PRESSURE DROP DUE TO THE PNEUMATIC CONVEYANCE QF GRAINS AND FORAGES Thesis for “10 Degree of M. S. MICHIGAN ' STATE UNIVERSITY Jack Wilbur Crane 1956 ........ PRESSURE DROP DUE TO THE PNEUMATIC CONVEIANCE OF GRAINS AND FORAGES By Jack W} grane AN ABSTRACT Submitted Jointly to the Colleges of Engineering and Agriculture Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1956 by 5/; )4; $6721, b.— {a daCK urane 1 1 . Until recent years the only important use being made of pneumatic conveying systems on the farm was for filling vertical silos and gran- aries. Both of these applications involved only short conveying distan- ces, usually less than hS feet. Due to the short conveying length, an impeller blower was generally used. In most instances, and particularly in the case of grains, the individual particles received their energy, not from the air stream, but from the blower blades. This indicates that the static pressure drop within the pipe is not an important con- sideration in the design of such a system. However, mechanization in the materials handling field has brought about the use of pneumatic conveying systems for transporting grains and forages from their storage location to the feed parlor. This type of system could possibly involve several hundred feet of pipe including elbows and lengths of varying inclinations. An impeller blower would not prove adequate for such a system. Therefore, it would be necessary to convert to a truly'pneu- matic system in which the particles are introduced ahead of the blower and obtain their energy from the air stream. In this type of a system, it would be very important for the design engineer to be able to predict the static pressure drOp for any situation in which the system might be used. The object of this research was to present equations which could be used to predict the pressure drop in a system, dependent only on the following variables: 1. Material being conveyed. 2. Solid flow rate. 3. Air velocity. h. Pipe diameter. 5. Pipe length. 6. Pipe inclination. Throughout the years, the problem of homogeneous fluid flow has been investigated, both experimentally and analytically, in a very thorough manner. However, there has been little attention given to pneumatic conveyance of solids. Almost all the work completed to date has been on an experimental basis with only a few investigators presen— ting a sound theoretical base for their experimental results. The few analytical developments which are available at the present time are of limited use, as they were set up for specific, and not general, situa- tions. Pinkus (30) presented a very convincing theory for the case of horizontal flow, and his experiments with sand proved the validity of his initial assumptions. The theoretical analysis presented in this report was based on the same initial assumptions, however, it has been extended to include pipes of any inclination, thus making the resultant equations of more value to the design engineer. These equations have been derived, as is presented in the Appendix, and their validity has been proved for soft white winter wheat being conveyed in a 3.89 inch I.D. tube. The equations, as well as the experimental results, indicate that the pressure drop due to the solids increased as the pipe inclination increased, with throughput and air velocity remaining constant. Also, the drop due to the solids increased as the air velocity decreased and the pipe angle increased. It was observed during the experiment that the minimum air veloc- ity which will carry wheat particles in a horizontal pipe was 65 feet per second. In a vertical pipe this velocity was 70 feet per second. Jack Crane 3. The maximum throughput of wheat in a 3.89 inch diameter pipe, which will allow smooth continuous Operation, was approximately 57.82 pounds per minute. PRESSURE DROP DUE TO THE PNEUMATIC CONVEYANCE OF GRAINS AND FORAGES By Jack W. Crane A THESIS Submitted Jointly to the Colleges of Engineering and Agriculture Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1956 ACKNOWLEDGEMENTS The author wishes to express his sincere thanks to Doctor W. M. Carleton for his inspiring guidance and helpful suggestions during the investigation upon which this thesis is based. He also wishes to thank Professor H. F. Mc Colly for his many helpful suggestions. Grateful acknowledgement is due to Doctor A. W. Farrell, Head of the Department of Agricultural Engineering, for granting the Graduate Research Assistantship which enabled the author to complete this work. The author sincerely appreciates the financial assistance of the New Holland Machinery Company of New Holland, Pennsylvania, which made this investigation possible.” Thanks are also due to the authors wife, Earilyn Crane, for her technical assistance on the subject of Specialized photography. The many hours of secretarial work which she gave are also much appreciated. TABLE OF CONTENTS INTRODUCTION .................................................. Reason for Study ........................................ Objectives .............................................. Limitations of Study .................................... REVIEW OF LITERATURE .......................................... THEORY ........................................................ APPARATUS ..................................................... ST PROCEDURE ................................................ 'Choice of Material ...................................... Physical Properties of the Test Material ................ Particle Flow Regulation ................................ Mechanics of Test Procedure ............................. Possible Sources of Error ............................... EXPERIMENTAL RESULTS .......................................... Physical Properties of Particles Tested ................. Pressure Dr0p Results ................................... SUMMARY AND CONCLUSIONS ....................................... Specific Equations for Soft White Winter Wheat .......... Practical Operating Range ............................... Possible Analysis of Silage Particles ................... Summary of Conclusions .................................. RECOMRTDATAPONS FOR FUTURE STUDY OOOOOOOOOOOOOOOOOOOQOO0.00....' APPENDH OOIOCOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOO00.0.0000... Derivation 0f Pressure Drop Equation 00000000000000.0000. Derivation of Velocity Equation Assuming “C" ='Constant . 13 36 36 38 39 50 52 52 52 72 72 81 83 85 86 90 91 9S Derivation of Velocity Equation Assuming "C" is a motion or“ 00.0.00...IOOOOOOOOOOOOOOOOOOOOOOO0.0.0.0. 100 Derivation of Orifice Equations ......................... 103 Examination of Error Due to the Compressibility of Air .. 107 Investigation of Error Due to Loss of Air Through the Bucket Wheel Feeder Vents ............................... 108 REFERENCES OOOOOOOOOOOOOOOOOOOOOO0.00......OOOOOOOOOOOOOOOOOOOO 109 NO. 2. 3. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. LIST OF FIGURES Coefficient of Resistance Versus Reynolds Number for Spheres oooooooooooooooooooooooooooooooooooooooooooocoooo LQYOUt Of Experimental Pneumatic System.................. Graph of Air Velocity Versus Differential Head for Orifice USBd in the Talt SYStem ooooooooooooooooooooooocooooooooo Test Setup Used to Determine the Solids' Velocity by the Photographic Method 00000009000900.0000...coco.ococoa.coo Photograph of Wheat Falling Through a 4" I.D. Glass Tube (High Density 0? Particles) ooooooooooooooooooooooooooooo Photograph of Wheat Falling Through a 4" I.D. Glass Tube (LOW DOUSity Of PartiCIOB) oooooooocoooooooo-oooooooooooo Photograph of the Shutoff Valves Installed on the Test Section ooooooooooooooooooooooeocoooooooooooccooooooooooo Cross Section of Particle Injector (50% Constriction) ... Cross Section of Particle Injector with Blobiaok Aperture (50% Constriction) ooooooooooooooooooooo...oooooooooooooo Cross Section of Particle Injector (68% Constriction) ... Bucket Wheel Pbedor ..................................... Photograph of Drive Used with Bucket Wheel Feeder ....... Location of Individual Stations “fithin the Test Section . Photograph of One Pressure Tap .......................... Photograph of the Pressure Tap Control Panel ............ Photograph of Calibrated Plates .......................... Photograph Showing Air Vents in the Bucket'Wheel Feeder .. Photograph of Test Apparatus (Pipe Inclination of 62.SO°). Photograph of Test Apparatus (Pipe Inclination of 90.000). Page 11 14 17 19 21 23 25 26 26 26 3O 31 32 33 34 h3 h5 ho No. 20. 21. 22. 23. 2h. Experimentally Determined Pressure Drop Versus Air Velocity Curve for Air Alone .............................. Experimental Graph of Air Velocity Versus Particle Veloc1ty(9:00) ................OOIOOOOOOOOOOO....000... Calculated Graph of Air Velocity Versus Particle Velocity (63 : 0°) ................................................. Graph of Solids' Friction Factor for Wheat Versus Air veIOCj-ty ......OOOOCOOOOCCOIOO..........OOOOOOOOOOOOOO0.... Graphs of Particle Velocity Versus Air Velocity for Various Pipe Inclination Between 0° and 90° ....................... 25 Through 32. Graphs of Air Velocity and Flow Rate Versus 33. 