs ranging from about 5 to 30%, in response to a large number of factors. Boyd et al. (2000) field–tested several manifolds and found lateral CVs in the range of 5 to 30%. Schrock et al. (1999) reported lateral

Article was submitted for review in November 2000; approved for publication by the Power & Machinery Division of ASAE in August 2001. Supported by Kansas Agricultural Experiment Station (contribution no. 01–190–J), USDA Small Business Innovative Research Program, and Capstan Ag. Systems, Inc The authors are Mark D. Schrock, ASAE Member Engineer, Professor, Randal K. Taylor, ASAE Member Engineer, Associate Professor, Darrell L. Oard, Research Assistant, and John D. Anderson, Student, Department of Biological and Agricultural Engineering, Kansas State University, Manhattan, Kansas. Corresponding author: M. D. Schrock, Kansas State University, Biological and Agricultural Engineering, Seaton Hall No. 147, Manhattan, KS 66506–2906; phone: 785–532–2907; fax: 785–532–5825; e–mail: [email protected].

CVs of 15 to 20% for conventional manifolds, 10.5% for a vertical dam manifold, and 3.8% for a multipoint pulse width modulation (PWM) system. Schrock et al. (1999) also reported that the vertical dam manifold and the multipoint PWM system were less sensitive to variations in hose length and tilt compared to the conventional manifold. Achieving uniform lateral distribution is complicated by the wide array of circumstances under which NH3 is applied. In the central United States, application rates may vary from 35 to 350 kg/ha (31 to 312 lb/acre), knife spacing from 0.3 to 0.76 m (12 to 30 in.), total applicator widths from 4.5 to 25 m (15 to 80 ft), ambient temperatures from –7 to 45°C (19 to 113°F), and travel speeds from 6 to 15 km/h (3.8 to 9.4 mph). The situation is compounded by dozens of combinations of manifolds, regulators, and knife styles. OBJECTIVES The objectives of this project were to measure the uniformity of lateral distribution produced by two commercially available NH3 manifolds, to evaluate potential modifications to improve uniformity, and to determine the effect of unequal–length outlet knife hoses on uniformity.

EQUIPMENT TESTED CONVENTIONAL MANIFOLD The conventional manifold was a Continental 01–07 cast–iron manifold with 18 outlets. For this study, nine of the outlets were plugged, yielding nine active outlets, evenly spaced around the manifold periphery (fig. 1). The effect of manifold pressure on lateral distribution is a concern for operators. In an effort to isolate that effect, two types of outlet hose barbs were tested. Standard, or open," hose barbs had a full opening of 5.6 mm (0.22 in.) inside diameter. Restrictor" hose barbs had a drilled 2.4 mm (0.09 in.) orifice (fig. 2). Similarly, the size of the knife tube opening is an issue of concern. Most standard knife tubes utilize a closed tube end and two cross–drilled holes of about 4 mm (0.16 in.)

Applied Engineering in Agriculture Vol. 17(6): 743–748

E 2001 American Society of Agricultural Engineers ISSN 0883–8542

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VERTICAL DAM MANIFOLD A small–body Continental Vertical Dam Manifold (VDM) was tested with an LG" 10–outlet metering ring having a rated capacity of 213 kgN/ha (190 lb/acre) on 30–cm (12–in.) spacing at 9.6 km/h (6.0 mph) (fig. 3). For the VDM, a vortex–type inlet geometry and 2.4–mm (0.09–in.) outlet hose barbs are fixed as a part of the design, and no modifications were attempted. All VDM tests were conducted with drilled knife tubes. The effect of outlet hose length was also investigated.

