simulation of rotary spreader

Mansoura University Faculty of Agriculture Agric. Eng. Dept.

SIMULATION OF ROTARY SPREADER BY

HATEM ALI ESMAIL MORSY B. Sc. in Ag. Sciences (Agric., Mech.), Mansoura Univ., 1998 M. Sc in Ag. Sciences (Agric., Eng.), Mansoura Univ., 2005

THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy In AGRICULTURAL SCIENCES (AGRICULTURAL ENGINEERING)

SUPERVISORS Prof. Dr. Z. I. Ismail Prof. of Power and Farm Machinery. Faculty of Agriculture Mansoura University, Egypt

Prof. Dr. A. E. Abou Elmagd Prof. of Agric. Eng. Faculty of Agriculture Mansoura University, Egypt

Prof. Dr. H. S. Hidia Prof. of Production Eng. Faculty of Engineering Mansoura University, Egypt

Associate Prof. Dr. J. Paliwal Prof. of Biosystems Eng. Fac. of Agric. & Food Sciences Manitoba University, Canada

2013

ACKNOWLEDGEMENT First and foremost, I would thanks Allah for his gracious, kindness in all endeavors, that author has taken up in his life. The author wishes to express his sincere thanks and appreciation to Prof. Dr. Z. I. ISMAIL, Prof. of Power and Farm Machinery, and Head of Agric. Eng. Dept., Fac. of Agric., Mansoura Univ., for his supervision, continuous scientific help, guidance, encouragement, revising the manuscript and valuable suggestions. The author also wishes to express his sincere appreciation to Prof. Dr. A. E. Abou El-magd, Prof. of Agric. Eng., Fac. of Agric., Mansoura Univ. for his supervision, continuous help and valuable suggestions. The author wishes to express his sincere appreciation to Prof Dr. H. S. Hidia, Prof. of Production Eng., Fac. of Eng., Mansoura Univ. for her kind assistance, helpful and support. The author wishes to express his sincere thanks and appreciation to Associate Prof. Dr. J. Paliwal, Biosystems Engineering Dept., Fac. of Agric. & Food Sciences, Manitoba Univ., Canada, for his supervision, continuous scientific help, guidance, encouragement, revising the manuscript and valuable suggestions. Many thanks to Prof. Dr. S. M. Abdel-Latif, Prof. of Agric. Eng., and Former Head of Agric. Eng. Dept., Faculty of Ag., Mansoura Univ., for his helpful suggestion and encouragement.

My warmest thanks are paid to Prof. Dr. H. N. Abdel-Mageed, Prof. of Agric. Eng., and Dean of Agric. Faculty, Mansoura Univ., for his kind, continuous help and encouragement.

Special thanks are also paid to All staff members of Agric. Eng. Dept., Faculty of Agric., Mansoura Univ. for their kind assistance. Special thanks are paid to All technicians of Biosystems Eng. Dept., Fac. of Agric. & Food Sciences, Manitoba Univ., Canada, for their continuous help. The More of Sincere Thanks and appreciation to the soul of My Father Prof. Dr. Ali. E. Morsy, Weave Engineering Dept., Faculty of Engineering, Mansoura University. Finally, many thanks are extended to My Mother, My Wife, my Daughters, My Sisters, My Brothers and My wife family for their support during the preparation of this work.

CONTENTS 1. INTRODUCTION 2. REVIEW OF LITERATURE 2.1. Advantages and Disadvantages of Rotary Spreader 2.2. Factors Affecting the Distribution Pattern 2.2.1. Physical and mechanical properties of fertilizer 2.2.2. Factors related to the spinner 2.2.2.1. Spinner diameter and speed 2.2.2.2. Spinner height above the ground 2.2.3. Factors related to the blades 2.2.3.1. Shape of blades 2.2.3.2. Angle of blades 2.2.3.3. Number of blades 2.2.4. Factors related to the feed rate 2.2.4.1. Application rate 2.3. Shape of Distribution Pattern 2.4. Testing Methods for Spread Pattern 2.5. Computer Simulation of Mathematical Model 2.5.1. Defining and Using Reasons 2.5.2. Mathematical models of the particles on and off a spinner spreader

3. MATERIAL AND METHODS 3.1. Materials 3.1.1. The mathematical model 3.1.1.1. The selected mathematical model equations 3.1.2. The fixed fertilizers spreader 3.1.2.1. The power source unit 3.1.2.2. The AC drive unit 3.1.2.3. The vertical electrical motor holder 3.1.2.4. The spinner 3.1.2.5. The funnel 3.2. Scope of variables 3.2.1. Type of fertilizers 3.2.2. Variables related to the fixed lab fertilizers spreader 3.3. Measurements and Measuring Instruments 3.3.1. Fertilizer Measurements 3.3.1.1. Particle shape 3.3.1.2. The particle size distribution 3.3.1.3. Coefficient of dynamic friction 3.3.1.4. Angle of repose 3.3.1.5. Particle density 3.3.2. Air measurements

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Page No. 1 3 3 4 5 6 7 8 8 8 8 9 10 10 11 11 13 13 13 15 17 17 18 21 21 23 24 26 27 28 28 28 29 29 29 31 32 37 38 39

3.3.2.1. Air pressure 3.3.2.2. Speed, temperature, and relative humidity of air 3.3.3. Particle motion measurements and evaluation factors 3.3.3.1. The radial velocity of fertilizer particle 3.3.3.2. Staying angle for the fertilizer particle on the disk, measured from the getting out position on the disk until its exit at the disk edge (Φ) 3.3.3.3. The horizontal distance that the fertilizer particle traveled into the air (from disk edge until the ground surface) 3.4. Statistical Analysis

4. RESULTS AND DISCUSSIONS 4.1. Physical and Mechanical Properties of Fertilizers Particles 4.1.1. Particle Shape 4.1.2. The particle size distribution 4.1.3. Coefficient of dynamic friction 4.1.4. Angle of repose 4.1.5. Particle density 4.2. Air measurements 4.2.1. Air pressure 4.2.2. Speed, temperature, and relative humidity of air 4.3. Evaluation of the Mathematical model Simulation 4.3.1. Evaluating of the first part of simulation (Particle motion on the disc) 4.3.1.1. The radial velocity of fertilizer particles 4.3.1.2. Staying angle of the fertilizer particle on the disc 4.3.2. Evaluating of the second part of simulation (Particle motion off the disc) 4.3.2.1. The horizontal distance that the fertilizer particle traveled into the air, from the disk edge until the ground surface

5. SUMMARY AND CONCLUSIONS REFERENCES APPENDIX (A) APPENDIX (B) ARABIC SUMMARY

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39 40 41 42 43 44 46 47 47 47 48 50 52 54 56 56 56 57 57 57 62 66 67 75 83 89 92

LIST OF FIGURES Fig. 2.1: 3.1: 3.2: 3.3: 3.4: 3.5: 3.6: 3.7: 3.8: 3.9: 3.10: 3.11: 3.12: 3.13: 3.14: 3.15: 3.16: 3.17: 3.18: 3.19: 3.20: 3.21: 4.1: 4.2: 4.3: 4.4: 4.5: 4.6: 4.7: 4.8:

Item Page No. Spinning disk 6 Top view diagram of the fertilizer particle motion and the impeller 19 Vertical electrical motor 22 AC drive unit 23 The vertical electrical motor holder 24 The motor holder 25 The investigated spinner construction spinner 26 The funnel 27 Accurate caliper to measure the fertilizer particles dimensions 30 Sieves group, used to get the particles size distribution of fertilizers 32 The force gauge used to get the horizontal pulling force on the fertilizer particles plate 33 The flat friction disc 35 A plate of glued fertilizer particles 35 Measuring method of dynamic friction coefficient 36 The tachometer that used to measure the disk rotation speed 36 The funnel supported with the holder was used to get a regular stack of fertilizer particles 37 The 10 ml graduated cylinder 38 The accurate digital balance 39 Precision Dial Barometer 40 Mini Thermo-Anemometer Plus Humidity device 41 Measuring method of the radial velocity of fertilizer particle 42 Measuring method of the horizontal distance that the fertilizer particle traveled into the air 45 The values of particles size distribution for fertilizers particles types (Urea and Ammonium Sulfate) 49 The average values of dynamic friction coefficient for fertilizers particles types on paint iron surface, and using different speeds 51 The frequency distribution curves for repose angle of fertilizers types 54 The radial velocity of Urea fertilizer particles (m/s) versus disc speeds (m/s) and the calculation different methods 58 The radial velocity of Ammonium Sulfate fertilizer particles (m/s) versus disc speeds (m/s) and the calculation different methods 58 The relationship between the predicted method of computer model and the laboratory measuring method of Urea particles radial velocity 60 The relationship between the predicted method of computer model and the laboratory measuring method of AMS particles radial velocity 60 The staying angle of Urea fertilizer particles (Radians) versus disc speeds (m/s), two different calculation methods, and three impact positions on the disc (0.06, 0.08, and 0.10 m, respectively) 63

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4.9:

4.10:

4.11:

4.12:

4.13:

The staying angle of Ammonium Sulfate fertilizer particles (Radians) versus disc speeds (m/s), two different calculation methods, and three impact positions on the disc (0.06, 0.08, and 0.10 m, respectively) The travelled horizontal distance of Urea particle (0.026 gram) in the air (m) versus three disc speeds (m/s), two different calculation methods, and two heights of the disc from the ground surface (0.8, and 1.0 m, respectively) The travelled horizontal distance of Ammonium Sulfate particle (0.026 gram) in the air (m) versus three disc speeds (m/s), two different calculation methods, and two heights of the disc from the ground surface (0.8, and 1.0 m, respectively) The travelled horizontal distance of Urea particle (0.030 gram) in the air (m) versus three disc speeds (m/s), two different calculation methods, and two heights of the disc from the ground surface (0.8, and 1.0 m, respectively) The travelled horizontal distance of Ammonium Sulfate particle (0.030 gram) in the air (m) versus three disc speeds (m/s), two different calculation methods, and two heights of the disc from the ground surface (0.8, and 1.0 m, respectively)

iv

64

68

69

70

71

LIST OF TABLES Table 3.1: 3.2: 4.1: 4.2: 4.3: 4.4:

Item Page No. Specifications of the power source unit of fixed fertilizers spreader 22 Specifications of the AC drive unit 23 The statistical analysis of the fertilizers particles dimensions and sphericity index 48 Maximum, minimum, average, standard deviation and coefficient of variance of repose angle for fertilizer types 53 The statistical analysis of the particle density for fertilizers types 55 The statistical analysis of the physical and mechanical properties of the air 56

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Symbols and Abbreviations a: AP: o C: CD: DP: H: mP: N: Nre: ρa: P b: R: t: U: V: Z: ϴ: ϴa: μ: μa : Ø: ω:

Radius to point of particle placement, m Frontal area of particle, m2 Degree centigrade Drag coefficient Particle diameter, m The horizontal distance that the fertilizer particle traveled into the air from disk edge until the ground surface, m Particle mass, gram The disc rotation speed, Cycle/minute Reynolds number Air density, kg/m3 Air barometric pressure, kPa Radius of disc, m The time to fall height, Sec Radial velocity of the particle at disc radius, m/sec Absolute particle speed, m/sec Fall height, m Angle of dispatch measured between radius at point of exit and the path of the particle, Radians Air temperature, K = oC + 273 Kinetic friction coefficient between particles and impeller Dynamic viscosity of air, N.Sec/m2 Angle throughout which disc rotates to move particle from a to R, Radians Angular velocity of disc, Rad./sec

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1. INTRODUCTION

Solid chemical fertilizers are one of important sources for plant nutrition, due to its low price compared to liquid chemical fertilizers, they provide the plant with important nutrients needed for growth during the periods of its growing life, and also it works to improve the properties of soil (soil structure and the acidity degree). In fact, there are many types of distribution machines of solid chemical fertilizers, but the most famous one is the centrifugal distribution machine, and this was due to its advantages, low cost, low power necessary, simplicity of mechanical design, ease of maintenance, its high performance, and its wide operation width, but the most important drawback with this machine is the lack of distribution accuracy of fertilizers at the rate desired. Consequently,

enhancing

the

distribution

patterns

of

the

rotary

distributor was the target of many research projects, and was followed in such research projects is to use trial and error method in the development of these machines, but this method is expensive and takes more time. And this was the reason that many researchers used Computer simulation instead of using trial and error method, but most researchers had

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used standard bearing balls instead of using real fertilizer granules during the simulation laboratory experiments. In addition the use of mathematical equations is based on a lot of inputs and obtaining some of these inputs in many cases in the simulation process is very difficult. Therefore, the aim of this study is to develop a mathematical model to simulate the discharge and spread of the real fertilizers particles from centrifugal spreader. To determine the possibility range of using this model with the different fertilizers particles, and conclude the using possibility range of the same model to deduce the fertilizers distribution patterns after that.