3h. 35. 36. 37. 38. 39. Pressure Drop for Various Pipe Inclinations ............... Graph Showing Variation in "fps "‘With Changes in "£9" and "41;" Graph Illustrating the Components of the Total Pressure Drop for One Throughput ooocoooooococooooooooooooooooooooo. Table of Pipe Inclination and Air Velocity Versus Pressure Drop for a Throughput of 25.93 #/Nin. ..................... Table of Pipe Inclination and Air Velocity Versus Pressure Drop foraThroughput Of 57. 82 #/Min. ......OOOOOOOOOOOOOOO Graph of Components of Total Pressure Drop and H. P. Required Versus Air Velocity .............................. Free Body Diagram of a Single Particle in an Air Stream ... Cross Section of Conveyor Pipe Near the Orifice ........... 57 59 6O 61 & 62 66 67 71 71 82 91 103 INTRODUCTI 0N Reason for study Pncunatic conveying systems have long been recognized as a labor-saving method of transporting solid particles. They were not generally introduced on the farm, however, until recent years, with the exception of the impeller blower used to fill vertical silos with varioustypos of forages. Other than this one application, it was felt that pneumatic conveying systems, as used at that time, were too expon- sivc and immobile for farm use. However, withtho introduction of an impeller blower which could be used on grains, without fear of excessive damgc, the number of those systems on farms steadily increased. The impeller system does have one distinct disadvantage when conveying tutorial which is susceptible to injury by impact. Since most of the energy is imparted to the particle by the impeller wheel, the particle has no inmodiatc source of energy to draw upon to replenish that lost throughout the piping system. This means that the transporting distance is limited by the energy loss of the particle. If the system contains bonds or long lengths of horizontal pips where energy losses are great, the maxinmm transporting distance will be very short unless it is possible to operate the impeller wheel at relatively high speeds. llcchanisation in the materials handling field has brought about the use of pneumtic blowers as a source of energy for transferring grains and forages from the storage location to the feed parlor. Since a large portion of the conveying pipe will be in a horizontal or inclined position, with a large number of elbows, an impeller type system would not be suitable. However, the use of a truly pneumatic conveying system Pa. offers interesting possibilities. Therefore, the remining discussion will pertain only to the latter. Objectives The objectives of this research include: (a) theoretical deriva- tion of an equation for the pressure drop, in pipes of any inclination, due to the friction of the solid phase and (b) experimental determination of the friction factors for various types of particles. With the above information, it will be possible to calculate the total pressure drop by assuming it to be canposed of three parts: 1. Drop due to the friction of the solid phase. 2. Drop due to the air friction. I 3. DrOp due to the static head of the solids. The static head canponent will vary from zero for horizontal pipes to a mximum value for vertical pipes. The velocity of the particles within the pipe proved to be a very important parameter in the development of the pressure drop equation. Two expressions for the solids' velocity will be derived and tested. (he assumu the coefficient of particle resistance as a constant, while the other assumes it is a function of Reynolds number. After the above equations have been established, it will be neces- sary to verify the theoretical derivations by actual experimentation. The results of each investigation will be canpletely described in this study. ' Limitations of the sttgy If unlimited time were available, it would be desirable to experi- mentally measure the pressure drop, dependent upon the following variables: velocity of the particles, solid flow rate, pipe length, pipe diameter, and pipe inclination. However, due to the limited time of study, only one pipe diameter will be used to test the validity of the initial assumptions. Before the equations developed can be assumed generally correct, the effect of the other variable must be determined. REVIEW 0? LITERATURE Throughout the years, the problem of homogeneous fluid flow has been investigated, both experimentally and analytically, in a very thor- ough manner. However, there has been little attention given to pneumatic conveyance of solids. Almost all the work completed to date has been on an experimental basis with only a few investigators presenting a sound theoretical base for their experimental results. The few analytical deve10pments which are available at the present time are of limdted use because they were set up for specific, and not general, situations. Segler (32) gives the results of accanplishments, during the past twenty years, in the field of pneumatic grain conveying as applied on farms. This book covers the general field thoroughly; however, the design data presented are derived primarily from‘experimental results. ‘cht and lhite (37) were partially successful in their attempt to derive expressions for pressure drops from the solid and fluid properties of the system. Experimental results were obtained from tests of the followb ing particles: steel shot, clover seed, wheat, and sand. Hariu and Nelstad (20) analyzed the pressure drop in vertical pipes. However, as was pointed out by the authors, the pressure drcp due to the initial particle acceleration was accidentally included in their experimental data, thus obscuring results obtained from test runs with sand particles. Pinkus (30) presented a very convincing theory for the case of horizontal flow, and his experiments with sand particles proved the validity of his initial assumptions. An attempt‘will be made during this research project to alter and.further extend his theory to grains and forages in pipes of varying inclinations. Lapple and Shepherd (23) developed equatims for calculating paths taken by particles undergoing accelerated motion. However, the value of this article is limited because the equations developed pertain only to an unconfined media. Chatley (8) in calcu- lating the power requirements of a grain conveyor, recognized that the energy lost due to friction betwem solids and pipe wall should be accounted for in the energr balance, but states that no infornntion is available for estimating this. Belden and Kassel (3) analyzed the pressure drcp in vertical tubes in a manner similar to that of Vogt and White (37). Belden and Kassel verified their initial assumptions by transporting sand particles of various sizes in vertical pipes. Jennings (21) developed equations relating the acceleration of a particle to its limiting velocity in vertical transport. Dallavalle (10) presents an analysis of the air velocities required to support and carry particles of cats, wheat, and corn. He also presents a review of Cramp's work (9) relating the horizontal and vertical pressure drop due to the trans- portation of grain particles. Davis (ll and 12) developed equations which relate the air velocity required to lift and suspend particles of varying shape, size and density. Longhouse, Brown, Simone and Albright (25) attempted to adapt a pneunntic transporting method used by the chemical industry to farm grains. Although their period of study was short, it was stated that the fluidization process looked promising. The bulk of the literature can be summarized by the following statements: As previously mentioned, very little theoretical work has been canpletsd on the subject of solid particles in fluid suspension. The large majority of that available emnates from work with catalytic cracking system in the chemical industry. The bulk of the experimental data has been developed from the horizontal and vertical transporting of farm grains. No data, experimental or analytical, could be found on the subject of transportation in inclined pipes, or truly pneumatic tranSporta- tion of forages. THEORY The following primary symbols and subscripts apply to all equa- tions developed in this study. I . Primary «skvcsb'hws'mcc. RN symbols : dianeter of particle (feet) diameter of duct (feet) frictional head (feet of H20) frictional head (inches of H20) friction factor (dimensionless) density (#/ft .3) dispersed sclids' density (#/ft.3 of pipe) volume (feats) absolute viscosity (#/ft. sec.) velocity (ft./seo.) time (seconds) distance (feet). Reynolds number (dimensionless) pressure (#/ft.2) quantity or number ease of particle (# coma/ft.) length (feet) sclids' mass flow (#/ft.2sec.) constant of gravitational acceleration (ft ./sec.2) might (#) acceleration (ft./sec.z) lift force (3%) drag force (#) 69 I pipe angle from the horizontal (degrees) 0 I area (ft . )2 P I Q flow rate (ft.3/sec.) II. Subscriptss a - air D - duct ds - dispersed solids f. - solids friction factor sh - static head sf - solids friction s - solids p - particle The following theoretical analysis will use as its base the work accomplished by Pinkus (so) and Hariu and Holstad (20). Pinkus investi- gated