PROCEDURE

Figure 1. Conventional manifold with nine alternating outlet barbs. Male threaded fitting on left is for pressure gage.

diameter. However, some manufacturers are supplying open, full–diameter outlets at the bottom of the knife tubes. Accordingly, tests were conducted both with cross–drilled tubes having two 4–mm (0.16–in.) orifices and with open tubes having the entire tube inside diameter of 5.6 mm (0.22 in.) available for discharge. Earlier studies (Schrock et al., 1999) indicated that the geometry of the inlet to the conventional manifold had a substantial influence on lateral distribution. These tests were conducted with a 1" NPT schedule 80 street elbow feeding the manifold. The manifold was tested in both top and bottom feed configurations. In addition, a modified street elbow having a 12.7–mm (0.50–in.) orifice installed at its outlet was tested in both top and bottom feed configurations (fig. 2). Current practice on most NH3 applicators is for equal–length hoses to be used on all knives. This factor requires that the excess hose for the knives closest to the manifold must be coiled or otherwise secured on the applicator frame. Given the inconvenience associated with equal length hoses, a series of tests was conducted with unequal length hoses.

Figure 2. Inlet and outlet fittings used on conventional manifold. Top: Inlet elbows with (left) and without (right) 12.7–mm orifice. Bottom: Hose barbs with 2.4–mm (left) and 5.6–mm (right) openings.

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Water absorption was used to capture the NH3 delivered by the knife tubes. Each water absorption bucket was suspended from a load cell, and the weight of the bucket, water, and NH3 was logged in real time by a computerized data acquisition system (fig. 4). The load cells sensed the turbulence and vibration created by the NH3 absorption process. This mechanical noise was addressed by sampling each channel 50 times per second and averaging the 50 readings into a single value. Linear regression was performed on the resulting 1–Hz data stream, and the slope of the weight versus time plot corresponds to the NH3 mass flow rate to each knife tube. Data were logged for a minimum of 30 s for high flow tests [681+ kgN/h (1500 lb/h)], 60 s for moderate flows, and 90 s for low flows [227 kgN/h (500 lb/h)]. Further details of the procedure are given in Schrock et al. (1999). Test durations were shorter at high flows primarily because of increased turbulence in the absorption bucket. Raw data were examined for startup transients, which were discarded prior to the weight regression. Data logging was terminated prior to stopping NH3 flow, so ending transients were not a factor. Absorption buckets of 18.9–L (5–gal) nominal capacity were used without lids. At high duty cycles, the absorption process created turbulence that reduced capacity to approximately 11.3 L (3 gal). The procedure limited the NH3 content of the water to less than 0.12 kg/L (1.0 lb/gal), far below the limit of 0.36 kg/L (3 lb/gal) reported by Kranz et al. (1994). In all cases, a Continental C–2500 regulator metered the NH3. The dial on the regulator was calibrated in mass of N per hour, as reflected in the fourth column of table 1. Ammonia

Figure 3. Disassembled Continental Vertical Dam manifold. Left to right: body, metering ring with 10 outlets, inlet housing, and nut with pressure port.

APPLIED ENGINEERING IN AGRICULTURE

RESULTS

Figure 4. Test apparatus showing conventional manifold with top inlet, regulator, and pressure transducer.

pressure was measured at the inlet of the regulator, at the manifold, and at the knife tube. Measurement Specialties MSP–300–250–P–3–N pressure transducers were used for the inlet and manifold, and an MSP–300–100–P–3–N transducer was used at one knife. Three repetitions were performed for each of the treatments shown in table 1. However, because of safety considerations and the amount of hardware modifications needed between treatments, the treatments were not randomized. Rather, the three repetitions for each test were conducted consecutively. Although the non–randomized test design weakens confidence in the results, a randomized test plan would not have been possible to conduct within the time, resource, and safety constraints of the project.

1

2

3

Treatment

Manifold

Inlet

1 2 3 4 5 6 7 8 9 10 11 12 6x 7x 13 14 15 16 17

Conv. Conv. Conv. Conv. Conv. Conv. Conv. Conv. Conv. VDM VDM VDM Conv. Conv. Conv. Conv. Conv. Conv. Conv.