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2. REVIEW OF LITERATURE Agriculture will remain the major source of incomes for most countries of the third world. Consequently, scientists must develop new creative models for agricultural machinery. To have better understanding of the centrifugal distribution machines of solid chemical fertilizers, the recent review of literature will be drawn as indicated below: 2.1. Advantages and Disadvantages of Rotary Spreader: Davis and Rice (1973) indicated that the centrifugal distributor is rapidly becoming the most widely used for the spread of fertilizer. This mechanism type has advantages of low cost, simplicity of operation, ease of cleaning and relatively small size for a given width of spread. Brinsifeld and Hummel (1975) reported that the centrifugal distributor has proven to give the most economical satisfaction. The popularity of this type is due to its design characteristics, ease of handling and cleaning, economy and compactness. However, all centrifugal distributors have the disadvantage of producing an uneven distribution pattern. Criffis and Ritter (1983) mentioned that the centrifugal distributor is the most popular of all distributors because of its simplicity, high ground clearance and wide swath width.

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Olieslagers et al. (1996b) said that the low price, easy maintenance and large working width could explain the success of centrifugal spreaders. The main disadvantage of this machine is the high sensitivity of spread pattern to flow rate variations. 2.2. Factors Affecting the Distribution Uniformity: The distribution uniformity of granular fertilizers on the land surface-using broadcaster depends on many factors from both the machine adjustments and the fertilizer condition. Reed and Wacker (1970) measured uniformity of application with various machines. They found that the distribution pattern of a broadcast spreader is affected by factors such as type and conditions of fertilizer, the spinner configuration, spinner-blade adjustment, spinner speed, delivery point of fertilizer into the spinner and the application rate. Parish and Chaney (1986) mentioned that variables affecting the distribution pattern include particle size, particle density, particles shape, and coefficient of friction of the particle on the impeller, critical relative humidity of the fertilizer, ambient relative humidity, impeller speed and machine ground speed. They add that the factors affecting the distribution pattern could be classified into groups as follows:

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2.2.1. Physical and mechanical properties of fertilizer: Physical and mechanical properties of fertilizer such as particle diameter, shape, density, friction coefficient and moisture content are important factors in determining the distribution uniformity. Reints and Yoerger (1967) showed that improving the uniformity of the distribution pattern of a broadcaster distributor is obtained by selecting the appropriate particle-diameter gradient. Reed and Wacker (1970) reported that bulk density and particle size have a significant effect on width and shape of the distribution pattern. Bhushan (1981) reported that high normal pressures and high sliding speeds can result in high interface (flash) temperatures that can significantly reduce the strength of most materials. He added that in some cases, localized surface melting reduces shear strength and friction drops to a low value determined by viscous forces in the liquid layer. Griffis and Ritter (1983) developed a comprehensive simulation model for single-impeller rotary distributor. They found that irregularly shaped particles and interactions among the particles introduce randomness into experimental distributions. Csizmazia (2000) explained that the evenness of the spread pattern, mostly depends on the physical properties of the fertilizer.

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Chowdhury and Helali (2006, 2007); Imada (1996); Imada and Nakajima (1995); and Komvopoulos and Li (1992) reported that for most materials when the velocity increases, friction decreases and when duration of contact increases, friction increases. They added that the dependence of friction on velocity may be explained in the following way. When velocity increases, momentum transfer in the normal direction increases producing an upward force on the upper surface. This results in an increased separation between the two surfaces which will decrease the real area of contact. Contributing to the increased separation is the fact that at higher speeds, the time during which opposite asperities compresses each other is reduced increasing the level on which the top surfaces moves. 2.2.2. Factors related to the spinner: Srivastava et al. (1993) indicated that there are two types of spinners, flat and cone shaped. The spinning disk is a flat disk when  = 0 and a cone-shaped disk when  > 0 as shown in Fig. (2-1).

Fig. (2-1): Spinning disk (Source: Srivastava et. al, 1993)

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2.2.2.1. Spinner diameter and speed: According to the theory of the centrifugal distributor, the particle motion depends on the diameter and rotational speed of plate. Parish and Chaney (1986) showed that the increase of the plate speed had small effect on the distribution pattern, but they expected that low speeds may adversely affect and substantially changes the pattern. They explained that by the fact that the friction and air resistance decrease the particle speed. Parish (1987) indicated that the pattern quality deteriorates when the speed varies substantially from the speed at which the spreader is designed to operate. He also added that the pattern changes do not differ statistically significant unless the speed is varied approximately 25 percent. Olieslargers et al. (1996b) showed that the spreading width of transverse distribution pattern increases with increasing angular velocity of the disc because the particles have a higher initial outlet velocity. As the relative amount of particles is higher for a lower angular velocity because the same amount is spread on smaller area. Abd El-Mageed et al. (2006) developed a locally broadcasting machine by linking an electronic circuit that capable to control automatically the flow rates of the fertilizer metering mechanism with respect to forward speed of the machine. The developed spreader was tested and evaluated under controlled and field

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conditions. The results indicated that the 30 cm spinner diameter gave good distribution pattern for all investigated feed rates, blade angels and fertilizer types. 2.2.2.2. Spinner height above the ground: Cunningham (1963) showed that the distance between plate and ground is very important to the distribution pattern because the height of plate affects the particle motion outside the plate. Parish and Chaney (1985) evaluated the effect of handle height on the pattern for three models spreader. A 76 mm variation in handle height had less effect on the pattern for the three models. 2.2.3. Factors related to the blades: 2.2.3.1. Shape of blades: Cunningham (1963) and Cunningham and Chao (1967) used various straight and curved vane configurations to perform an analysis of particle motion on the spinner. 2.2.3.2. Angle of blades: Cunningham and Chao (1967) used six straight blades on the disk surface. The blades were pitched alternately around the spinner 14.5 degrees forward and 4.7 degrees backward (the blades 1,3 and 5 were pitched backward the other blade 2, 4 and 6 were pitched forward). The results indicated that the use of two values of blade pitch on the spinner should provide a positive means of imparting

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diverging velocities to fertilizer. Bernaki et al. (1972) performed an analysis of the particle speed on spinner with radial blades, forward, and backward-pitched blades. The blades on the spinner were also set alternately at angles (-20 and 0) deg. in that analysis. They indicated that the increase in blade positive angle of setting reduced the swath width of spreader, while an increase in the negative angle worsened the distribution uniformity. Sayed-ahmed (1989) studied the effect of blade angle on the distribution pattern. The most important result given in that study indicates that the use of backward blades set at 10 degrees provides acceptable patterns. Abd El-Mageed et al. (2006) evaluated the effect of blade angle on the distribution pattern. The results showed that the best distribution pattern for distributing granule fertilizer was obtained at blade angel of 0 degree (radial blades). 2.2.3.3. Number of blades: Cunningham (1963) used in his study a spinner with four blades, while Glover and Baird (1973) used three blades and Berancki et al. (1972) used six blades. Ahmed (1988); Sayed-ahmed (1989) and Ahmed et. al.(1992) studied the effect of the number of blades on the distribution pattern. They reported that four

9

blades spinner do an excellent job in distribution performance than five and six blade spinners. 2.2.4. Factors related to the feed rate: 2.2.4.1. Application rate: Reed and Wacker (1970) found that increasing the application rate frequently causes deterioration in the uniformity of the distribution pattern and it may also change the pattern shape considerably. Bernaki et al. (1972) reported that the smaller of application rate, the more difficult to maintain, the uniformity in the pattern distribution. Small rates were almost unattainable but normally distributed pattern tended to be less uniform at high rates than at low rates. Ahmed (1988) used feed rates of 0.96, 0.5, 0.22 and 0.06 kg/s, respectively. He found that a feed rate of 0.06 kg/s consistently gave the lowest standard deviation and hence it was chosen as the optimum feed rate. Parish (1999 b) evaluated rate changes of a drop spreader and rotary spreader using 2 spreader settings each at fill levels of 100, 50, and 10% of capacity. He concluded that rate changes with the drop spreader due to hopper fill level were highly significant statistically and could have agronomic impact. Rate changes with the rotary spreader were also highly significant with the delivery rate 45% lower at 10% fill than the rate at 50% fill. His study confirms that hopper fill

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level is a concern when developing spreader settings. 2.3. Shape of Distribution Pattern: Kepner et al. (1978) observed that most of the patterns obtained from centrifugal broadcasters could be approximated by one of the following four types: pyramid, flat top, oval and humped pattern. They reported that uniformity of application is influenced by the shape of the pattern from the spreader and the amount of overlap. The flat top pattern is excellent if the driver selects and maintains the correct swath width. The humped spread pattern is undesirable because, with normal driving, the highest rates are overlapped; further increase the error of swath width. Pitt et al. (1982) derived approximating equations for the spread patterns of rotary distributors for granular fertilizer to describe the particle trajectories as influenced by particle size. They showed by statistical simulation the variability in particle size has little effect on the shape of the spread pattern, although the mean particle size is still important. 2.4. Testing Methods for Spread Pattern: Parish et al. (1987) studied different methods of spreader pattern distribution tests and determined that collection pans meeting (ASAE S341.2) are the best represent the actual pattern obtained in the field. They also showed that type and size of collection device have a major effect on the apparent pattern.

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Parish and Porter (1994) stated that conducting the tests on a hard surface allows particles to bounce into the collection trays, thus distorting the apparent pattern. They made a comparison between pattern tests conducted according to ASAE S341.2 on smooth concrete and two species of turf-grass. For the turf-grass tests, the samples were collected in plastic cups set flush with the thatch in round holes cut by a golf cup hole cutter. The results showed a major change in both pattern width and apparent delivery rate with large, heavy fertilizer particles. Grift and Hofstee (2002) developed an alternative method for fertilizer spread pattern determination based on predicting where individual fertilizer particles land on the ground, in contrast to the traditional method of collecting the particles in pans (ASAE 341.2). A small broadcast granular fertilizer spreader (lowery 300) was equipped with an optical sensor designed to measure the velocity and diameter of individual particles shortly after they leave the impeller disc. The measured velocity and diameter of individual particles were input into a ballistic model that predicted where particles land on the ground. The results have shown that the optical sensor is capable of automatically determining the spread pattern of a fertilizer on the fly. They added that the sensor could be a key component in the development of uniformity-controlled fertilizer application systems.