the pressure drop in horizontal pipes due to the flow of solid catalysts in a pneunmtio system. Hariu and Mclstad investigated the same phenomenon in vertical pipes, but used a scmlewhat different theoretical approach. Both of these investigations developed fran work with catalytic- cracking systems in the chemical industry. Their interest was focused on particles of much smaller diameter than those encountered in agricultural [neuritic systems; however, the same type of theoretical analysis should apply in either case. Four basic eqmticns will be presented in this section. Three of drag hr cs (#) a"! I pipe angle from the horizontal (degrees) 0 I A - area (ft.)2 Q flow rate (ft.3/sec.) II. Subscriptss a - air D - duct ds - dispersed solids f. - solids friction factor sh - static head sf - solids friction s - solids p - particle The following theoretical analysis will we as its base the work accomplished by Pinkus (50) and Hariu and Related (20). Pinkus investi- gated the pressure drop in horizontal pipes due to the flow of solid catalysts in a pleunatio system. Hariu and Molstad investigated the same phenomenon in vertical pipes, but used a smewhat different theoretical .approach. Both of these investigations deve10ped from work with catalytic- eracking systems in the chemical industry. Their interest was focused on particles of much smaller diameter than those encountered in agricultural memtic systems; however, the same type of theoretical analysis should apply in either case. Pour basic equaticns will be presented in this section. Three of FD - drag force (#) 0 I pipe angle from the horizontal (degrees) A - area (ft.)2 Q - flow rate (ft.3/sec.) II. Subscript" a - air I) - duet ds - dispersed solids f. - solids friction factor sh - static head sf - solids friction s - solids p - particle The following theoretical analysis will use as its base the work accomplished by Pinkus (30) and Hariu and Molstad (20). Pinkue investi- gated the pressure drop in horizontal pipes due to the flow of solid catalysts in a pleunatic system. Hariu and Molstad investigated the same phenomenon in vertical pipes, but used a somewhat different theoretical approach. Both of these investigations developed fran work with catalytic- cracking systems in the chemical industry. Their interest was focused on particles of much snaller diameter than those encountered in agricultural pnelmatic systems; however, the same type of theoretical analysis should apply in either case. Tour basic eqmtials will be presented in this section. Three of them will be of practical use to the designer, while the other will be used only to obtain the solids' friction factor (f3). It is necessary to determine this constant since it appears as a variable in each of the other three expressions. These equations will later be proved or disproved by the experimental data obtained. "1‘.” will be experimentally determined from the following ox- pression: D [03 C AP (vs - v3)2 - 2 g vpl; Sin 8] (5) fs = 2 V ' P {OP vs A complete derivation of this constant is given in the Appendix under Section I. As can be seen from equation 5 the velocity of the solids is a very important parameter in the experimental determination of " 3". This can be determined from measurements of the mass flow rate (Gs) and the density of the dispersed solids (1398). The relationship which enables this calculation to be wade is as follows: Dimensionally the equation beeches: 2 ft. 3 lbs! ft. sec. sec. Ibo ft This expression will be used extensively throughout the analysis. The following equation will be used to predict the total pres- sure drop in a given length of pipe. CE} 10 . 2 AH _ fa vsLDGs GBLD51ne faLDva ’08 (6) 2Dg(‘° v [0 2138/00 320 8 H20 H2 The derivation of this equation is given in the Appendix under Section I. Assuming that the solids' friction factor (f3) has been determined experimentally, the only other unknown preventing the practical use of equation 6 is that of the velocity of the solids. Two expressions for "v." will be presented here. The derivation of these expressions will be found respectively in Sections II and III of the Appendix. The range over which each of these expressions is valid is shown by Figure I. This figure shows an experimental plot of "C” (drag coefficient) versus "RN" (Reynolds number) as presented by Dallavalle (10). In effect, this curve permits the force due to the air stream, exerted on a particle to be cal- culated for any given slip velocity. The two other curves sham are assumptions nade to derive the two expressions for the particle's velo- city. (hle assumes "C" as a constant equal to 0.44, while the other asslmes “C" as a function of "RN“ and equal to 0.4 +42. The range over which the assured curves approximte the experimentalngurves, and there- fore the range over which the assumptions are valid, is as follows: 1. Assuming "C" as a constant, the range of "RN" is between 103 and 104's. 2. Assuming "C" as a function of "RN" and equal to 0.4 cgg, the range of "RN" is from 100'5 to 104°25. N The latter case should encompass the entire range of velocities o3 m.m o.m m.~ o.~ m4 0; m5 082 8% 83 can 8H 9: 0.3 38 O o I 3.. hi $573 ”span obnso Hancosaucnxm on» we figoacfi 92 :85. .256 338 2a 83 0352 3 go aflegaoea acuongm new acosnz «3°ch was.» 85.2% no 230338 an 9°U'19I998 JO 1U919TJJ°°O I O.I+ 90 300* a. 90 '1'“ no. 3 3 sA"A)d 8°91 12 found in farm pneumatic conveying systems. The two expressions for the velocity of the particles are as follows: (1) Assuming "C" equals a constant: _ DmCAPVaZ-ngzsme] vs - ‘ (7) PaGApvaD Jagnfoacip (2gnsine fstT-ngzfsSine (2) Assuming "C" = f (RN) = O.h 59 RN - -2 C}; (8) 02-f022-h0301 The constants in equation 8 are: 0.2 AP ,4; rs Cl : -————————— —— -——- m g 2 D "C2'— .14 AP vapa 20 Apiaa m g m g d 0.2 P v2 20 4 v a a 03" AP AP 3 a —gSine m g m g d Since equation 7 is valid over only a small range of "RN", the use of the more general expression given by equation 8 is recommended. It is now possible for the engineer, using equations 6 and 8, to calculate the pressure drop in any straight section of pipe where steady state conditions prevail (acceleration of the particles equals zero) knowb ing only the design specifications. 13 APTmRATUS After the theoretical analysis was completed, it was necessary to construct a test apparatus which could be used to prove or disprove the equations derived. Since the individual measurements which must be made during a test cycle consume appreciable time, it was felt that a continu- ous system would have a distinct advantage over the type in which it was necessary to recharge the hcpper manually. It was also necessary to de- sign the system so that the test section could be adjusted to any angle between 0° and 90°. This was accomplished by placing a slip joint between two 90° elbows as shown in the layout of the test apparatus (Fig. 2). The pipe used throughout the system, with the exception of the 90° elbows, was four inch (outside diameter) aluminum irrigation pipe. This particular diameter was chosen for its ease of handling, low cost, and availability. Any diameter, within a reasonable working range, would fUnction equally well since this variable is included in the development of the pressure drcp equations. One possible source of error in the system is the variation in the friction factor which would be present between aluminum.tubing and the steel tubing, the latter being used in most actual pneumatic systems. This error is assumed to be negligible, since after each type of tubing becomes internally polished, the two friction factors will be very nearly equal. Even if there were an appreciable difference, the resulting error in the experimentally determined friction factor (f3) would be small. This is evident when the three subdivisions of the total pressure drop are exa- mined. As stated in the Theory Section of this report, these errors are: 1. That due to the air alone. 2. That due to the particles striking each other and the pipe wall. 3. That due to the solids' static head. r/mr! EQUILIY J‘Pfltffl 0. 07/2: " (7/4. PHEJJ‘URE TflPs' 177' £77677 5734770”. A 8’ 7 E m A risr Sicr/a/V P/ Var: “ 45007 729/: J0/N7' —— L SHUT-0” 647731 3.87570 res-r arenas/«J [ \ PR ~4- IN TER/Vfll (‘0 M - \fioppfg [a w 5350.47; Bu: 7/ 01V ENc/ N: Blah/6R —-— J “—— e , Q SflUf-OI’FG'ITI _ ’: ___ - 1 , " 3a x-zow CONTRO‘ 31/0! JUCHII' Mil/[El F5506}? 771/” Pt 47'! OR 1F] c: A942 (Os/Srfilrr/ozv It‘ll! file“ I: , \ 1‘76. 2 EXPERIMKNT/VZ PNEUMflf/C SYSTFM 051’” 7'0 MfflSl/FZE PRESS‘URE BRO/’5‘ 15 The first conponent can be determined for any type of system since, as was p-eviously mentioned, the problem of homogeneous flow has been thoroughly investigated. The third component does not depend upon any friction factor. The second part of the second conpment is the only source of error due to the use of a different tube material. The blower used with the system was of the low-pressure type with radial, forward-curved blades. While backward-curved blades would have improved the efficiency slightly, the forner type has two distinct advan- tages, these being: 1. A lower shaft speed for a given capacity. 