Top Top Top Top Top Top Top Bottom Bottom Top Top Top Top Top Top–O Top–O Bottom–O Bottom–O Bottom–O

[a]

4

Table 1. Results of manifold and orifice configuration.[a] 5 6 7 8 9

Meter Hose Set Barb ID (kgN/h) (mm) 227 454 908 454 227 227 454 227 454 227 454 681 227 454 227 454 227 454 454

LATERAL DISTRIBUTION The first three treatments in table 1 correspond to the standard manifold operated with a top inlet, open hose barbs, and cross–drilled knife tubes. Although inlet pressure was nearly constant, manifold pressure and knife pressure increased substantially at higher flows. Column 10 shows the mean flow for each of the nine knives in terms of NH3. However, after column 10 was multiplied by the number of knives (9) and the 0.82 mass correction was applied, flows were somewhat lower than the meter settings shown in column 4. Lateral CVs for the first three treatments fell in the 15 to 20% range. The ratio of mass flow rate from the highest flow knife to the lowest flow knife (max/min ratio) ranged from 1.7 to 1.8. Run–to–run CVs, calculated for each outlet and averaged, were low for the first two treatments, but relatively high for the third treatment (7.6%). The high flow of the third treatment caused much greater bucket motion and water turbulence, which may have led to the greater run–to–run variation. In view of the inability to conduct replicated tests, two efforts were made to document the repeatability of the test procedure. First, the run–to–run CV’s for flow were calculated for each knife and treatment. The average CV for the nine or ten knives is reported in column 13 of table 1. With two exceptions all treatments showed run–to–run CV’s of less than 5%. Secondly, following several manifold changes, two treatments (6 and 7) were repeated with similar results for flow, lateral CV and run–to–run CV. Treatments 4 and 5 examined the influence of open knife outlets. The larger knife openings reduced back pressure and created noticeably greater water turbulence in the absorption buckets. This led to a high run–to–run CV for treatment 4, which was the higher of the two flows. Lateral CVs were 14.6 for the low–flow and 25.0 for the high–flow runs.

5.6 5.6 5.6 5.6 5.6 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 5.6

Knife Outlet ID (mm)

Inlet Press (KPag)

2 × 4.0 2 × 4.0 2 × 4.0 5.6 5.6 2 × 4.0 2 × 4.0 2 × 4.0 2 × 4.0 2 × 4.0 2 × 4.0 2 × 4.0 2 × 4.0 2 × 4.0 2 × 4.0 2 × 4.0 2 × 4.0 2 × 4.0 2 × 4.0

823 820 813 859 878 846 846 926 949 880 895 882 1011 1034 965 958 967 958 1069

10

11

12

Man Knife Mean Flow Lateral Press Tube Press per Knife CV Lateral (KPag) (kPag) (kgNH3/h) (%) Max/Min 25 172 319 154 21 283 575 287 607 131 363 535 280 586 310 581 317 586 145

11 41 110 21 7 14 39 14 48 7 34 76 14 44 14 48 14 48 57

25.5 59.9 119.2 50.8 23.4 26.2 58.0 24.9 55.7 22.5 54.4 83.2 26.0 56.2 27.1 58.6 28.4 58.5 59.7

17.1 19.1 15.5 25.0 14.6 18.4 19.8 9.7 8.0 12.2 10.8 11.3 19.0 24.2 4.3 5.5 6.1 4.3 22.7

1.72 1.80 1.70 2.16 1.62 1.73 1.81 1.35 1.32 1.43 1.40 1.43 1.78 2.22 1.14 1.21 1.21 1.14 2.03

13 Run–to– Run CV (%) 2.1 1.7 7.6 11.5 3.4 2.0 3.1 3.0 4.6 2.2 3.7 4.3 1.9 4.8 2.8 1.8 1.9 3.0 2.7

Information in each row (except for CV’s) is average of three repetitions.