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2.5. Computer Simulation of Mathematical Model: 2.5.1. Defining and Using Reasons: Article of Wikipedia (2012) defined a computer simulation as a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system. Computer simulations have become a useful part of mathematical modeling of many natural systems in physics (computational physics), astrophysics, chemistry and biology, human systems in economics, psychology, social science, and engineering. Simulations can be used to explore and gain new insights into new technology, and to estimate the performance of systems too complex for analytical solutions. Computer simulations vary from computer programs that run a few minutes, to network-based groups of computers running for hours, to ongoing simulations that run for days. 2.5.2. Mathematical models of the particles on and off a spinner spreader: Davis and Rice (1974) performed a simulation of the discharge of fertilizer particles from a centrifugal distributor and their subsequent ground impact point using the language “Continuous Systems Model Program” (CSMP). The results indicated that the simulated travel distance values were close to the experimental values. Pitt et al. (1982) derived approximating equations for particles trajectories

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as influenced by particle size. The results showed that the approximate solutions can be used to predict fertilizer spread patterns with small error. Griffis et al. (1983) developed a comprehensive simulation model for single-impeller rotary distributors. The particles discharge onto impeller, the particles motion on the impeller, the particles trajectory in the air, and the particles impact with the ground surface had been simulated. The simulation results were compared with the experimental study of the R-7X rotary spreader manufactured by O. M. Scott and Sons. The results indicated that the swath widths can be predicted well and the peaks locations in the pattern can be approximated for the materials in the study. Olieslagers et al. (1996a) developed a simulation model of single and twindisc spreaders to calculate the spreader patterns. The results showed that the approximation model gives good reality values of the spread patterns, after taking the particles interactions into account. They added that, the shape of the distribution pattern and the spreading widths are very sensitive to changes of spreader settings. Dintwa et al. (2003) derived a simulation model of the particle motion on a rotating flat disc of centrifugal fertilizer spreader. The results showed that the simulation model could be useful in the automatic control systems design for disc spreaders. Additionally, the simulation model represents a potential tool in

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spreader design and optimization. Aphale et al. (2003) performed a comprehensive experiments and analytical study to investigate particle trajectories on and off a spinner spreader. Sixteen different granular fertilizers were used. The results indicated that the experimental data for on-spinner particle trajectories generally lie between the analytical models for the pure-rolling and pure-sliding conditions using friction coefficient of 0.5. The average relative error between the experimental data for the horizontal distance travelled by the fertilizer materials after being thrown from the spinner plate and the combined on- and off-spinner models is 20% for the 540 rpm spinner speed.

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3. MATERIALS AND METHODS The main purpose of this study is to develop a mathematical model to simulate the discharge and spread of the real fertilizers particles from centrifugal spreader. To determine the possibility range of using this model with the different fertilizers particles, and conclude the using possibility range of the same model to deduce the fertilizers distribution patterns after that. Five stages of work were carried out. Tests and experiments had been done as follows: 1. Studying the pervious review of literature to state the main factors affecting the spreader performance. 2. Selecting the mathematical model and making the simulation program of this model by MATLAB program. 3. Carrying out the preliminary experiments to measure the physical and mechanical properties of two types of solid chemical fertilizers, namely: Urea and Ammonium Sulfate, to get some of the basic data necessary for my simulation program. 4. Construction of fixed lab spreader parts and assembling the spreader unit in the workshop in Biosystems Eng. Dept., Faculty of Agric. and Food Sciences at the University of Manitoba, Canada.

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5. Carrying out the final experimental work using a fixed lab spreader unit under many of the different variables, to get the other basic data necessary to complete my simulation program. 3.1. Materials The materials and equipment used to establish the present study may be described as follows: 3.1.1. The mathematical model Referring to the studying and analysis of the previous mathematical models of rotary distributer systems, mathematical model is selected, computer simulated and tested experimentally. The selected mathematical model was based on the following criteria:  Easing inputs.  Giving more accurate results.  Relating to the real fertilizers properties. The selected mathematical model was based upon the following assumptions:  Air currents had no effect on fertilizer particles motion.  The fertilizer particles do not fracture upon impact with the impeller surface.  The fertilizer particles do not bounce upon impact with the impeller surface.

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3.1.1.1. The selected mathematical model equations The equations of mathematical model are divided into two groups namely, motion equations on the disc and motion equations off the disc: A. Motion on the disc equations: Patterson and Reece (1962) found that: V   2 R2  U 2 U  R (  2  1   )

  tan 1

R U

 tan 1 (

1

 1   2

)

Ritter et al. (1980) stated that: R Cosh 1 ( ) a  2  1  

where: V = absolute particle speed, m/sec ω = angular velocity of disc, Rad./sec R = radius of disc, m U = radial velocity of the particle at disc radius, m/sec µ = kinetic friction coefficient between particles and impeller ϴ= dispatch angle measured between radius at point of exit and the path of the particle, Radians a = radius to point of particle placement, m

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Fig. (3-1): Top view diagram of the fertilizer particle motion and the impeller

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B. Motion off the disc equations: Pitt et al. (1982) found that: t

Ln( B  B 2  1) 2C1C 2

H 

Ln(C1 V t  1) C1

C1  (0.5 C D Pa AP / m P ) C2 

g C1

B  2e 2C1Z  1

where: t = the time to fall height, Sec H = the horizontal distance that the fertilizer particle traveled into the air from disk edge until the ground surface, m CD = drag coefficient Pa = air density, kg/m3 Ap = frontal area of particle, m2 mp= particle mass, gram Z = fall height, m

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Nian-Sheng Cheng (2009) reported that:



CD 

24 0.38 (1  0.27 N re ) 0.43  0.47 1  exp ( 0.04 N re ) N re

N re 

Pa V DP

Pa 



for N re  2  10 5

a

29 Pb 8.314  a

 a  4.79  10 6  e 0.6780.00227

a

where: Nre = Reynolds number Dp = particle diameter, m µa = dynamic viscosity of air, N.Sec/m2 Pb = air barometric pressure, kPa ϴa = air temperature, K

3.1.2. The fixed fertilizers spreader The fixed fertilizers spreader system consisted of the following components: 3.1.2.1. The power source unit Vertical electrical motor was used as a power source unit, Fig.(3-2). The specifications of power unit are shown in Table (3-1):

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Fig. (3-2): Vertical electrical motor.

Table (3-1): Specifications of the power source unit of fixed fertilizers spreader Brand Name Model Power Frequency RPM Voltage Current SF Mass

EMERSON, Made in Poland EL07 2 Hp (1.5 kW) 60 Hz 1800 208-230/460 5.8-5.4/2.7 1.4 29.5 kg

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3.1.2.2. The AC drive unit To obtain different rotational speeds for the spinner disc, AC drive unit was used as an electrical controller of the vertical electrical motor speed, Fig.(3-3). The specifications of the AC drive unit are shown in Table (3-2):

Fig. (3-3): AC drive unit.

Table (3-2): Specifications of the AC drive unit Brand Name Power Frequency Voltage Current

ABB, Made in China 2 hp (1.5 kW) 60 Hz 200 ~ 240 V 7.5 A

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3.1.2.3. The vertical electrical motor holder The two main components of the vertical electrical motor holder are as follows, Fig.(3-4):

Fig. (3-4): The vertical electrical motor holder.

1. The motor holder H-shape holder made of steel sheet (5 mm thick.), was designed and fabricated to hold the electrical motor in vertical direction. Two telescopic legs were made of steel with square cross section to support the motor holder and to allow vertical motion up and down. Every telescopic leg consisted of two pieces of steel, The cross section dimensions of the small piece are 40 x 40 mm, and 52 x 52 mm for the large one, Fig. (3-5).

24

Fig. (3-5): The motor holder.

2. The motor holder base Motor holder base was made of steel sheet, fabricated to fix the electrical motor and the holder on the floor. The main dimensions of this steel base are 915 x 815 x 8 mm. There are four small screw legs fixed in corners of the iron base to support the horizontal balance of the fertilizers spreader system.

25

3.1.2.4. The spinner The spinner was constructed from metal sheet 6 mm thickness and drilled to fix the four blades at an angle of 900 between every two blades as shown in Fig.(3-6). The flat type spinner with 30 cm diameter was used. The straight radial shape blades were used for spreading both kinds of fertilizers.

Fig. (3-6): The investigated spinner construction.

26

3.1.2.5. The funnel A plastic funnel was used to permit fertilizer particles to fall individually on the spinner surface through 8 mm dia. orifice, Fig. (3-7). The fertilizer funnel was hanged on vertical carrier, and 10 mm vertical clearance was used between the funnel orifice and the spinner blades upper surface, to prevent bouncing of fertilizer particles on the spinner surface.

Fig. (3-7): The funnel.

27

3.2. Scope of variables To realize the purpose of the present study, series of laboratory experiments were carried out to evaluate selecting mathematical models. The following different variables are introduced in the study: 3.2.1. Type of fertilizers Two different types of fertilizers, namely, Urea and Ammonium Sulfate were used during evaluating the mathematical model. 3.2.2. Variables related to the fixed lab fertilizers spreader The variables that are introduced in the present study could be classified into three groups as follows: 1. Variables related to fertilizer properties such as: A. Two types of fertilizers, Urea 46-0-0 and Ammonium Sulfate 21-0-0 B. Two fertilizer particles mass, 0.026 and 0.030 gram 2. Variables related to spreader properties such as: A. Eight different speeds of 4.8, 5.5, 6.2, 6.7, 7.6, 8.6, 9.6, and 10.5 m/s (300, 345, 390, 420, 480, 540, 600, and 660 rpm) 3. Variables related to particles motion properties such as: A. Two different levels of disk height from the ground level, 0.8, and 1.0 m B. Three impact positions of the fertilizer particles on the disk, 0.06, 0.08, and 0.10 m

28

3.3. Measurements and Measuring Instruments 3.3.1. Fertilizer Measurements Physical and mechanical properties of the tested fertilizers were estimated according to the following procedures: 3.3.1.1. Particle Shape A random sample of 100 particles was taken from each fertilizer type. The shape of each type was studied in terms of maximum diameter (dc), and sphere diameter of the same volume as the object (de). These dimensions were determined using a caliper with an accuracy of ± 0.01 mm, as shown in Fig. (3-8). The measured data were used to calculate the sphericity of each sample for fertilizer types, using the next formula according to Curray (1951) as follows:

sphericity 

de 

3

de …………………………. (3-1) dc

6 m …………………………. (3-2) .

 

29

where: de = sphere diameter of the same volume as the object, mm. dc = maximum diameter of the fertilizer particle, mm. m = mass of the fertilizer particle, g. ρ = particle density, g/mm3.

According to Curray formula, the particle sphericity values of (=1), (< 1, but very near to 1), and (< 1, but far from 1) are totally spherical, very near to spherical, and far from spherical shapes respectively. The estimated sphericity data of fertilizer particles were statistically analyzed to get each of the mean values, maximum values, minimum values, standard deviation (SD), and coefficient of variation (CV).

Fig. (3-8): Accurate caliper to measure the fertilizer particles dimensions.

30

3.3.1.2. The particle size distribution Also, a random sample of 4 kg was taken from each fertilizer type, and mixed together very well. The particle size distribution was measured and replicated for 10 times for every kind of fertilizer, and every sample mass was 0.2 kg, to get the mean particle size distribution. Sieves group was used to determine the particle size distribution. The numbers and mesh diameters of the sieves were as follows: 4 (4.75 mm), 8 (2.38 mm), 10 (2.00 mm), 12 (1.70 mm), and 20 (0.85 mm), as shown in Fig. (3-9). The particle size distribution was calculated from the following equation:

PS ( n ) 

PSW ( n ) PTW

 100 …………………………. (3-3)

where: PS(n) = the percentage of fertilizer particles on sieve number (n), %. PSW(n) = the mass of fertilizer particles on sieve number (n), g. PTW = the sample mass of fertilizer particles, g.

31

Fig. (3-9): Sieves group, used to get the particle size distribution of fertilizers.

3.3.1.3. Coefficient of dynamic friction The coefficient of dynamic friction was measured using the force gauge Fig. (3-10) and a nylon wire, which connects the force gauge and the plate of fertilizer particles.

32

Fig. (3-10): The force gauge used to get the horizontal pulling force on the fertilizer particles plate.

After fixing the flat friction disc Fig. (3-11) on the vertical electrical motor, a plate of glued fertilizer particles Fig. (3-12) has to be set on friction surface then, the electrical motor switched on, and the flat metal disc started to rotate, and due to the flat disc motion, the horizontal pulling force on the plate is gradually increased

33

starting from zero and after that, it takes the direction of decreasing and it becomes constant at the end. At this moment, the force gauge reading was taken Fig. (3-13). Thus the coefficient of dynamic friction is calculated using the following general equation:



N W

………………………… (3-4)

where: μ = coefficient of dynamic friction, dimensionless. N = the horizontal pulling force on the fertilizer particles plate, N. W= weight of fertilizer particles plate, N.