2. Less variatim in air velocity if the resistance of the system is varied. The diameter of the fan was 20 inches. Its maximum capacity, in terms of static head, was 17 inches of water at a shaft speed of 2800 R.P.M. A variable speed electric motor in the three to five H.P. range would have been an ideal source of power for the blower. However, since this was not available, a portable 30 H.P. internal combustion engine was used. In an actual installatim, wl'ere variation in blower speed is not necessary, an electric motor would be the most practical power unit. The quantity of air flowing through the pipe was measured by a thin plate orifice placed in the system approximately two feet before the solids' inlet. This orifice constricted the pipe area by 19.4%. The physical dimensions of the orifice, as well as the orifice coefficient, were taken from reference 29. The laws applying to the flow of liquids through orifices hold only if the liquid is inconpressible. Therefore, 16 if the fluid flowing is air, some correction factor must be included in the orifice equation if the results are to be accurate. To determine the magnitude of this correction factor for this specific sitmtion, the assumption was mde that the orifice pressure differential would never exceed ten inches of water. This assumption proved overly sufficient when the actual testing began. This gives an absolute pressure ratio EL. 2 1100 equal to 0.975. The numerator of this fraction repre- Psents standan absolute pressure in inches of water. The coupressibility correction factor therefore, varies from 0.98, for a 0.00 inch pressure differential (Ref. #29). Since this factor was so nearly unity, it was neglected in the derivation of the orifice equation. The equation for the velocity of the air is as follows: 6529 04 ./Ah (1h) Where: v velocity-ft/seo. D pipe diameter - ft. h static head in inches of water 1 and 2 are, respectively, locations before and at the orifice. This equation was derived assuming an atmospheric pressure (1‘ 29.92 inches of Hg and a temperature of 50° Fahrenheit. For this specific situation, equation 13 further simplifies to: v = hh.25 Jan (15) This expression was used to ocnstruct the graph in Fig. 3. l7 0mg .oom\.sa auaooass use .0 A: .e «an om-e-a mm =~m.mm n chemmcam m com 0933989 vegan Amm .csmv cow.o pcsaosacmoo so . scam .mw.m . ea so comes 62a $24 s8 a q 338 mesons 03H 30 savouI m7 OH 18 As was mentioned earlier, it is essential that the velocity of the particles be known before the value of the solids' friction factor (f5) can be computed. There are two methods which can be used to deter- mine this value. The first, and perhaps the most obvious, would be to directly measure the velocity of scme particle within the pipe. The second method would be to indirectly obtain the velocity by measurement of the mass flow rate (Gs) and the density of the dispersed solids ([38), after which the velocity is computed using the following expression: V - G8 8 - ...— Pds This equation is more completely described in the Theory Section of this report. The first procedure considered involved the use of radioactive tracers. It was thought that if a few particles could be irradiated and named with the rest of the mass, their path through the pipe could be traced by a radiation-pickup instrument. If the time could be recorded for a given length of path, the velocity could in turn be computed. Howb ever, after discussing the instrumentation problem with Professor Mont- gomery of the Michigan State University Physics Department, it was decided that while the idea was theoretically feasible, it was financially imprac- tical. The next method considered involved the use of photography. The basic idea was as follows: A transparent tube, with an attached scale, was to be placed in the actual test section. Then as the particles moved through this section, a camera mounted approximately four feet away exposed a sheet of film for a predetermined time. The average length of 19 the streaks could be determined from the scale on the transparent tube. The exposure time would be recorded so the velocity could be determined by: vs _ length of streak shutter speed of camera There were two minor sources of error in this system. The first was caused by the possible variation in the depth of field. In other words, the particles which were being photographed could have been can one or the other extremes of the pipe wall (the scale was in the center) which would cause variati ms in the apparent lengths of the streaks. However, as the distance between the camera and objects increased, the error would decrease. The second source of error lies in changing the surface of the test section which would change its frictional characteristics. Beaver, this change would be relatively small as explained earlier in this section. A null test set-up shown in Fig. 4 was constructed to determine the feasibility of the nethod just described. . r— Particles enter here /0 -l[- '4 __ 4:: Camera T {Transparent tube 6 V‘ 4 O J i ch. T Fig. 4. Test set-up used to determine the solids' velocity by the photographic method. 20 A speed graphic camera with a focal-plane shutter was used to expose the film. The shutter speed was varied from 1/00 second to l/ZOO second. Five #2 photofloods were used as illumination. Photographs were taken with and wdthout a polarizing filter. The use of this filter re- duced glare, but also restricted the amount of light passing through the lens. Particles of beans and wheat were used in these tests. A small number of the individual particles of each type were painted black. This was done with the hope that perhaps the contrasting particle color would produce a well defined streak on the film. This idea proved false as is evident frcm Fig. 5. The first series of pictures were taken through a four-inch lucite tube using super panchro press type "B" film. With the photofloods illup ndnating the plastic tube, the particles were drcpped through the upper end, (approximately ten feet above the test section.) Streaks, due to both the natural and painted particles, were easily visible to the naked eye. Sixteen exposures were made with varying shutter speeds and light- ing arrangements. Also, since the reading observed on the light meter was measuring only the light around the exterior of the tube, and not that present on the interior, it was necessary to allow more light than the meter recommended. This amount was varied from the correct amount (on the meter) to the maximum allowable on the camera. Upon development, the negatives gave a perfect picture of every- thing outside the tube but absolutely nothing was visible on the inside. This indicated insufficient light was penetrating the tube wall. The reason for this was traced to the fact that plastics are excellent diffusers of light and therefore, while the outside of the tube was well illuminated, the light waves never reached the particles inside the tube in sufficient quantity to allow a picture to be taken. Fig. 5. Natural and painted particles of wheat falling through a 4" I.D. glass tube. Picture taken with Royal-Pan film at a shutter speed of 1/50 sec. and a lens opening of 5.6. 21 22 Before the second series of pictures were taken, a four inch glass tube was substituted for the plastic one and special high speed Royal-Pan film was used in the camera. The deveIOpment of these films proved that the lighting problem had been solved but in its place had appeared another. This problem is clearly evident in Fig. 5. With a large number of particles in the pipe it is impossible to distinguish betwmn individual streaks. Fig. 6 shows that if the density of particles is very sparse, the method gives ex- cellent results. This again suggests the possibility of attempting to distinguish a few particles frcsn the whole mass. A possible way of accomplishing this would be to paint a few particles with luminous paint and then expose the film in a dark media. This presented more instmmen- tation problems, however, and it was felt that too much time was being spent on this phase of the project. The two methods of measuring ”v." discussed thus far are that of _ radioactive tracers and photography. While neither of these methods were actually used, they both presented interesting possibilities. However, both have one comma: defect. It is impossible to accurately measure the average velocity of particles when the system is composed of particles which vary widely in their size range. This problem becomes serious when any type of, forage mterial is being transported through the pipe. This method would, however, work well for uniform size particles such as would be found in the pieumatic conveyance of farm grains. The method of masuring "v3" finally decided upon involved the use of the following relationship. As stated earlier in this sectim, it is: m a}! m“ Fig. 6. Natural colored particles of wheat falling through a h" I.D. glass tube. The particles are just entering the glass section as is indicated by the lines in the upper part of the photograph. Royal-Pan film was used at a shutter speed of 1/50 sec. and a lens opening of 1‘05. 