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Treatments 6 and 7 are identical to 1 and 2, except for the substitution of restrictor hose barbs. The restrictors substantially increased the manifold pressures in treatments 6 and 7, while knife pressure remained similar to treatments 1 and 2. Lateral CVs, run–to–run CVs, and max/min ratios were similar for all four treatments, indicating that increased manifold pressure did not improve performance. Treatments 8 and 9 were identical to 6 and 7, except for inverting of the manifold position, so that the inlet elbow fed NH3 into the bottom of the manifold. Pressures were similar at similar flows, but lateral CVs and maximum/minimum ratios were much lower for the bottom inlet. Treatments 10, 11, and 12 used the VDM with drilled knife tubes. The vertical dam concept involves centrifugal separation of the liquid and vapor NH3. Because gravity is involved in merging the two phases as they flow out of the VDM, only the top–feeding configuration was evaluated. Supply and knife pressures for the VDM were similar to those of the standard manifold with restrictor barbs, but manifold pressure was somewhat lower for the VDM at similar flows. This may have been due to the additional outlet on the VDM. Lateral CVs for the VDM fell within a narrow range from 10 to 13%, and max/min ratios were about 1.4. Average run–to–run CVs were under 5%, indicating consistent performance of individual outlets. Treatments 13 through 17 tested an attempt to manage NH3 flow on the inlet side of the standard manifold. A 12.7 mm (0.50 in.) orifice was added at the elbow’s discharge. The rationale supporting this modification was drawn from Liimatta et al. (1971), who studied mixture distribution of a multicylinder carbureted engine. They concluded that distribution uniformity of the two–phase fuel–air mixture could be improved by an orifice–like restriction below the carburetor, which moved the liquid fuel away from the manifold wall and into the airstream. The 12.7 mm (0.50 in.) orifice used in the current study was selected to produce a large increase in NH3 velocity at the entry into the manifold, with the intent of increasing turbulence in the manifold and improving the mixing of liquid and vapor phases. An additional pressure transducer was installed to monitor pressure drop across the inlet orifice. Treatments 13 and 14 are identical to treatments 6 and 7, except for the added inlet orifice in the latter tests. The inlet orifice changed pressures little, but lateral CVs were reduced greatly, from roughly 19% down to about 5%. Treatments 15 and 16 were identical to treatments 8 and 9, but with the added inlet orifice. Again, the inlet orifice improved performance, reducing CV from about 9% to about 5.5%. For

[a]

Treatment

Manifold

Meter Set (kgN/h)

1b 2b 6b 7b 10b 11b 12b

Conv. Conv. Conv. Conv. VDM VDM VDM

227 454 227 454 227 454 681

treatments 13 through 16, maximum/minimum ratios were 1.21 or lower, and run–to–run CVs were under 3%, indicating very consistent flows from each outlet. Treatment 17 is identical to treatment 16, but with open [5.6–mm ID (0.22–in.)] hose barbs instead of the restricted barbs. The resulting lateral CV was very high, almost 23%, and the run–to–run CV was under 3%. Pressure drop across the 12.7–mm (0.50–in.) inlet orifice was measured at about 20 kPa (3 psi) for treatments 13 and 15, 30 kPa (4 psi) for treatments 14 and 16, and 56 kPa (8 psi) for treatment 17. The open hose barbs greatly reduced manifold pressure during treatment 17, increasing the pressure drop across the inlet orifice and across the regulator. The poor lateral uniformity of treatment 17 has not been explained and is indicative of the complex nature of the two–phase flow division process that occurs within the manifold. KNIFE HOSE LENGTH Table 2 shows the results of the tests of unequal knife hose lengths. For these tests, two hoses of one–half length and two hoses of double length were installed on the manifolds. Otherwise, the hose lengths were identical to the original treatments [2.1 m (6.9 ft)]. The comparisons of equal with unequal hose lengths were performed by normalizing the individual outlet flows from the original and the b" tests to correct for the small differences in mean flow for the two tests. Next, the normalized flows for each outlet were compared for the equal length and unequal length (b") tests. For treatments 1b and 2b, the short knife hoses produced about 5% greater flow and the long hoses produced about 10% less flow than the corresponding equal length hoses. Note that treatments 1 and 2 used open hose barbs, so manifold pressures were quite low. Even at the 454–kgN/h (1000–lb/h) flow, over 80% of the total pressure drop occurred at the regulator. Treatments 6b and 7b showed much lower sensitivity to knife hose length, with flows for both the long and the short hoses within 2% of the flow in the standard length hoses. Note that the restrictor hose barbs used in these tests resulted in much higher manifold pressures, especially at high flows. The restrictor hose barbs reduced the importance of hose friction in comparison to the total pressure drop between manifold and outlet. Treatments 10b through 12b showed that the VDM also has low sensitivity to hose length. In these tests, flows for the short and long hoses were within 3% of the flow for the standard hoses. The relatively high manifold pressures of the VDM tend to support the conclusion that hose length