It should be denoted that dynamic coefficient of friction for fertilizer particles was determined versus painted iron material, and it was measured under four different disk rotation speeds of 100, 200, 300, and 400 rpm. The disk rotation speed was measured by the tachometer Fig. (3-14).

34

Fig. (3-11): The flat friction disc.

Fig. (3-12): A plate of glued fertilizer particles.

35

Fig. (3-13): Measuring method of dynamic friction coefficient.

Fig. (3-14): The tachometer used to measure the disk rotation speed.

36

3.3.1.4. Angle of repose The repose angle of fertilizer particles was laboratory measured using the digital photography as a new technique, to get the highest possible accuracy of the results. At first, the funnel supported with the holder was used to get a regular stack of fertilizer particles, as shown in Fig. (3-15) and after that, many pictures for the fertilizer particles stack was taken with the digital camera (CASIO, Model EX-F1) so, the pictures were printed on the paper and the repose angle was determined using the protractor.

Fig. (3-15): The funnel supported with the holder was used to get a regular stack of fertilizer particles.

37

3.3.1.5. Particle density According to Aphale et al. (2003), the volume and mass of fertilizer particles sample were determined by using 10 ml graduated cylinder Fig. (3-16) with water and accurate digital balance (± 0.001 gram accuracy) Fig. (3-17), respectively. The particle density was calculated using the following equation:



M ……………………………. (3-5) V

where: ρ = particle density, kg/m3. M = mass of fertilizer sample, kg. V= volume of fertilizer sample, m3.

Fig. (3-16): The 10 ml graduated

cylinder.

38

Fig. (3-17): The accurate

digital balance.

3.3.2. Air measurements Physical and mechanical properties of the air were estimated according to the following procedures: 3.3.2.1. Air pressure The air pressure in the laboratory area was measured by using precision dial barometer (± 0.5% of reading accuracy), as shown in Fig. (3-18).

39

Fig. (3-18): Precision Dial Barometer.

3.3.2.2. Speed, temperature, and relative humidity of air The speed, temperature, and relative humidity of air in the laboratory area were measured by using Mini Thermo-Anemometer Plus Humidity device (± 3.0%, ± 1 oC deg., and ± 1% of air speed, temperature, and humidity reading accuracy), as shown in Fig. (3-19).

40

Fig. (3-19): Mini ThermoAnemometer Plus Humidity device.

3.3.3. Particle motion measurements and evaluation factors High speed (up to 1000 frames/sec) digital camera (CASIO EX-FH25) with 10 megapixels resolution and Sony Vegas Pro 9.0 program were used to follow and measure the motion performance of fertilizers particles on and off spinner. After that, a comparison was carried out between the results gotten from the selected mathematical model and the other results gotten from the laboratory experiments, to validate range of the new program, as explained in the following measurements:

41

3.3.3.1. The radial velocity of fertilizer particle The fertilizer particle was dropped off from the funnel orifice to make an impact with the spinner surface (the funnel orifice was fixed at the nearest position to the spinner surface, 10 mm above the disc impellers), and the radial velocity was calculated (by video capturing) as an average velocity along the impeller started from the first contact point between the particle and impeller until the particle departure point at the edge of the spinner, as shown in Fig. (3-20).

Fig. (3-20): Measuring method of the radial velocity of fertilizer particle

42

The frames rate of 1000 frames/sec was used to calculate this velocity as a high speed video capturing, the frames were counted to calculate the time, and the distance between the first contact point (between the particle and impeller) and the particle departure point at the edge of the spinner, were measured to calculate the distance, and the radial velocity was obtained by dividing the distance by time. 3.3.3.2. Staying angle for the fertilizer particle on the disc, measured from the emission on the disc until its exit at the disc edge (Φ) By using frames rate of 1000 frames/sec, the time start from emission point of fertilizer particle on the disc surface until the ejection point of the same particle at the edge of the spinner was calculated by counting the frames, and by making a relationship between the disc rotation speed and the previous mentioned time, the particle staying angle was calculated in very accurate method using the following equation: Φ (radian) = (Tf * Sd/60) * 2Π ………………. (3-6) or, Φ (degree) = (Tf * Sd/60) * 360 ………..……. (3-7) where: ϕ = staying angle Value. Tf = the fertilizer particle staying time on the disc surface, sec. Sd = the disk speed, rpm.

43

3.3.3.3. The horizontal distance that the fertilizer particle traveled into the air (from disk edge until the ground surface) The horizontal distance that the fertilizer particle traveled into the air was laboratory measured by using thin layer of the white sugar and dark blue plastic sheet as new technique, to get the highest possible accuracy of the results. At first, the fertilizer particle was ejected from the spinner edge as a start point to impact with the ground surface as an end point. The ground surface was covered by dark blue plastic sheet and supported by thin layer of the white sugar above it, as shown in Fig. (3-21). The marks of the fertilizers particles in the white sugar with dark blue background were determined, and after that, the distance between those two points was measured using the following equation (Appendix (A), page 91):

   1 R . sin       A . sin     sin A   …………….. (3-8)  H     sin     

where: H = the horizontal distance that the fertilizer particle traveled into the air from disk edge until the ground surface, m.

44

A= the horizontal distance measured from the disk center until the particle impact point with the ground surface, m. ϴ = dispatch angle measured between radius at point of exit and the path of the particle, degree. R = radius of disc, m.

Fig. (3-21): Measuring method of the horizontal distance that the fertilizer particle traveled into the air

45

3.4. Statistical Analysis The obtained data for physical, mechanical properties, and fixed lab spreader of the tested fertilizers were analyzed using program of Microsoft Excel to calculate the maximum value, minimum value, average value, standard deviation of values and coefficient of variance of values in Dept. of Agric. Eng., Faculty of Agric., Mansoura University.

46

4. RESULTS AND DISCUSSIONS

4.1. Physical and Mechanical Properties of Fertilizers Particles The great variation in size, shape, density, and dynamic friction coefficient of the fertilizers particles are important factors affecting the fertilizers distribution patterns. 4.1.1. Particle Shape The maximum diameter and mass of the particles were measured for random sample of 100 particles of the two fertilizer types. The data for each of maximum diameter, the mass, and the sphericity of fertilizer particles were statistically analyzed to get the mean values, maximum values, minimum values, standard deviation, and coefficient of variation (Table 41). The average values of particles sphericity index were 87.58 and 77.22 for Urea and Ammonium Sulfate respectively.

47

Table (4-1): The statistical analysis of the fertilizers particles dimensions and

Urea Ammonium Sulfate

Fertilizers types

sphericity index. Mass, gram

Sphericity index

Max. Min. Av. S.D. C.V.,% Max. Min. Av. S.D.

Max. diameter, mm 4.77 3.06 3.88 0.32 8.35 6.19 3.46 4.65 0.60

0.037 0.014 0.027 0.005 18.92 0.074 0.026 0.043 0.009

98.20 77.27 87.58 4.39 5.01 89.66 60.05 77.22 6.73

C.V.,%

12.93

21.12

8.71

From the previous table, it is clear that, Urea particles are more spherical than Ammonium Sulfate particles. Consequently, under the same conditions, if Urea and Ammonium Sulfate particles have the same physical properties except the particle shape property, the Urea particles will travel horizontal distances in the air more adjacent than Ammonium Sulfate particles, because the variance coefficient value of Urea particles is smaller than the variance coefficient value of Ammonium Sulfate particles. 4.1.2. The particle size distribution On the other hand, particle size distribution was measured, and many sieves were used, numbers of the sieves were 4 (4.75 mm), 8 (2.38 mm), 10 (2.00 mm), 12 (1.70 mm), and 20 (0.85 mm). The results of particle size distribution for Urea on the sieves 4, 8, 10, 12, 20, 48

under the sieve number 20 were as follows: 0%, 62.4%, 28.9%, 5.9%, 2.2%, 0.6%, respectively, while the results of particles size distribution for Ammonium Sulfate fertilizer on the same sieves were as follows: 0%, 85.8%, 9.3%, 2.6%, 2.1%, 0.2%, respectively. The values of particles size distribution for fertilizers particle types (Urea and

Particles Size Distribution, %

Ammonium Sulfate) are shown in Fig (4-1). 100 90

UREA

80

AMS

70 60 50 40 30 20 10 0

A.S.No.4

A.S.No.8

A.S.No.10

A.S.No.12

A.S.No.20

U.S.No.20

Sieves No.

Fig. (4-1): The values of particle size distribution for fertilizers particles types (Urea and Ammonium Sulfate).

From Fig. (4-1), it is clear that the largest percentage of particles size was 62.4%, while it was 85.8% on sieve no. 8 (2.38 mm) for both of Urea and Ammonium Sulfate fertilizers, respectively. So, under the same conditions, if Urea and Ammonium Sulfate particles have the same physical properties except the 49

particles size distribution property, most of Ammonium Sulfate particles will travel horizontal distances in the air greater than the traveled horizontal distances of urea particles in the air, because the centrifugal force on the Ammonium Sulfate particles will be greater than the centrifugal force on the Urea particles. The centrifugal force on the fertilizers particles equation is as the following:

F  m r 2 where: F = centrifugal force, N. m = mass of the particle, kg. r = radius of the disc, m. ω = angular velocity of the disc, rad/s. 4.1.3. Coefficient of dynamic friction The dynamic friction plays an important role in most fields of agricultural mechanics, especially during the movement of agricultural materials. The average values of dynamic friction coefficient (µ) for fertilizers particles types (Urea and Ammonium Sulfate) on painted iron surface, and using different speeds (0.8, 1.6, 2.4, and 3.2 m/sec) were measured and plotted in Fig (4-2).

50

0.65

Co. of dynamic friction

UREA AMS

0.55

0.45

0.35

0.25 0.8

1.6

2.4

3.2

Disc speed, m/s

Fig. (4-2): The average values of dynamic friction coefficient for fertilizer particles types on painted iron surface, and using different speeds

Generally, increasing the disc speed for both of two fertilizers particles types decreases the dynamic friction coefficient. But, the dynamic friction coefficient of Urea particles was greater than the dynamic friction coefficient of Ammonium Sulfate particles using the same levels of speed. Results of the dynamic friction coefficient for Urea particles using the speeds 0.8, 1.6, 2.4, and 3.2 m/sec were as follows: 0.570, 0.532, 0.508, 0.496, respectively, while the results of the dynamic friction coefficient for Ammonium Sulfate particles using the same speeds were as follows: 0.510, 0.411, 0.359, 0.335, respectively. Consequently, the Urea particles will remain on the disc surface for longer time than Ammonium Sulfate particles. That result trend means, the staying angle 51

of Urea particles on the disc surface will be greater than staying angle of Ammonium Sulfate particles. For fertilizers particles types under the study, (Urea and Ammonium Sulfate) the mathematical relationships between the dynamic friction coefficient and the disc speed may be represented by the following equations: For Urea fertilizer particles: µ = 0.5572 S-0.102

R2 = 0.998

For Ammonium Sulfate fertilizer particles: µ = 0.4751 S-0.308

R2 = 0.998

where: µ = the dynamic friction coefficient. S = the disc speed, m/s.

4.1.4. Angle of repose The average values of repose angle for the different fertilizer types were determined. The data presented in Table (4-2) indicate that the values of repose angle were 0.624 rad. (36 deg), and 0.652 rad. (37 deg) for fertilizer types (Urea and Ammonium Sulfate), respectively.

52

Table (4-2): Maximum, minimum, average, standard deviation and coefficient of

Urea Ammonium Sulfate

Fertilizers types

variance of repose angle for fertilizer types.

Repose angle (deg)

Repose angle (rad.)