23 With "G." known from initial cmditions, and "/35" determined from measurement, the velocity of the solids' can be calculated. The method used to measure the density of the solids in the pipe "’35" was as fol- lows: Two half-round, air-tight, spring-loaded, shut-off valves were placed in the actual test section. These valves, as they are located on the pipe, are shown in Fig. 7. The trigger mechanism of the valves is synchronized to allow the two gates to close instantaneously, thus block- ing off a section of the test pipe. An instant later another spring loaded valve stops the inflow of particles at the hopper. Now all that rennins is to remove the particles in the blocked portim of the pipe, weigh them, and divide by the volume of the blocked portim of pipe, thus giving ”/38". This system has a distinct advantage over the other two in that it is applicable to any system of particles , uniform or irregular, since it is not dependent upon any one particle but rather on the whole mass. Assuming the velocity measurement problem solved, the method of entering the particles into the air stream will be discussed. Three basic methods of introducing solid particles into pneumatic conveying pipes are in general use. These are: l. The injector feeder, or constricted area type, for low-pressure systems. 2. The auger-feeder for low to medium pressures. Since this type does not provide a canplete air seal, it is usually used in conjunction with an injector feeder. 3. The bucket-wheel feeder for high pressure systems. fig. 70 method by which each of the two half-round, spring-loaded, shut- off valves are attached to the test pipe. 25 uh 26 : E , <§§§K l , \fil/j E ——*- AIR 6‘07. CONS TRICTIOM g I , SFCTION M F/é‘. 8 556770” 19*” 1‘76. 9 A —+- am 6'6 :5 mus-7216770 IV { 55677019! 4-» FIG. ,0 Son: 3' ., mu [6 7'0»? ram: ass-a 26 SfCT/ON M F76. 8 $56770” flv? “FIG. 9 _————______—_——————————_____——_— A —* AIR 6'8 2 calvsvw/c 770 IV ; SEC7'IOIV l-fl FIG: ,0 5"“! 30",: INJEC 70f? . FOR/W5 U550 26 W E ——"/7//'? 5‘07. CONSTR/C‘TIOIV {1 A , SFCT/ON M ms. 8 \ BLOW'BHCH APE-37.01%!- ~3—b-I7‘i ‘V" ‘v' b A \Q“ 5'9 7. CONSTR/C TION g . SFCf/ON A-n FIG. 9 M “g” 1’ ——*- 4m ‘2 6‘8 2 cams-775v: 770 IV { SFCTION l-fl F76 ,0 5‘6“! 3'"=/' MAI/.76 70f? . FORMS (ASE-U 27 An injector type feeder was first built into the test system. The construction and operation of this feeder is very simple. It operates on the principle that an increase in velocity will cause a decrease in pressure. The velocity increase is accomplished by having a constriction in the pipe line Just before the feed inlet which causes the static line pressure to be momentarily transformed into velocity head. This allows the particles to enter the air stream without being blown back by the escaping air. Figs. 8, 9 and 10 show the systems which were used on the test set up. Fer reasons which will be explained later, none of these set-ups were successful. An.exeellent discussion of injector feeders is given by Segler in Ref. 32. One inherent disadvantage of this type of system is the energy loss due to the transformation of energy from static head to velocity head and subsequently back to static head. This loss varies wdth the shape of the constriction, but values given by segler list a 65% loss for an 80% constriction down to a 26% loss for a 50% constriction. (based on the fact that the loss would be m for 0% constriction.) The first type of injector used on the test fixture is shown in Fig. 8. The reduction in area was insufficient, thus allowing cmsid- erable blowback and intermittent particle flow. The next type shown in Fig. 9 provided a greater constriction and also had a blowback aperture. The blcwback aperture was installed to allow the air to escape without passing through the incoming particles. This sytem worked much better than the first, but still the flow of particles was intermittent. 28 Next, an attempt was made to prevent blow back by increasing the pipe constriction to 68% as sham in Fig. 10. When tested this was found to prevent blow back but the energy loss was so great that there was in- sufficient energy remaining beyond the inlet to carry the particles. This could have been remdied by using a positive displacement blower which would produce higher static pressures than were possible with the exist- ing blower. However, such a blower was not available so the entire idea of an injector feeder was discarded. It is felt that the principal reason for the failure of the injec- tor system was the size of pipe used. Segler (32) recommends the injector feeder be used cm systems where the static pressure is below 10 inches of water and the pipe size is between 6 and 12 inches. The test apparatus met the first requirement, but not the secmd. The injector feed has two serious drawbacks when being used in a test apparatus. First, even if the correct pipe constriction is found for a given capacity and pipe length, this will not insure that it would be correct if the two conditions were changed. For ample, if no blow back were occurring for a given capacity, and it was decided to increase this capacity, which would increase the resistance, blow back would occur. It would also occur if any change were introduced which would increase the resistance of the system. The quantity of air blown back or drawn in would undoubtedly be insignificant in actual practice but in a test fixture where the volume of air is an important parameter in the theory, it could introduce serious error. If this system had been used, this undesired air movement would have had to have been measured. The system finally decided upon was a bucket wheel feeder. This 29 works on the revolving-door principle of always offering an air tight seal between two surfaces, independent of its angular location. A dia- gram of the bucket wheel used on the test apparatus is shown in Fig. 11 The power for this unit was a 1/3 H.P. electric motor driven through a 40 to l worm gear reduction unit. A picture of the set-up is shown in Fig. 12. The aerodynamic efficiency of this system approaches 100 per cent. Segler (32) reconrrends the use of bucket wheel feeders in medium pressure systems where the static pressure is below 40 inches of water and the pipe diameter is between 4 and 8 inches. The test apparatus falls within both of these limits. The procedure used to determine the various pressure differentials will be explained in the following discussion. Static pressure taps were located at four foot intervals along the test section as is shown in the layout drawing (Fig. 2). As des- cribed in the review of literature, other investigators have obtained false data by including acceleration losses in the steady state measure- nents. It is felt that the possibility of introducing this error is completely eliminated by having several stations along the test section instead of the customary one or two. “3th the pressure taps as shown, the type of flow is imediately evident. If steady state conditions prevail, each of the four stations will register equal pressure differ- entials. However, if the particles are still undergoing acceleration the pressure differential recorded at each station will becane successively smaller as the particle acceleration diminishes, until constant readings are recorded when the particle acceleration is zero. If was found neces- sary to install an extra eight feet of pipe (Fig. 2) after the first SHIV/’7' S'Pl'E'D - 40 RPM .51 [0! gr “sit-2.7.12.1 JPRING ’ """""" "”11 1 0405.0 mar ”W" 1 g--.“ P‘SSA‘f ; §‘:.“"*—‘- - 'k\\\\\" . ?‘ -""-“- -.- - —-.——_—-— _ SECTION 4-4 some .7 ‘5- / ’ FIG. // BUCKET WHEEL FEFflFfi’ Fig. 12. Drive used to transmit the power output of a 1/3 H.1=.. 1750 11.9.35. electric motor to the input shaft of the bucket wheel feeder. 31 32 180 degree bend to allow the particles to reaccelerate before they entered the test section. Even with this additional pipe, some accel- eration could still be recorded at the first two stations. The stations Within the test section are shown in Fig. 13. L 20. A |'~Statj_on h +Station 3 + Station 2 +Station 1 “l H 1 n J 4——Flow IO-Shut off valves in these 1 planes Fig. 13. Location of the individual stations within the test section. Three individual pressure taps were made at the junction of each station. The actual hole through the pipe wall was 0.03125 inches in diameter. Each of these individual taps were in turn connected to a dampening chamber from which one outlet led to one side of an inclined well type manometer. A photgraph of one of the five systems of taps is shown Fig. 14. Extreme care was exercised in removing the burr from the inside of the pipe after the drilling operation. Had any projections remained around the pressure tap, the internal static head would have been locally converted to velocity head, therefore giving incorrect results. Two nanometers were used, in! conjunction with the cmtrol panel, shown in Fig. 15 to record all pressure differentials. One was used con-t tinuously to register the orifice pressure differential while the other was used to individually indicate the various test station differentials. The control panel made this last set of masurements possible with one manometer by connecting the outlets to successive test stations. It was found that the manometer reading from the orifice flucuated fig. 14e me of the five systems of pressm-e taps couplets with damping chamber. 