Table 2. Results of hose length comparisons.[a] Hose Barb Inlet Man Knife Tube ID Press Press Press (mm) (kPag) (kPag) (kPag) 5.6 5.6 2.4 2.4 2.4 2.4 2.4

896 903 879 858 934 927 913

22 172 310 586 179 358 545

14 47 14 36 10 38 72

Mean Flow per Knife (kgNH3/h)

∆Flow (%) 1/2 Length

∆Flow (%) 2×Length

23.3 53.5 25.6 57.0 23.6 50.8 78.9

4.9 5.5 0.4 1.3 –3.0 0.8 1.9

–10.7 –9.7 –1.5 1.8 .4 –.4 –1.8

Information in each row is average of two repetitions. All tests were with 2– × 4.0–mm knife outlets.

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becomes less important when the pressure drop between manifold and knife is greater than about seven times the knife pressure. THERMODYNAMIC CONSIDERATIONS To gain understanding of changes in manifold performance, we estimated the percent vapor at key points throughout the metering and distribution system. Calculations were based on the primary assumption that the NH3 state remains on the saturation line as it passes through the system. Furthermore, heat transfer occurs between the surroundings and the NH3 was neglected, as was hose pressure drop between the supply tank and the entry of the NH3 regulator. The assumption of saturation follows from the fact that two phases are present in the same pressure vessel, and ambient conditions change at a relatively slow rate. The second assumption, of adiabatic flow and state changes, is more questionable. However, given the relatively high NH3 flow rates, the large heat of vaporization of NH3, and the relatively small surface areas involved, adiabatic flow is not an unreasonable starting point for analysis. The calculations started by determining the enthalpy of the saturated liquid NH3 at inlet pressure. The percentage of NH3 changing to vapor as it passed through the regulator was calculated by maintaining constant enthalpy while reducing pressure to the manifold pressure; the specific volume and inlet velocity of the NH3 follow. Table 3 shows the results of the calculations, for each of the treatments shown in table 1. Column 5 shows the pressure at the inlet to the NH3 regulator, which provides a basis for estimating initial enthalpy. Column 7 shows the estimated mass percentage of vapor that entered the manifold. The mass percentage varies from a low of 4% vaporized, during a treatment with very high manifold pressure, to a high of 18.6% vaporized, during a treatment with very low manifold pressure. Column 8 shows the proportion of vapor entering the manifold on a volume basis.

1

2

Treatment Manifold 1 2 3 4 5 6 7 8 9 10 11 12 6x 7x 13 14 15 16 17 [a]

Conv. Conv. Conv. Conv. Conv. Conv. Conv. Conv. Conv. VDM VDM VDM Conv. Conv. Conv. Conv. Conv. Conv. Conv.

During all of the treatments, 83% or more of the volume in the manifold was occupied by vapor. Column 9 in table 3 shows the estimated specific volumes for the two–phase mixtures in the manifold. Because of the large difference in densities of the liquid and vapor phases, the specific volume of the mixture is highest when manifold pressure is lowest. Average velocity of the two–phase mixture as it enters the manifold is shown in column 10. The velocity results are counter–intuitive in the sense that velocity is reduced as mass flow rate is increased. This is a consequence of the fact that low flows produced low manifold pressures, which led to a high percentage of vaporization, which then increased specific volume and inlet velocity. Attempts were made to correlate lateral CV to %vapor, specific volume, inlet velocity, manifold pressure, and knife tube pressure. Those attempts did not lead to broad generalizations. However, for the limited data set shown in figure 5, a relationship between lateral CV and the estimated manifold inlet velocity was evident. Treatments shown are limited to those using 2.4–mm hose barbs and a top inlet and include both VDM and conventional manifold tests. The trend suggests that manifold configurations and operating conditions that result in a relatively high manifold inlet velocity tend to produce more uniform lateral distribution.

CONCLUSIONS 1. With the conventional manifold without the inlet orifice, the bottom inlet produced lateral CVs of 8 to 10%, numerically lower than the 15 to 20% CV’s for the top inlet. 2. At the flows tested, restrictor hose barbs [2.4 mm ID (0.09 in.)] greatly increased pressure in the conventional manifold, but had little influence on uniformity of lateral distribution.