38

0.663

34

0.593

36

0.624

0.94

0.016

Max. Min. Av. S.D. C.V.,% Max. Min. Av. S.D. C.V.,%

2.6 41

0.716

35

0.611

37

0.652

1.56

0.027 4.2

On the other hand, the results illustrated in Fig. (4-3) show that, the highest frequencies of particles repose angle were recorded at 0.624 Rad. (36 deg), and 0.663 Rad. (38 deg) for fertilizer types of Urea and Ammonium Sulfate, respectively. Therefore, to have continuous flow of fertilizer particles under this study through the hopper orifice to the rotary disc, the inclined angle of hopper walls should be more than 410.

53

Frequency

12 10 8

6 4 2

0 34

35

36

37

38

39

40

41

40

41

Repose angle, Urea

Frequency

12 10 8

6 4

2 0

34

35

36

37

38

39

Repose angle, AMS

Fig (4-3): The frequency distribution curves for repose angle of fertilizer types.

4.1.5. Particle density Density of the fertilizer particle, play an important role in the particle movement through the air (from the disc edge until the impact surface). The particle density was measured for two fertilizer types, and the average values of particle density for the different fertilizer types were determined. As presented in Table (4-3) the recorded values of particle density were 1297, and 1791 kg/m3 for fertilizer types (Urea and Ammonium Sulfate), respectively. 54

Table (4-3): The statistical analysis of the particle density for fertilizers types.

Urea Ammonium Sulfate

Fertilizers types

Particle density, kg/m3 Max. Min. Av. S.D. C.V.,% Max. Min. Av. S.D.

1340 1241 1297 21.7 1.7 1844 1739 1791 27.7

C.V.,%

1.5

From the previous table, it is clear that, Urea particle density is smaller than Ammonium Sulfate particle density. So if we suppose that Urea and Ammonium Sulfate particles have the same physical properties except the particle density; the Urea particles will travel horizontal distance in the air smaller than the travelled horizontal distance of Ammonium Sulfate fertilizer particles, because the centrifugal force on the Urea particles will be smaller than the centrifugal force on the Ammonium Sulfate particles.

55

4.2. Air measurements Physical and mechanical properties of the air are important factors affecting on the fertilizers distribution patterns. 4.2.1. Air pressure The air pressure in the laboratory area was measured and determined, the average value of air pressure inside the laboratory was 100 kPa. 4.2.2. Speed, temperature, and relative humidity of air The speed, temperature, and relative humidity of air inside the laboratory area were measured and determined. The average values were 0 m/s, 25 oC, and 29% for speed, temperature, and relative humidity of the air, respectively.

Table (4-4): The statistical analysis of the physical and mechanical properties of the air. Air temperature,

Air pressure, kPa

Air speed, m/sec

Max.

100.5

0

26

32

Min.

99.5

0

24

26

Av.

100

0

25

29

56

o

C

Air relative humidity, %

4.3. Evaluation of the mathematical model Simulation 4.3.1. Evaluating of the first part of simulation (particle motion on the disc) Experiments were proceeding in the laboratory to test and evaluate the motion performance of fertilizers particles (The radial velocity of fertilizer particles and staying angle value for the fertilizer particle) on spinner. Also, a comparison is made between the results obtained from the mathematical model and others obtained from the laboratory experiments, under the following different operational conditions: 1. Two types of fertilizers: Urea 46-0-0 and Ammonium Sulfate 21-0-0. 2. Five different disc speeds, 420, 480, 540, 600, and 660 rpm. 3. Three impact positions on the disc, 0.06, 0.08, and 0.10 m. 4. Six replicates. 4.3.1.1. The radial velocity of fertilizer particles An experimental study on the radial velocity was carried out in the laboratory to evaluate the motion performance of fertilizers particles. The comparison between the results obtained from the mathematical model and the other results obtained from the laboratory experiments was done. Results of the radial velocity of fertilizer particles (m/s) versus disc speeds (m/s) and the calculation by different methods (mathematical model and laboratory experiments) for the two fertilizer types (Urea and Ammonium Sulfate) are shown in Figs. (4-4) and (4-5). 57

Particle radial velocity, m/s

Experimental method

Mathematical method

9 8 7 6 5 4 3 2 1 6

7

8

9

10

11

Disc speed, m/s

Fig. (4-4): The radial velocity of Urea fertilizer particles versus disc speeds and the calculation by different methods.

Particle radial velocity, m/s

Experimental method

Mathematical method

9 8 7 6 5 4 3 2 1 6

7

8

9

10

11

Disc speed, m/s

Fig. (4-5): The radial velocity of Ammonium Sulfate fertilizer particles versus disc speeds and the calculation by different methods.

58

The general trend of this relationship is that the particles radial velocity (U, m/s) increases with the increase of disc speed for both of two fertilizers types using the two calculation methods. For Urea fertilizer, the results of the radial velocity of fertilizer particles (m/s) versus the disc speeds 420, 480, 540, 600, and 660 rpm and using the mathematical calculation method were as follows: 4.16, 4.79, 5.41, 6.04, and 6.67 m/s, respectively, while the results of the radial velocity of fertilizer particles (m/s) versus the same disc speeds, but using the laboratory experiments method were as follows: 2.32, 2.77, 3.24, 3.71, and 4.23 m/s, respectively. Meanwhile, for Ammonium Sulfate fertilizer, the results of the radial velocity of fertilizer particles (m/s) versus the disc speeds 420, 480, 540, 600, and 660 rpm and using the mathematical calculation method were as follows: 4.85, 5.61, 6.38, 7.15, and 7.94 m/s, respectively, while the results of the radial velocity of fertilizer particles (m/s) versus the same disc speeds, but using the laboratory experiments method were as follows: 2.59, 3.09, 3.58, 4.10, and 4.64 m/s, respectively. Figures (4-6) and (4-7) show the relationships for Urea and Ammonium Sulfate fertilizer particles between the predicted method of computer model and the laboratory measuring method of particle radial velocity.

59

Fig. (4-6): The relationship between the predicted method of computer model and the laboratory measuring method of Urea particles radial velocity.

CALC Lab. U (m/sec)

6

4

2 y= x R² = 0.99 0 0

2

4

6

Compu. Model U (m/sec)

Fig. (4-7): The relationship between the predicted method of computer model and the laboratory measuring method of AMS particles radial velocity.

CALC Lab. U (m/sec)

6

4

2 y= x R² = 0.99

0 0

2

4

Compu. Model U (m/sec)

60

6

Generally, the radial velocity values using the mathematical model method were greater than the radial velocity values using the laboratory calculation method, for both of Urea and Ammonium Sulfate fertilizers. The previous results happened because of the delay time of fertilizer particle on the disc, and this happen when the particle start to impact with the disc surface after its dropping out from the funnel orifice. After impacting, the particle does not move immediately in the direction of the disc edge, but it remains for small period of time in its impacting arch until the moving impeller touches it. At this moment, the particle starts to move toward the disc edge in touching with the disc impeller. Therefore, to get more accurate when calculating the radial velocity of fertilizer particles under the study, (Urea and Ammonium Sulfate) using the mathematical model method, the equations may be as follows: For Urea fertilizer: U = 0.0361ωr.µ-3.189

R2 = 0.995

For Ammonium Sulfate fertilizer: U = 0.1379ωr.µ-0.924

R2 = 0.999

where: U = the radial velocity of fertilizer particles, m/s. ω = the disc angular velocity, rad/s. r = the disc radius, m.

61

4.3.1.2. Staying angle of the fertilizer particle on the disc Results of staying angle of the fertilizer particles (Radians) versus five disc speeds (6.7, 7.6, 8.6, 9.6, and 10.5 m/s), two different calculation methods (Ritter et al. (1980) and laboratory experiments), and three impact positions of the fertilizer particles on the disc (0.06, 0.08, and 0.10 m) for both of two fertilizers types (Urea and Ammonium Sulfate) are shown in Figs. (4-8) and (4-9). The general trend of this relationship is that the staying angle of the particles decreases with the increase of disc speed, for both of two fertilizers types using Ritter calculation method and the laboratory method.

62

Experimental method

Ritter eq.

φ angle, Radians

2.7 2.5 2.3 2.1 1.9 1.7 1.5 1.3 6

7

8

9

10

11

Disc speed, m/s

Experimental method

Ritter eq.

φ angle, Radians

2.2 2.0 1.8 1.6 1.4 1.2

1.0 6

7

8

9

10

11

Disc speed, m/s

Experimental method

Ritter eq.

φ angle, Radians

1.7 1.5

1.3 1.1

0.9 0.7 6

7

8

9

10

11

Disc speed, m/s

Fig. (4-8): The staying angle of Urea fertilizer particles versus disc speeds, two different calculation methods, and three impact positions on the disc (0.06, 0.08, and 0.10 m, respectively) 63

Experimental method

Ritter eq.

φ angle, Radians

2.4 2.2 2.0 1.8 1.6 1.4

1.2 6

7

8

9

10

11

10

11

Disc speed, m/s

Experimental method

Ritter eq.

φ angle, Radians

2.0 1.8 1.6 1.4 1.2 1.0 0.8 6

7

8

9

Disc speed, m/s

Experimental method

Ritter eq.

φ angle, Radians

1.6 1.4 1.2

1.0 0.8 0.6

6

7

8

9

10

11

Disc speed, m/s

Fig. (4-9): The staying angle of Ammonium Sulfate fertilizer particles versus disc speeds, two different calculation methods, and three impact positions on the disc (0.06, 0.08, and 0.10 m, respectively) 64

For Urea fertilizer particles, the results of staying angle versus disc speeds 420, 480, 540, 600, and 660 rpm, compared with two calculation different methods (Ritter, and laboratory experiments), and three impact positions of the fertilizer particles on the disc (0.06, 0.08, and 0.10 m), were greater than staying angle results of Ammonium Sulfate fertilizer particles versus the same previous conditions. The previous results happened because the dynamic friction coefficients of Urea fertilizer is greater than the dynamic friction coefficients of Ammonium Sulfate fertilizer, so the Urea particles will remain for longer time than Ammonium Sulfate particles on the disc surface. In addition, the staying angles results of Urea and Ammonium Sulfate fertilizers using Ritter calculation method had the same trend of the staying angle results of the same fertilizers using laboratory method. For the two types of fertilizers, the results of staying angle versus disc speeds 420, 480, 540, 600, and 660 rpm, and three impact positions of the fertilizer particles on the disc (0.06, 0.08, and 0.10 m), using the laboratory measuring method, were smaller than the staying angle results using Ritter calculation method versus the same previous conditions by average percentage 38% for Urea and 34% for Ammonium Sulfate. The previous results may be because the mathematical calculation method (Ritter et al., 1980) did not use the disc speed as independent variable in calculation formula of the staying angle.

65

Therefore, to get more accurate when calculating the staying angle of fertilizer particles under the study, (Urea and Ammonium Sulfate) using the mathematical calculation method, the Ritter et al. (1980) equation may be modified as follows:

R Cosh1 ( ) a   (0.727  0.222 ) 2  1   where: Ø = the staying angle of fertilizer particles, Radians. R = the disc radius, m. a = radius to point of fertilizer particle placement, m.

4.3.2. Evaluating of the second part of simulation (Particle motion off the disc) Experiments were proceeding in the laboratory to test and evaluate the motion performance of fertilizers particles (The horizontal distance that the fertilizer particle traveled into the air, from the disk edge until the ground surface). Also, a comparison was made between the results obtained from the mathematical model and the other results getting from the laboratory experiments, under the following different operational conditions: 1. Two types of fertilizers, Urea 46-0-0 and Ammonium Sulfate 21-0-0. 2. Three different disc speeds, 300, 345, and 390 rpm. 3. Two heights of the disc from the ground surface, 0.8, and 1.0 m. 66

4. Two different particle masses, 0.026, and 0,030 gram. 5. Five replicates. 4.3.2.1. The horizontal distance that the fertilizer particle traveled into the air, from the disk edge until the ground surface An experimental study was carried out in the laboratory to evaluate the motion performance of fertilizers particles from the disk edge until the ground surface. The comparison between the results obtained from the mathematical model and the other results obtained from the laboratory experiments was done. Results of the travelled horizontal distance of two different particle masses (0.026, and 0,030 gram) in the air (m) versus three disc speeds (4.8, 5.5, and 6.2 m/s), two different calculation methods (mathematical equations and laboratory experiments), and two heights of the disc from the ground surface (0.8, and 1.0 m) for both of two fertilizer types (Urea and Ammonium Sulfate) are shown in Figs. (4-10), (4-11), (4-12), and (4-13).