33 “Se 150 Cmtrol panel used to record all pressure differentials. The individual statims of the test section are shown on cor- responding panel taps. 34 35 over a small range. These fluctuations did not follow a harmonious pat- tern but rather were quick, uneven, movements. This situation was remedied by installing a damper in the line extending from each outlet of the manometer. These dampers were steel cylinders approximately eight inches long and four inches in diameter with one and blocked and the other covered by'a thin sheet of rubber. Now as the increased pres— sure, due to a small fluctuation, moved into the damping chamber, the ‘ excess energy was absorbed in expanding the rubber sheet rather than moving the column of fluid in the manometer tube. This concludes the discussion of the test apparatus. To this point, the construction has been completely described, including dis- cussion, and dimensions of the pertinent component parts. 36 TEST PROCEDURE ghpice of material Thus far, the theoretical analysis has been completed and the test apparatus which was used to prove or diSprove the initial assumptions has been discussed. The next logical step is to explain the test procedure which was followed during the determination of the experimental results. Assuming that the theory developed was valid, the ultimate objec- tive of this research was to determine friction factors for various grains and solids. It was decided that a complete series of tests should be run on one type of particle before an attempt was made to determine friction factors for other solids. By doing this, the complete theoret- ical analysis was checked for one type of particle by experimental re- sults. If at any of the intermediate steps the experimental results had shown a substantial and consistent variation from the theoretical re- sults, the initial assumptions, and thus the theoretical analysis would have had to have been assumed incorrect. If this situation had devel- Oped, there would have been no point in continuing with the experimental procedure for that, or for any other type of solid, until adjustment was made in the initial assumptions. If this initial test had proved succes- ful, there was still no guarantee that all other types of particles could be examined in a similar manner, since one of the initial assumptions was that "C", the drag coefficient, was based on the shape of the parti- cle. This could have meant that the theoretical analysis would hold for wheat where the particles are relatively uniform.and yet not apply to the flow of forages, where the particles not only vary in uniformity but also in density. 37 The material finally chosen for this initial test was soft white winter wheat. The reasons for this choice are as follows: 1. Availability of the material. 2. Uniformity of the material. 3. Practical use to which data obtained could be put. h. Ease with which the particles could be injected into the air stream. 5. Stability of the material with successive trips through the blower circuit. Before the wheat was introduced into the test circuit, it was thoroughly cleaned in a fanning mill. Even with a stable item such as wheat, difficulty in keeping the material free from cracked residue was encountered after it had been blown through the circuit several times. It was felt that the cracking which was observed emanated.from the fol- lowing sources: 1. Binding between the bucketdwheel feeder wall and the individ- ual paddles. 2. Impact with the pipe wall at elbows, etc. 3. Impact with other stationary particles when the grain was blown back into the inlet hopper. In order to maintain consistent and accurate test results, the wheat was removed from the hopper and again run through the fanning mill when the number of cracked particles appeared to be approximately five per cent. This limit was usually reached after approximately three hours of continuous testing. After the wheat had been cleaned three times it was completely discarded and a new sample was introduced. These samples were all taken from one bin.which contained the harvest of one field. 38 This insured that the physical preperties of the wheat would remain the same from sample to sample. The amount of wheat in the hopper for any given test varied from 100 pounds to 125 pounds, only a fraction of this being in the actual test circuit at any given time. ghysicalgprqperties of the test material Since the pressure drop equation developed involved, as variables, the physical properties of the material being conveyed, it was necessary to experimentally determine these properties before the theoretical equa- tions could be checked by the experimental pressure drape obtained. The two basic quantities needed were the average density and the average vol- ume of the individual wheat particles. From these two quantities, the remaining physical properties could be calculated by assuming the shape of each individual particle to be that of a Sphere. This assumption is compatible with the curve chosen to represent the drag coefficient(C) as a function of Reynolds' number for the particles. The actual method used to measure these properties was that of water displacement. Three individual tests were run and the average of these taken as the final results. The wheat for each of these tests was obtained by random sampling from the test hopper. The procedure followed during each of these tests was as follows: 1. Count out 600 wheat kernels. 2. weigh the kernels. 3. Place them in a 250 milliliter graduate filled with approxi- mately 75 milliliters of water at 600 F. h. Stir to release all entrapped air. 5. Observe the volume of water displaced. 39 6. From this data, and by assuming the particles to be spheres, the density, volume per particle, projected area per particle and the weight per particle could be calculated. Values of these properties will be given later. The use of this approximate method for determining the density of wheat presents two possible sources of error. The first could be caused by the particles absorbing some of the fluid in which they were immersed. This error was kept to a minimum in this experiment by recording the water diaplaced as soon as possible after the wheat had entered the graduate. The second possible source of error could have been due to confined air in the creases and in the brush of the kernels. This confined air would cause more water to be displaced which would result in a lower density. This error was kept to a minimum by continual agitation of the particles as they were being introduced into the graduate. The average value obtained for the density of soft white winter wheat was 83.h #/ft.3. This agreed very well with Zink's (hO) results which gave a value of 82.h #/ft.3 for the same type of wheat. It was felt that the small variation was more likely to have been due to actual physical differences between the two samples tested rather than errors due to experimental technique. Particle flow regulation The first method used to control the flow of particles from the hopper into the air stream was a simple slide valve. This valve is shown in Fig. 11 and is located just below the hopper. Trouble was en- countered with this system when it was desired to obtain a constant flow rate with varying air velocities. This irregular flow was a result of the wheat being metered by’a long narrow slot, since under normal con- ho ditions the slide valve was only about one-fourth open. This type of sys- tem also had the disadvantage of making it almost impossible to duplicate a given flow rate, since only a small movement of the slide caused a large variation in flow rate. The above problem was solved by making a set of five plates with circular inlets of various diameters. These plates are illustrated in Fig. 16. Any one of these could be conveniently inserted in the slot which the slide valve had occupied with the assurance that any of the five flow rates could be easily duplicated at any future time. The five flow-regulating plates were all calibrated before the h0pper was installed on the test apparatus. The plates were calibrated by mounting the hopper approximately three feet above the ground and catching the outflow for a one minute period. Four of these one minute tests were run on each of the five plates and the results averaged to obtain the final calibration values shown in Fig. 16. After the plates were calibrated and the hopper installed on the test apparatus, it was still necessary to check the flow rate of the various plates while the system was in operation and to compare these with the values obtained in the previous calibration test. This was accomplished by inserting a flow-deflecting plate in the main pipe line, thus diverting the flow from the pipe into a separate collector before it re-entered the hopper. The weight of material in the collector was recorded for a given unit of time, thus giving the flow rate. This value should compare with the previous