Table 3. Results of phase estimation.[a] 6 7 8

3

4

5

9

10

11

12

Inlet

Meter Set (kgN/h)

Inlet Press (kPag)

Man Press (kPag)

Manifold %Vapor by Mass

Manifold %Vapor by Vol.

Manifold Sp. Vol (m3/kg)

Man. Inlet Velocity (m/s)

Knife Tube Press (kPag)

Lateral CV (%)

Top Top Top Top Top Top Top Bottom Bottom Top Top Top Top Top Top–O Top–O Bottom–O Bottom–O Bottom–O

227 454 908 454 227 227 454 227 454 227 454 681 227 454 227 454 227 454 454

823 820 813 859 878 846 846 926 949 880 895 882 1011 1034 965 958 967 958 1069

25 172 319 154 21 283 575 287 607 131 363 535 280 586 310 581 317 586 145

17.7 12.1 8.3 13.2 18.6 9.6 4.0 10.4 4.7 14.2 8.3 5.1 11.6 6.1 10.4 5.2 10.2 5.2 15.8

99.3 97.5 94.4 97.9 99.3 95.6 83.4 95.9 85.3 98.2 93.9 87.2 96.4 88.5 95.6 86.9 95.5 86.7 98.3

.17 .05 .03 .06 .18 .03 .01 .03 .01 .07 .02 .01 .04 .01 .03 .01 .03 .01 .08

21.0 15.9 15.1 15.6 21.0 4.1 2.7 4.1 2.9 9.0 7.0 5.4 4.9 3.7 17.2 13.5 17.6 13.3 90.7

11 41 110 21 7 14 39 14 48 7 34 76 14 44 14 48 14 48 57

17.1 19.1 15.5 25.0 14.6 18.4 19.8 9.7 8.0 12.2 10.8 11.3 19.0 24.2 4.3 5.5 6.1 4.3 22.7

Assumes 100% liquid at regulator inlet, adiabatic change in state.

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REFERENCES

Figure 5. Relationship between estimated ammonia velocity at manifold inlet and lateral CV.

3. The vertical dam manifold produced lateral CVs of 10 to 13%. 4. As manifold pressure is increased, either by the use of restrictor outlet barbs or the vertical dam manifold, hose length becomes less significant. If the ratio of manifold pressure to knife pressure is 7 or higher, hose length variations of up to 4:1 have a negligible influence on flow rate. 5. When using a top feed inlet and restricted hose barbs, evidence suggests that higher NH3 velocity at the manifold inlet tends to improve uniformity of lateral distribution.

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Boyd, P. M., H. M. Hanna, J. L. Baker, M. White, and T. Colvin. 2000. Field evaluation of anhydrous ammonia distribution manifolds. ASAE Paper 00–1140. St. Joseph, Mich.: ASAE. Kerkman, E. W., and T. S. Colvin 1997. Knife to knife variation within an anhydrous ammonia applicator. ASAE Paper MC97–105. St. Joseph, Mich.: ASAE. Kranz, W., C. Shapiro, and R. Grisso. 1994. Calibrating anhydrous ammonia applicators. Nebraska Cooperative Extension EC 94–737–D. Lincoln, Nebr. Liimatta, D. R., R. F. Hurt, R. W. Deller, and W. L. Hull. 1971. Effects of mixture distribution on exhaust emissions as indicated by engine data and the hydraulic analogy. SAE Paper 71–3. Warrendale, Pa.: SAE. Schrock, M. D., D. L. Oard, R. K. Taylor, J. Grimm, M. Trefz, G. Love, and A. Peterson. 1999. Lateral distribution of anhydrous ammonia with conventional and pulse–width–modulation metering systems. ASAE Paper 99AETC102. St. Joseph, Mich.: ASAE. Smil, V. 1991. General Energetics. New York: John Wiley & Sons. Van Wylen, G. J., and R. E. Sonntag. 1985. Fundamentals of Classical Thermodynamics, Third Ed. New York: John Wiley.