67

The travelled horizontal distance of particle in the air, m

Experimental method 4.0

Z= 0.8 m 3.5 3.0 2.5

2.0 1.5 4.5

5.0

5.5 Disc speed, m/sec

Experimental method The travelled horizontal distance of particle in the air, m

Mathematical method

6.0

6.5

Mathematical method

4.0

Z= 1.0 m 3.5 3.0 2.5

2.0 1.5 4.5

5.0

5.5 Disc speed, m/sec

6.0

6.5

Fig. (4-10): The travelled horizontal distance of Urea particle (0.026 gram) in the air versus three disc speeds, two different calculation methods, and two heights of the disc from the ground surface (0.8, and 1.0 m, respectively)

68

The travelled horizontal distance of particle in the air, m

Experimental method 4.0

Z= 0.8 m 3.5 3.0 2.5

2.0 1.5 4.5

5.0

5.5 Disc speed, m/sec

Experimental method The travelled horizontal distance of particle in the air, m

Mathematical method

6.0

6.5

Mathematical method

4.0

Z= 1.0 m 3.5 3.0 2.5

2.0 1.5 4.5

5.0

5.5 Disc speed, m/sec

6.0

6.5

Fig. (4-11): The travelled horizontal distance of Ammonium Sulfate particle (0.026 gram) in the air versus three disc speeds, two different calculation methods, and two heights of the disc from the ground surface (0.8, and 1.0 m, respectively)

69

The travelled horizontal distance of particle in the air, m

Experimental method

Mathematical method

4.0

Z= 0.8 m 3.5 3.0 2.5

2.0 1.5 4.5

5.0

5.5 Disc speed, m/sec

The travelled horizontal distance of particle in the air, m

Experimental method

6.0

6.5

Mathematical method

4.0

Z= 1.0 m 3.5 3.0 2.5

2.0 1.5 4.5

5.0

5.5 Disc speed, m/sec

6.0

6.5

Fig. (4-12): The travelled horizontal distance of Urea particle (0.030 gram) in the air versus three disc speeds, two different calculation methods, and two heights of the disc from the ground surface (0.8, and 1.0 m, respectively)

70

The travelled horizontal distance of particle in the air, m

Experimental method

Mathematical method

4.0

Z= 0.8 m 3.5 3.0 2.5

2.0 1.5 4.5

5.0

5.5 Disc speed, m/sec

The travelled horizontal distance of particle in the air, m

Experimental method

6.0

6.5

Mathematical method

4.0

Z= 1.0 m 3.5 3.0 2.5

2.0 1.5 4.5

5.0

5.5 Disc speed, m/sec

6.0

6.5

Fig. (4-13): The travelled horizontal distance of Ammonium Sulfate particle (0.030 gram) in the air versus three disc speeds, two different calculation methods, and two heights of the disc from the ground surface (0.8, and 1.0 m, respectively)

71

The general trend of this relationship is that the travelled horizontal distance of two different particle masses (0.026 and 0,030 gram) in the air (m) increases with the increase of disc speed, for both of the two fertilizers types and for both of the two heights of the disc from the ground surface using the two calculation methods. For Urea fertilizer particles, the results of the travelled horizontal distance of two different particle masses (0.026 and 0,030 gram) in the air (m) versus disc speeds 300, 345, and 390 rpm, two different calculation methods (mathematical equations and laboratory experiments), and two heights of the disc from the ground (0.8, and 1.0 m), were smaller than the travelled horizontal distance of Ammonium Sulfate fertilizer particles versus the same previous conditions. For fertilizers particles (mass of 0.026 gram), the results of the travelled horizontal distance of the particles in the air (m) versus disc speeds 300, 345, and 390 rpm, using the laboratory calculation method, were greater than the travelled horizontal distance of the particles in the air versus the same previous conditions using the mathematical calculation method by averages 7% (Urea) and 8% (Ammonium Sulfate) for both of two heights of the disc from the ground 0.8, and 1.0 m, respectively. On the other hand, for fertilizers particles (mass of 0.030 gram), the results of the travelled horizontal distance of the particles in the air (m) versus disc speeds 300, 345, and 390 rpm, using the laboratory calculation method, were greater than the travelled horizontal distance of the particles in the air versus the same previous

72

conditions using the mathematical calculation method by average percentages 22% (Urea) and 23% (Ammonium Sulfate) for both of the two heights of the disc from the ground 0.8, and 1.0 m, respectively. The previous results were happened because of, little particle mass effect in calculations of the travelled horizontal distance of the fertilizers particles in the air. Therefore, to get more accurate when calculating the travelled horizontal distance of the fertilizers particles (Urea and Ammonium Sulfate) in the air, using the mathematical calculation method, the Pitt et al. (1982) equation will be modified as follows: For Urea fertilizer:

H  90.037 (m p )1.2126 

Ln(C1 V t  1) C1

For Ammonium Sulfate fertilizer:

H  151.13 (m p )1.3551 

Ln(C1 V t  1) C1

where: mp = the fertilizer particle mass, gram. In other words, to get very accurate results, when calculating fertilizers particles motion on, and off the disc, using the mathematical model, the equations will be modified as follows:

73

For Urea fertilizer: A. Motion on the disc equations:   0.5572 S 0.102 U  0.0361 .R. 3.189 R Cosh1 ( ) a   (0.727  0.222 ) 2  1  

B. Motion off the disc equations: H  90.037 (m p )1.2126 

Ln(C1 V t  1) C1

For Ammonium Sulfate fertilizer: A. Motion on the disc equations:   0.4751 S 0.308 U  0.1379 .R. 0.924 R Cosh1 ( ) a   (0.727  0.222 ) 2  1  

B. Motion off the disc equations: H  151.13 (m p )1.3551 

Ln(C1 V t  1) C1

74

5. SUMMARY AND CONCLUSIONS Solid chemical fertilizers are one of the important sources for plant nutrition. They provide the plant with important nutrients needed for growth during the period of its life. The most famous machine types of solid chemical fertilizers is the centrifugal distribution machine, and this was due to its advantages, low cost, low power necessary, simplicity of mechanical design, ease of maintenance, its high performance, and its wide operation width, but the most important drawback with these machines is the lack of distribution accuracy of fertilizers at the rate desired. Thus, the aim of this study is to develop a mathematical model to simulate the discharge and spread of the real fertilizers particles from centrifugal spreader. To determine the possibility range of using this model with the different fertilizers particles, and conclude the using possibility range of the same model to deduce the fertilizers distribution patterns after that. To achieve the objectives of this study, there were four main topics covered: 1. Choose the appropriate mathematical model for the study. 2. Studying some physical and mechanical properties of the fertilizers types under study (Urea - Ammonium Sulfate). 3. Create a constant unit to distribute the fertilizers with centrifugal system within the laboratory in Biosystems Engineering Department,

75

Faculty of Agriculture and Food Sciences at the University of Manitoba, Canada. 4. Compare the results obtained from laboratory trials of the centrifugal distribution unit of fertilizers with the obtained results from the mathematical model. First: The mathematical model: The mathematical model was chosen as an approximate model with a simple and few inputs easily obtained. It had been dealing with this model using MATLAB program to obtain the mathematical results of the program. The program inputs were: the disk radius, the disk rotational speed, the coefficient of dynamic friction between the fertilizer particles and the disk surface, radius of the fertilizer particle impact position on the disk, the air temperature, the air barometric pressure, diameter and density of the fertilizer particle, and height of the disk on the ground surface. Meanwhile, the outputs of this program were: the absolute speed and radial speed of fertilizer particle, departure angle of fertilizer particle, the staying angle of fertilizer particle on the disk measured from the position of getting out on the disk until it exits at the edge of the disk, and the travelled horizontal distance of the fertilizers particles (Urea and Ammonium Sulfate) in the air.

76

Second: Studying of some physical and mechanical properties of the fertilizer types under the study: 1. Estimating the particle density for both types of fertilizers under study, and it was for Urea fertilizer 1297 kg / m3 and for the Ammonium Sulfate fertilizer was 1791 kg / m3. 2. Repose angle estimation using the digital photography to get the highest possible accuracy of the results. The largest repose angle of Urea was 380 and the smallest angle was 340, while the largest repose angle of Ammonium Sulfate fertilizer was 410, and the smallest angle was 350. 3. Estimating the size distribution of the fertilizer particles under the study. The results of particles size distribution for Urea on the sieves 4, 8, 10, 12, 20, under the sieve number 20 were as follows: 0%, 62.4%, 28.9%, 5.9%, 2.2%, 0.6%, respectively. Meanwhile, the results of particle size distribution for Ammonium Sulfate fertilizer on the same sieves were as follows: 0%, 85.8%, 9.3%, 2.6%, 2.1%, 0.2%, respectively. 4. Measuring the dynamic friction coefficient of the fertilizers under the study using the speeds 0.8, 1.6, 2.4, and 3.2 m/sec, it was for Urea fertilizer as follows: 0.570, 0.532, 0.508, 0.496, respectively. Meanwhile, it was as follows: 0.510, 0.411, 0.359, 0.335, respectively, for Ammonium Sulfate fertilizer.

77

Third: The unit of fertilizer distribution with centrifugal System:  Constant unit for fertilizers distribution by centrifugal system was set up in the laboratory, the parts of this unit and its characteristics were as follows: 1. Vertical electric motor (EMERSON, Model EL07), with power of 2 hp, at speed of 1800 rpm, frequency 60 Hz, and mass of 29.5 kg. 2. Painted flat disk of iron, it had 300 mm as a diameter and thickness of 6 mm. 3. Four radial vanes spaced every 900 installed on the flat disk. 4. Iron holder for the engine and the disk with a vertical movement up and down property. 5. AC drive (ABB) has Max. power of 2 hp and frequency 60 Hz to control the speed of the electric motor, start from speed of zero rpm until the maximum speed 1800 rpm.  Experiments plan: A. Factors of the study: 1. Two types of fertilizers, Urea 46-0-0 and Ammonium Sulfate 21-0-0. 2. Eight different disc speeds, 300, 345, 390, 420, 480, 540, 600, and 660 rpm. 3. Three impact positions on the disc, 0.06, 0.08, and 0.10 m. 4. Two heights of the disc from the ground surface, 0.8, and 1.0 m.

78

5. Two different particles mass, 0.026, and 0,030 gram. B. Measurements and evaluation factors: 1. The radial velocity of fertilizer particles. 2. Staying angle of the fertilizer particle on the disc. 3. The horizontal distance that the fertilizer particle traveled into the air, from the disk edge until the ground surface. Fourth: The obtained results from the laboratory experiments of the fertilizer distribution unit comparing to results of the mathematical model:  Laboratory results were compared with the mathematical model results, and yielded the following points: 1. The radial velocity values using the mathematical model method were greater than the radial velocity values using the laboratory calculation method, for both of Urea and Ammonium Sulfate fertilizers. 2. The results of staying angle (Radians) of Urea fertilizer particles, versus disc speeds 420, 480, 540, 600, and 660 rpm, two calculation different methods (Ritter, and laboratory experiments), and three impact positions of the fertilizer particles on the disc (0.06, 0.08, and 0.10 m), were greater than staying angle results of Ammonium Sulfate fertilizer particles versus the same previous conditions.