calibrations, however, it did not. Also, it was noted that the deviation became larger as the flow rate in- creased. This observation led to the following hypothesis. As the in- dividual buckets of the bucket wheel feeder moved past the happer inlet 57.82 you,” 74_4() ./m. Fig. 16. Calibrated plates used to regulate the solid flow rate. 142 passage, they released a packet of air which had been picked up as they discharged their load into the pipe system. Also a small amount of air ‘was observed to lead past the bucket wheel paddles. The only outlet for this air was the hole in the calibrated plate through which the wheat particles were flowing. This, of course, would decrease the flow through the calibrated plate. The reason for the larger diviation as the flow rate increased was that the static head within the pipe also increased, thus increasing the amount of air being forced through the calibrated plate. The above hypothesis was proved correct when a static pressure tap was inserted in the hopper inlet as is shown in Fig. 17. The ma- nometer recorded fluctuating pressures up to six inches of water with the paddle wheel operating. However, with the bucket wheel injector shut off, but with the blower still running, and with an Obstruction in the pipe line to maintain a high static pressure, the manometer recorded only a small constant static pressure, which ranged up to approximately one inch of water. To correct the above situation, it was found necessary to pro- vide a vent in the top of the bucket wheel feeder which would allow the entrapped air to excape before it entered the inlet passage. Two other vents were also provided in the inlet passage to allow for any addition- a1 air leakage. Both of the vents are shown in Fig. 17. With these outlets installed, the manometer reading did not go above 0.2 inches of water for any of the five flow rates. Also, when the actual flow rates were again checked, they agreed with the values obtained in the first calibration runs. Fig. 17. Bucket wheel feeder showing pressure tap and air vents used to obtain constant flow rates. ’43 mechanics of test procedure As was previously mentioned, it was decided to run a complete series of tests on wheat before considering other types of particles. The four principal variables in this test were: 1. Flow rate. 2. Pipe diameter. 3. Pipe inclination. h. Air velocity. The first variable was fixed by the size and number of the cal- ibrated plates. The second was fixed in this experiment at 3.89 inches for the inside diameter. Before the material presented in this report can be assumed generally correct, the effect of varying pipe diameter on the solids' friction factor (f8) must be determined. The effect of the third variable was inepected at pipe angles of 0°, 32.730, 62.500, and 90.000. Fig. 18 and Fig. 19 illustrate the test apparatus at pipe inclinations of 62.500 and 90.000. The air velocity was varied over as ‘wide a range as was possible with the blower unit used. The minimum air velocitwaas governed by the point at which the particles ceased to be carried by the air stream. This velocity was approximately 65 feet per second. The maximum air velocity was governed by the output of the blower. This was approximately 110 feet per second. After the apparatus had been constructed, it was necessary to run the machine until the internal surface of the pipe became sufficiently polished to insure that the pressure drop would be independent of time for any set of conditions. This point was reached after approximately six hours of continuous operation at the maximum.possible throughput. “ ‘\ " "flip“: .JJ‘Hi F'W'" '3'" 'aavw ._t‘ Us 9.» 2'; L —‘ < . . l l, .l n‘l. [Iii] , 1" ‘:v"',:r '_ an '\ H E: kI 1 ‘[‘.|'; ‘,-. 2'; 2'1; gm j‘ ‘v :1 I Fig. 18. Test apparatus'with a pipe inclination of 62,5 . 115 Fig. 19. Test apparatus with a pipe inclination of 90.000. ‘ 1:6 h? The next step was to determine the static pressure drOp, per foot of pipe, as a function of velocity. This was necessary since a method was de- sired by which pressure drop due to the solids could be differentiated from the total drcp which the manometers would register under actual operating conditions.' Now by assuming that the pressure drop due to the air alone remains constant for a given velocity, with or without parti- cles in the pipe, it is possible to obtain the drop due to the solids alone. This was obtained by subtracting the air drOp from the total drop observed under actual operating conditions.‘ The overall picture of the series of tests on wheat in a 3.89" I.D. pipe, which have been completed to date, is as follows: 1. At a pipe angle of 0°, five constant throughputs were tested. At each of these constant throughputs, the air velocity was varied from approximately 65 feet per second to 110 feet per second, and the correSponding pressure drop recorded. 2. At a pipe angle of 32.730, four constant throughputs were tested with the air velocity varying as at a pipe angle of 0°. 3. At a pipe angle of 62.500, four constant throughputs were tested with the air velocity varying as at a pipe angle of 0°. h. At a pipe angle of 90.000, four constant throughputs were tested'with the air velocity varying as at a pipe angle of 0°. The actual procedure followed during one of the five tests, with the pipe at an angle of 0°, was as follows: l. 2. 3. b. S. h8 The calibrated plate, which would give the desired flow rate, was inserted through the slide valve opening. Next, the spring loaded shut off gates, one of which is shown in Fig. 7, were cocked into firing position. The blower and bucket wheel feeder were then put into motion. At this point, air was blowing through the test circuit but no wheat was being conveyed. To introduce wheat particles into the bucket wheel feeder, and thus into the air stream, the spring loaded shut off gate shown in Fig. 11 was cocked. The blower speed was then adjusted to provide the minimum air velocity required to carry the particles. The pressure drop was checked at each of the four stations shown in Fig. 13. It was found that the pressure drop at station 1 and that at station 3 was less than that at station 2, but the drop at station 3 and h were equal. This indi- cated that the particles were still accelerating as they passed through station 1, but reached their terminal velocity at some point along station 2, thus giving constant pressure drops in stations 3 and h. This situation prevailed at all throughputs, pipe angles, and air velocities with the exe ception of the largest throughput at a pipe angle of 90°. In this one case, the particles did not reach their terminal ve- locity until some point along station 3. ‘With the exception of the latter situation, it was possible to measure the com- bined pressure drop over stations 3 and h, thus giving a 7. 9. 10. h9 larger drcp which could be measured more accurately. This drop could be measured to 0.01 of an inch of water by the in- clined manometer shown in Fig. 15. As soon as possible after the pressure drop for the combined station 3 plus h was recorded, the reading on the manometer connected to the thin plate orifice was recorded. Since a larger range was needed on this measurement, it was necessary to use the manometer tube in an upright position as is shown in Fig. 15. This caused a decrease in the sensitivity of the instrument which prevented variations of less than 0.10 inches of water from being detected. This is the point in the procedure at which a check could be made on the solid flow rate if it were desired to do so. This check is made by inserting a deflecting plate in the main pipe line and weighing the throughput for a given unit of time. The next step in the procedure was to pull the trip releasing the two shut off gates, thus trapping a sample of wheat in the eight foot section of the pipe. Immediately after releasing these gates, the trip on the spring loaded inlet passage gate was released, thus stopping the in- flow of particles to the bucket wheel feeder. It was then necessary to remove the entrapped sample of wheat which represented the density of the diSpersed solids. This entrapped wheat was removed by a special vacuum device, through an air tight trap within the blocked off section of pipe. This trap, in a closed position, is visible in Fig. 7. Then the weight of the entrapped wheat was recorded to the nearest 0.01 of a gram. From this it was possible to calculate the density of the diapersed solids, and thus the average velocity of the individual wheat particles. This ends one complete test cycle for one air velocity. At this point the air velocity was then increased and another test cycle was completed. Approximately 30 of these cycles were completed for each of the various flow rates at each pipe inclination. Possible sources of error Two possible sources of error were investigated at this point. The first is due to the compressibility of the air within the pipe line. If appreciable compression did take place, it would mean that the density of the diapersed solids would not be independent of pipe length, thus steady state conditions would never prevail. If this condition existed, the experimental