79

3. The staying angles results of Urea and Ammonium Sulfate fertilizers using Ritter calculation method had the same trend of the staying angle results of the same fertilizers using laboratory method. 4. The results of the travelled horizontal distance of two different particles mass of Urea fertilizer (0.026 and 0,030 gram) in the air (m) versus disc speeds 300, 345, and 390 rpm, two calculation different methods (mathematical model and laboratory experiments), and two heights of the disc from the ground (0.8, and 1.0 m), were smaller than the travelled horizontal distance of Ammonium Sulfate fertilizer particles versus the same previous conditions. 5. The results of the travelled horizontal distance of the fertilizers particles (mass of 0.026 gram) in the air (m) versus disc speeds 300, 345, and 390 rpm, using the laboratory calculation method, were greater than the travelled horizontal distance of the particles in the air versus the same previous conditions using the mathematical model method by average percentages 7% (Urea) and 8% (Ammonium Sulfate) for both of two heights of the disc from the ground 0.8, and 1.0 m, respectively. 6. The results of the travelled horizontal distance of the fertilizers particles (mass of 0.030 gram) in the air (m) versus disc speeds 300, 345, and 390 rpm, using the laboratory calculation method, were greater than the travelled horizontal distance of the particles in the air versus the same previous conditions using the mathematical model

80

method by average percentages 22% (Urea) and 23% (Ammonium Sulfate) for both of two heights of the disc from the ground 0.8, and 1.0 m, respectively. Recommendations: 1. It’s advised to use the digital photography technique, to get the highest possible accuracy results of the repose angle. 2. It’s possible to use (CASIO EX-FH25) camera with 10 megapixels resolution in the scientific experiments as a high speed digital camera. 3. It’s preferred to use (SONY Vegas Pro) program to analyze the high speed videos. 4. It’s advised to use dark plastic sheet (black, blue, red…etc.) supported by thin layer of the white sugar above it, to measure the travelled horizontal distance of fertilizers particles in the air. 5. To get more accurate when calculating the radial velocity of fertilizer particles under the study, (Urea and Ammonium Sulfate) using the mathematical model method, the equations may be as follows: U = 0.0361ωr.µ-3.189

For Urea fertilizer

U = 0.1379ωr.µ-0.924

For Ammonium Sulfate fertilizer

81

6. To get accurate results when calculating the staying angle of fertilizer particles, (Urea and Ammonium Sulfate) using the mathematical model method, the Ritter (1980) equation may be modified as follows: R Cosh1 ( ) a   (0.727  0.222 ) 2  1  

7. To get more accuracy when calculating the travelled horizontal distance of the fertilizers particles (Urea and Ammonium Sulfate) in the air, using the mathematical model method, the Pitt et al. (1982) equation will be modified as follows: H  151.13 (m p )1.3551 

Ln(C1 V t  1) C1

For Urea fertilizer

H  90.037 (m p )1.2126 

Ln(C1 V t  1) C1

For Ammonium Sulfate fertilizer

82

REFRANCES

Abd El-Mageed H. N.; A. E. Abou El-Magd; O. M. Kamel and S. Marey. (2006). Coordinating fertilizer application rates automatically to the travel speed of spreader. Mansoura Univ. J. Agric. Sciences. 31 (7): 243-261. Ahmed S. F. (1988). The performance of a centrifugal fertilizer distributor model. Misr J. Agr. Eng. 5 (1): 13-23. Ahmed S. F.; M.A. Shaibon and A. A. Sayed-ahmed. (1992). Factors affecting the performance of a centrifugal fertilizer distributor. Misr J. Agr. Eng. 7 (3): 238-249. Aphale A.; N. Bolander; J. Park; L. Shaw; J. Svec and C. Wassgren. (2003). Granular fertilizer particle dynamics on and off a spinner spreader. Biosystems Engineering. 85 (3): 319-329. Awady M. N. (1965). Transport of particulate materials in axisymmetric turbulent air jets. Ph.D. Thesis, California Univ., Davis. Bernacki H.; I. Haman and C. Kanafojski. (1972). Agricultural machinesTheory and construction. U. S. Dept. of Agric. and The National Science Foundation; Washington; D. C.: 571-600. Bhushan B. (1981). Effect of Shear Strain Rate and Interface Temperature on Predictive Friction Models. Proc. Seventh Leeds-Lyon Symposium on

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Tribology (D. Dowson; C. M. Taylor; M. Godet and D. Berthe; eds.), pp. 3944, IPC Business Press, Guildford, UK. Brinsifeld R. B. and J. w. Hummel. (1975). Simulation of a new centrifugal distribution design. Trans. of the ASAE, 18 (12): 213-220. Chowdhury M. A. and Helali M. M. (2006). The Effect of Frequency of Vibration and Humidity on the Coefficient of Friction. Tribology International (39), pp. 958-962. Chowdhury M. A. and Helali M. M. (2007). The Effect of Frequency of Vibration and Humidity on the Wear rate. Wear (262), pp. 198-203. Csizmazia Z. (2000). Some physical properties of fertilizer particles. Aspects of Applied Biology 61: 219-226. Cunningham F. M. (1963). Performance characteristics of bulk spreaders for granular fertilizer. Trans. of the ASAE, 6 (2): 108-114. Cunningham F. M. and E. Y. S. Chao. (1965). Design relationships for centrifugal fertilizer distributors. ASAE Paper No. 65-605, ASAE, St. Joseph, Mich. 49085. Cunningham F. M. and E. Y. S. Chao. (1967). Design relationships for centrifugal fertilizer distributors. Trans. of the ASAE, 10 (1): 91-96. Curray J. K. (1951). Analysis of sphericity and roundness of quartz grains. MSc. Thesis in Mineralogy, The Pennsylvania State Univ., University Park, Pa.

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Davis J. B. and C.E. Rice. (1973). Distribution of granular fertilizer and wheat seed by centrifugal distributors. Trans. of the ASAE, 16 (5): 867-868. Davis J. B. and C.E. Rice. (1974). Predicting Fertilizer distribution by a centrifugal distributor using CSMP; a simulation language. Trans. of the ASAE, 17 (6): 1091-1093. Dintwa E.; P. V. Liedekerke; R. Olieslagers; E. Tijskens and H. Ramon. (2004). Model for simulation of particle flow on a centrifugal fertilizer spreader. Biosystems Engineering. 87 (4): 407-415. Glover I. W. and I. W. Baird. (1973). Performance of spinner type fertilizer spreaders Trans. of the ASAE, 16 (1):48-51. Griffis C. L.; D. W. Ritter and E. J. Matthews. (1983). Simulation of rotary spreader distribution patterns. Trans. of the ASAE, 26 (1): 33-39. Grift T. E. and J. W. Hofstee. (2002). Testing an online spread pattern determination sensor on a broadcast fertilizer spreader. Trans. of the ASAE, 45 (3): 561-567. Imada Y. and Nakajima K. (1995). Effect of humidity on the friction and wear properties of Sn. Journal of Tribology (117), pp.737–44. Imada Y. (1996). Effect of humidity and oxide products on the friction and wear properties of mild steel. Journal of Japanese Society of Tribologists (114), pp.131–40.

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Kepner R. A.; R. Bainer and E. L. Barger. (1978). Principles of farm machinery. 5th Ed. AVI Publishing Company. Komvopoulos K. and Li H. (1992). The effect of tribofilm formation and humidity on the friction and wear properties of ceramic materials. Journal of Tribology (114), pp.131–40. Nian-Sheng cheng. (2009). Comparison of formulas for drag coefficient and settling velocity of spherical particles. Powder Technology. 189: 395-398. Olieslargers R.; H. Ramon and J. De Baerdemaeker. (1996a). Calculation of fertilizer distribution patterns from a spinning disc spreader by means of a simulation model. J. Agri. Eng. Res. 63, 137-152. Olieslargers R.; H. Ramon and J. De Baerdemaeker. (1996b). Design of a centrifugal spreader for site-specific fertilizer application. Precision agriculture. Proceedings of the 3rd international conference, Minneapolis, Minnesota, USA, 23-26 June, pp. 745-756. Parish R. L. (1987). The effect of speed on performance of a rotary spreader for turf. Trans. of the ASAE, 30 (1): 232-240. Parish R. L. (1999). The effect of spreader fills level on delivery rate. Applied Eng. in Agric. 15 (6):647-648. Parish R. L. and P. P. Chaney. (1986). Pattern sensitivity of location of fertilizer drop point on a rotary spreader. Trans. of the ASAE, 29 (2): 374-377.

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Parish R. L. and W. C. Porter. (1994). Spreader patterns using ASAE S341.2 compared to Actual patterns on turf-grass. Amer. Soc. Agric. Eng. No. 941062, 12 pp. Parish R. L.; P.P. Chaney and D. L. Fuller. (1987). Comparison of laboratory methods of spreader pattern evaluation with agronomic response. Trans. of the ASAE, 30 (2): 237-240. Patterson D. E. and Reece A. R. (1962). The theory of the centrifugal distributor. I: Motion on the disc; near-centre feed. J. Agri. Eng. Research. 7 (3): 232240. Pitt R. E.; G. S. Farmer and L. P. Walker. (1982). Approximating equations for rotary distributor spread pattern. Trans. of the ASAE, 25 (6): 1544-1552. Reed W. B. and E. Wacker. (1970). Determining distribution pattern of dry fertilizer applicators. Trans. of the ASAE, 13 (1): 85-89. Reints R. E. and R. R. Yoerger. (1967). Trajectories of and granular fertilizer. Trans. of the ASAE, 10 (2): 213-216. Ritter D. W.; C. L. Griffis and E. J. Matthews. (1980). Computer simulation of rotary spreader distribution patterns. ASAE Paper No. 80-1504. ASAE, St. Joseph, Mich. 49085. Sayed-ahmed A. A. (1989). Design relationships for fertilizer broadcasters. MSc. Thesis. Alexandria Univ. Egypt.

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Srivastava A. K.; C. E. Goering and R. P. Roharbach. (1993). Engineering principles of agricultural machines. ASAE Textbook No. (6), published by American Society of agricultural Eng. Wikipedia,

the

free

encyclopedia.

(2012).

http://en.wikipedia.org/wiki/Computer_simulation

33

Computer

simulation.

Fig. (A-1): The simulation program in case of calculating the outputs for Urea fertilizer

89

Fig. (A-2): The simulation program in case of calculating the outputs for Ammonium Sulfate fertilizer

90

The calculating method of the horizontal distance (H) that the fertilizer particle traveled into the air from disk edge until the ground:    tan 1

.R U



A R H   Sin a Sin r Sin h



A R H   Sin (180   ) Sin r Sin h

 R . Sin (180   )    r  Sin 1   A  

  h 180  ( r   a)  R . Sin h   H    Sin r 

Fig. (A-8): Top view diagram of H and A distances

   1 R . Sin        R . Sin 180    a  Sin A       H    R . Sin        A   

   1 R . Sin       A . Sin    Sin A      H    Sin      91

The MATLAB Simulation Program function varargout = SimulationFinal_modi(varargin) % SIMULATIONFINAL_MODI M-file for SimulationFinal_modi.fig % SIMULATIONFINAL_MODI, by itself, creates a new SIMULATIONFINAL_MODI or raises the existing % singleton*. % H = SIMULATIONFINAL_MODI returns the handle to a new SIMULATIONFINAL_MODI or the handle to % the existing singleton*. % % SIMULATIONFINAL_MODI('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in SIMULATIONFINAL_MODI.M with the given input arguments. % SIMULATIONFINAL_MODI('Property','Value',...) creates a new SIMULATIONFINAL_MODI or raises the % existing singleton*. Starting from the left, property value pairs are % applied to the GUI before SimulationFinal_modi_OpeningFcn gets called. An % unrecognized property name or invalid value makes property application % stop. All inputs are passed to SimulationFinal_modi_OpeningFcn via varargin. % % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)". % % See also: GUIDE, GUIDATA, GUIHANDLES % Edit the above text to modify the response to help SimulationFinal_modi % Last Modified by GUIDE v2.5 08-Sep-2012 04:47:49 % Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @SimulationFinal_modi_OpeningFcn, ... 'gui_OutputFcn', @SimulationFinal_modi_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []); if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end

29

if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT % --- Executes just before SimulationFinal_modi is made visible. function SimulationFinal_modi_OpeningFcn(hObject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % varargin command line arguments to SimulationFinal_modi (see VARARGIN) % Choose default command line output for SimulationFinal_modi handles.output = hObject; % Update handles structure guidata(hObject, handles); % UIWAIT makes SimulationFinal_modi wait for user response (see UIRESUME) % uiwait(handles.figure1); % --- Outputs from this function are returned to the command line. function varargout = SimulationFinal_modi_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Get default command line output from handles structure varargout{1} = handles.output; function discradiustxt_Callback(hObject, eventdata, handles) % hObject handle to discradiustxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of discradiustxt as text

29

%

str2double(get(hObject,'String')) returns contents of discradiustxt as a double

% --- Executes during object creation, after setting all properties. function discradiustxt_CreateFcn(hObject, eventdata, handles) % hObject handle to discradiustxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function discrotaionspeedtxt_Callback(hObject, eventdata, handles) % hObject handle to discrotaionspeedtxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of discrotaionspeedtxt as text % str2double(get(hObject,'String')) returns contents of discrotaionspeedtxt as a double % --- Executes during object creation, after setting all properties. function discrotaionspeedtxt_CreateFcn(hObject, eventdata, handles) % hObject handle to discrotaionspeedtxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function minradiustxt_Callback(hObject, eventdata, handles) % hObject handle to minradiustxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of minradiustxt as text

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%

str2double(get(hObject,'String')) returns contents of minradiustxt as a double

% --- Executes during object creation, after setting all properties. function minradiustxt_CreateFcn(hObject, eventdata, handles) % hObject handle to minradiustxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function maxradiustxt_Callback(hObject, eventdata, handles) % hObject handle to maxradiustxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of maxradiustxt as text % str2double(get(hObject,'String')) returns contents of maxradiustxt as a double % --- Executes during object creation, after setting all properties. function maxradiustxt_CreateFcn(hObject, eventdata, handles) % hObject handle to maxradiustxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end % --- Executes on button press in calculate1btn. function calculate1btn_Callback(hObject, eventdata, handles) % hObject handle to calculate1btn (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) R = str2num (get(handles.discradiustxt,'string')); %#ok

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N = str2num (get(handles.discrotaionspeedtxt,'string')); %#ok amin = str2num (get(handles.minradiustxt,'string')); %#ok amax = str2num (get(handles.maxradiustxt,'string')); %#ok W = (2*pi*N)/60; if (get(handles.radbtnUREA,'Value') == get(handles.radbtnUREA,'Max')) F = 0.5572*(2*pi*R*N/60)^-0.102; U = 0.0361*W*R*(F^-3.189); else F = 0.4751*(2*pi*R*N/60)^-0.308; U = 0.1379*W*R*(F^-0.924); end V = sqrt((W^2*R^2)+U^2); THETA = atan (W*R)/U; FAYmin = (0.727-0.222*F)*acosh (R/amax)/((F^2+1)^0.5-F); FAYmax = (0.727-0.222*F)*acosh (R/amin)/((F^2+1)^0.5-F); set(handles.absolutespeedtxt,'string',num2str(V)); set(handles.radialvelocitytxt,'string',num2str(U)); set(handles.dispatchangletxt,'string',num2str(THETA)); set(handles.minfaytxt,'string',num2str(FAYmin)); set(handles.maxfaytxt,'string',num2str(FAYmax)); % --- Executes on button press in clear1btn. function clear1btn_Callback(hObject, eventdata, handles) % hObject handle to clear1btn (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) set(handles.discradiustxt,'string',''); set(handles.discrotaionspeedtxt,'string',''); set(handles.minradiustxt,'string',''); set(handles.maxradiustxt,'string',''); set(handles.absolutespeedtxt,'string',''); set(handles.radialvelocitytxt,'string',''); set(handles.dispatchangletxt,'string',''); set(handles.minfaytxt,'string',''); set(handles.maxfaytxt,'string',''); function absolutespeedtxt_Callback(hObject, eventdata, handles) % hObject handle to absolutespeedtxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

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% Hints: get(hObject,'String') returns contents of absolutespeedtxt as text % str2double(get(hObject,'String')) returns contents of absolutespeedtxt as a double % --- Executes during object creation, after setting all properties. function absolutespeedtxt_CreateFcn(hObject, eventdata, handles) % hObject handle to absolutespeedtxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function radialvelocitytxt_Callback(hObject, eventdata, handles) % hObject handle to radialvelocitytxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of radialvelocitytxt as text % str2double(get(hObject,'String')) returns contents of radialvelocitytxt as a double % --- Executes during object creation, after setting all properties. function radialvelocitytxt_CreateFcn(hObject, eventdata, handles) % hObject handle to radialvelocitytxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function dispatchangletxt_Callback(hObject, eventdata, handles) % hObject handle to dispatchangletxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

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% Hints: get(hObject,'String') returns contents of dispatchangletxt as text % str2double(get(hObject,'String')) returns contents of dispatchangletxt as a double % --- Executes during object creation, after setting all properties. function dispatchangletxt_CreateFcn(hObject, eventdata, handles) % hObject handle to dispatchangletxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function minfaytxt_Callback(hObject, eventdata, handles) % hObject handle to minfaytxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of minfaytxt as text % str2double(get(hObject,'String')) returns contents of minfaytxt as a double % --- Executes during object creation, after setting all properties. function minfaytxt_CreateFcn(hObject, eventdata, handles) % hObject handle to minfaytxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function maxfaytxt_Callback(hObject, eventdata, handles) % hObject handle to maxfaytxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

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% Hints: get(hObject,'String') returns contents of maxfaytxt as text % str2double(get(hObject,'String')) returns contents of maxfaytxt as a double % --- Executes during object creation, after setting all properties. function maxfaytxt_CreateFcn(hObject, eventdata, handles) % hObject handle to maxfaytxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function airtemptxt_Callback(hObject, eventdata, handles) % hObject handle to airtemptxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of airtemptxt as text % str2double(get(hObject,'String')) returns contents of airtemptxt as a double % --- Executes during object creation, after setting all properties. function airtemptxt_CreateFcn(hObject, eventdata, handles) % hObject handle to airtemptxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function airpressuretxt_Callback(hObject, eventdata, handles) % hObject handle to airpressuretxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

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% Hints: get(hObject,'String') returns contents of airpressuretxt as text % str2double(get(hObject,'String')) returns contents of airpressuretxt as a double % --- Executes during object creation, after setting all properties. function airpressuretxt_CreateFcn(hObject, eventdata, handles) % hObject handle to airpressuretxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function particlemaxdiatxt_Callback(hObject, eventdata, handles) % hObject handle to particlemaxdiatxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of particlemaxdiatxt as text % str2double(get(hObject,'String')) returns contents of particlemaxdiatxt as a double % --- Executes during object creation, after setting all properties. function particlemaxdiatxt_CreateFcn(hObject, eventdata, handles) % hObject handle to particlemaxdiatxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function particledensitytxt_Callback(hObject, eventdata, handles) % hObject handle to particledensitytxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

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% Hints: get(hObject,'String') returns contents of particledensitytxt as text % str2double(get(hObject,'String')) returns contents of particledensitytxt as a double % --- Executes during object creation, after setting all properties. function particledensitytxt_CreateFcn(hObject, eventdata, handles) % hObject handle to particledensitytxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function fallheighttxt_Callback(hObject, eventdata, handles) % hObject handle to fallheighttxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of fallheighttxt as text % str2double(get(hObject,'String')) returns contents of fallheighttxt as a double % --- Executes during object creation, after setting all properties. function fallheighttxt_CreateFcn(hObject, eventdata, handles) % hObject handle to fallheighttxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end % --- Executes on button press in calculate2btn. function calculate2btn_Callback(hObject, eventdata, handles) % hObject handle to calculate2btn (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB

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% handles structure with handles and user data (see GUIDATA) TC = str2num (get(handles.airtemptxt,'string')); %#ok Pb = str2num (get(handles.airpressuretxt,'string')); %#ok Dpmax = str2num (get(handles.particlemaxdiatxt,'string')); %#ok Pp = str2num (get(handles.particledensitytxt,'string')); %#ok Z = str2num (get(handles.fallheighttxt,'string')); %#ok Ve = str2num (get(handles.absolutespeedtxt,'string')); %#ok TK = TC+273; Pa = (29*Pb)/(8.314*TK); Ua = 4.79*10^-6*exp(0.678+(0.00227*TK)); if (get(handles.radbtnUREA,'Value') == get(handles.radbtnUREA,'Max')) Dpe = 0.88*Dpmax; else Dpe = 0.77*Dpmax; end Nre = (Pa*Ve*Dpe)/Ua; CD = 24/Nre*(1+(0.27*Nre))^0.43+(0.47*(1-exp(-0.04*Nre^0.38))); C1 = (0.75*CD*Pa)/(Pp*Dpe); C2 = sqrt(9.81/C1); B = (2*exp(2*C1*Z)) - 1; T = log(B+sqrt((B^2) -1))/(2*C1*C2); if (get(handles.radbtnUREA,'Value') == get(handles.radbtnUREA,'Max')) H = (((85238/6)*Pp*pi*Dpe^3)-1.225)*log((C1*Ve*T)+1)/C1; else H = (((100660/6)*Pp*pi*Dpe^3)-1.622)*log((C1*Ve*T)+1)/C1; end set(handles.particlehorizondistxt,'string',num2str(H)); % --- Executes on button press in clear2btn. function clear2btn_Callback(hObject, eventdata, handles) % hObject handle to clear2btn (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) set(handles.airtemptxt,'string',''); set(handles.airpressuretxt,'string','');

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set(handles.particlemaxdiatxt,'string',''); set(handles.particledensitytxt,'string',''); set(handles.fallheighttxt,'string',''); set(handles.particlehorizondistxt,'string',''); function particlehorizondistxt_Callback(hObject, eventdata, handles) % hObject handle to particlehorizondistxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of particlehorizondistxt as text % str2double(get(hObject,'String')) returns contents of particlehorizondistxt as a double % --- Executes during object creation, after setting all properties. function particlehorizondistxt_CreateFcn(hObject, eventdata, handles) % hObject handle to particlehorizondistxt (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end % --- Executes on button press in radbtnAMS. function radbtnAMS_Callback(hObject, eventdata, handles) % hObject handle to radbtnAMS (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hint: get(hObject,'Value') returns toggle state of radbtnAMS % --- Executes on button press in radbtnUREA. function radbtnUREA_Callback(hObject, eventdata, handles) % hObject handle to radbtnUREA (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hint: get(hObject,'Value') returns toggle state of radbtnUREA

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% --- Executes on button press in togglebutton1. function togglebutton1_Callback(hObject, eventdata, handles) % hObject handle to togglebutton1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hint: get(hObject,'Value') returns toggle state of togglebutton1 % --- Executes on button press in checkbox1. function checkbox1_Callback(hObject, eventdata, handles) % hObject handle to checkbox1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hint: get(hObject,'Value') returns toggle state of checkbox1 % --- Executes on button press in checkbox2. function checkbox2_Callback(hObject, eventdata, handles) % hObject handle to checkbox2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hint: get(hObject,'Value') returns toggle state of checkbox2 % --- Executes on key press with focus on radbtnUREA and none of its controls. function radbtnUREA_KeyPressFcn(hObject, eventdata, handles) % hObject handle to radbtnUREA (see GCBO) % eventdata structure with the following fields (see UICONTROL) % Key: name of the key that was pressed, in lower case % Character: character interpretation of the key(s) that was pressed % Modifier: name(s) of the modifier key(s) (i.e., control, shift) pressed % handles structure with handles and user data (see GUIDATA)

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The program flowchart

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