friction factor (f3) could not be assumed generally correct. This condition was investigated assuming a pressure drop of 0.10 of an inch of water per foot of pipe for 150 feet of pipe. This gave a total head loss of 15 inches of water. It is shown in the.Appendix under Section V that due to the compressibility of the air at this head differential, the velocity of the air at point 2, 150 feet from point 1, will be 0.966 of that at point 1. Even with this large head differential, which would probably never be reached in a farm.pneumatic system, the velocity variation is insignificant. The previous statement holds since this loss is only one of three losses in the entire system, and the sum of these three can rarely go above 15 inches of water without exceeding the capacity of the average blower. DL The second possible source of error was introduced when the air vents were installed in the bucket wheel feeder to insure a uniform flow rate at all air velocities. It might then have been argued that an appreciable air loss would result from these vents. If this air loss were significant, it would have to be accounted for in the calculation of the experimental friction factor (fs)’ By assuming the maximum pos- sible loss to be 11.71 ft.3/min. for an air flow of 500 ft.3/min., the percentage loss is 2.25. The validity of these assumptions is proved in the Appendix under Section VI. This 2.25 per cent loss can be considered insignificant when the accuracy of the orifice coefficient is considered. 52 EXPERIMENTAL RESULTS Physical properties of particles tested The method employed to experimentally determine the physical properties of the soft white winter wheat used in these tests was ex! plained in the previous section. The averages of the results obtained are as follows: Density per particle " p" = 83.h lb/ft.3 Volume per particle "V " = 0.993 x 10-6 ft.3 Projected area per pariicle "AP" = 120.5 x 10"6 ft.2 Diameter of particle "d" = 12.39 x 10'.3 ft. -6 weight per particle "W?" 82.6 x 10 1b. Equation 6 and 7 can be considerably simplified by the introduction of these constants. These equations in simplified form, will be given in the next section. Pressure drop results The first actual test which was run, after the pipe had been internally polished, was conducted to determine the pressure drop per foot of pipe when air alone was being conveyed. The results of this test are shown in Fig. 20. The curve shown is actually an average of those obtained for varying atmospheric conditions. A check was run on this curve at the beginning of each day's testing and if deviation was observed, this was taken into account in the analysis of the results. For any given atmospheric condition, the curve resulting was offset a consistent amount from the average curve shown in Fig. 20. The dotted curves in this figure illustrate the maximum and minimum deviation from the average curve. 53 .oom ow .wae .pe auaeeaes sa< -eoo eaeeeeuoapa meamquee as can soapaasen sseaxwxul;l.|.ul.lu assoc owuuosd 00 03. on. CM8JHIN «093 a: n .e .H 25 aeoa< ua< see cease ensued.» aaa..suu.> ease. igneous— 35309 .. alga b JIV sun on Ammo enq ‘edxd JG 4005 Jed ‘doaq eansseag 08%?” .38 ease 22 0w ow .mae ow neoo cauenemoEpd wsewcwno o» 050 soapua>ea sseaxwxul:l.nnul.|n o>hdo omwho>¢ .o .3 .a. am Ed. .33 amen ... .n .H «9.8 esod< add you o>pso hpeooam> HH< monum> dose onsumonm poeHEAOpoQ haawpsosaamaxm ”Li/WI WV 5 11v sun 04 ATuo enq ‘edtd JO 1003 led ‘doxq GJHSSGJd Sh It was rufl;possible to obtain the pressure drcps, due only to the solid phase, by subtracting the drop, due to air alone, as obtained in Fig. 20, from the total drop observed for a given flow rate and air ve- locity. At the beginning of the tests, it was hoped that a graph of par- ticle velocity versus air velocity could be obtained. From this data and by use of equation 5, a graph of solids' friction factor (f8) versus air velocity could be obtained. Then by assuming "f8" remained constant for wheat being conveyed at any flow rate, pipe diameter, or pipe incli- nation, the pressure drOp, for any actual condition, could be calculated by the use of equation 6. These calculated values could then be checked by the actual observed pressure drops, thus proving, or disproving, the validity of the initial assumptions leading to equations 5, 6, and 8. It can be seen from Fig. 21 that the data obtained from the weight of the entrapped solids, which permitted the density of the dis- persed solids, and their solids' velocity, to be calculated, proved to be very inaccurate. There are two possible sources of error which might lead to in- consistent as well as consistent variation in the data obtained. The inconsistent error, which is very evident in Fig. 21, could have been due to the very small quantities of wheat being trapped between the two shut off gates. This weight ran from a low of 18 grams, for low through- puts and high air velocities, to a high of 183 grams, for high through- puts and low air velocities. The consistent error which would not be evident from.Fig. 21 could have been caused by one of the shut off gates consistently closing before the other. Both of these errors could have 55 He .eaa .oem\.pe assesses sea ow . 14 < # 4.4 1 a4 a 4« Join.élw-luwwr __ ”Ink. ..v. :QI...1 «.1.%LTM.+L.¢.\O+¢. Haht it... . 4» ...K...T.1.H.Ianl.Ha.ira...+.a ..W... 1..-...t eel. 7.3+... ,. A A 5? To 4.1)?«L ITI..79 r 41*.0...4.+.,$ .. .. . a . . rP41. v. ‘ . sir... . Ti 4 0 LI i... . .91. V v . 04.74 .055'. 1§l0.¢1i. 96 ..-Ol Y‘ 9.0 .lvl... 0 .I ..V,Y~.s1 1. . . olvfilxtrj .. c ' ...... r..¥i v0.9 4 #1 TQ.......Y....§.1T,§..Q.T YY.. .. 4,01 1.41... r... T? 1%.- T11...¢.O. -i.» . Jelli4.» .tha 4 ._ ..1 a _ ...< . 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It appears that at least 25 feet of pipe between the shut off gates would be necessary to insure accurate results. Rather than rebuilding the test apparatus, another method was devised to determine the graph of solids' velocity versus particle velocity. This method is explained in the following paragraph. The experimental pressure drops were plotted against air veloc- ity on a graph such as Fig. 25. Next a line of best fit was drawn through each group of points representing one of the five throughputs. (These are not the dotted lines shown in the figure.) From each of the five experimentally determined curves, it was possible to calculate a‘ curve of air velocity versus particle velocity. This curve was comp patible with the experimentally determined points for that one through— put. Theoretically, the five pressure drop versus air velocity curves should transpose into one identical curve on the graph of air velocity versus particle velocity. The method of calculating the latter curve from the former is as follows: Equation 6 was solved for "£8” and set equal to equation 5, thus elinimating ”f8" as a parameter. For any given air velocity and throughput, the only variables left in the above equation were the solids' velocity (v8) and the coefficient of resis- tance (C). Now O.h -th/79.7 (va - vs) could be substituted for “C", thus leaving a simple quadratic equation in one unknown, "v8”. The five curves, along with the proposed average curve, are shown in Fig. 22. It should be noticed that the average air velocity versus particle velocity curve agrees reasonably well with the experimental points in Fig. 21. There is, however, a consistent offset which may have been due to uneven closing of the shut off gates as explained earlier. 57 «w .mam .oom\.pm saaooao> and owd OHH OOH om cm on o>hoo emano>< oomOQOHm II.I.II I: .. Mm . mm : wo.am = mo.ms = No.5m .caz\.ng og.a~ no>hoo oocwe uhmuoa haaapcoewuogxm .o .3 .e “an om-m~nm «mean oo.o n oamaq oaum 2mm.m H .n .H mafia enema easemenm umphoano pan ea oopaasonuo u hwaooaeb ua< usages hyaoonos.naoaou¢m O m 0 '093/‘13 Ahtooten °I°T¢J‘d O 00 58 It is now possible by using Fig. 22 and equation 5 to calculate a curve representing "fan as a function of the air velocity. This curve is shown in Fig. 23. It is valid for any throughput, pipe angle, or air velocity. This curve is one of the most important results of the re- search since it makes it possible to predict the pressure loss for any pipe angle, throughput, or air velocity. The validity of the curve will be tested by calculating the pressure drop for various pipe inclinations and then comparing these with the experimentally determined pressure drops.- The first step in the calculation of the pressure drop versus air velocity curve from Fig. 23 was to calculate the velocity of the particles at various pipe inclinations. A comparison of the calculated curves for particle velocity versus air velocity at each pipe incli- nation is shown in Fig. 2b. These curves were calculated from equation 8. As would be expected, the rate of change of "v8" with respect to "9" decreases as "9" approaches 90°. The curves of Fig. 2h, along with equation 6, were next used to calculate the curves of pressure drops versus air velocity which are represented in Figs. 25, 26, 27, and 28. 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IIIIIIO 4:36.. no.3... . .hIat Gutiflbio Ofltgu BUb‘Jq-OJCD >JJ‘P.UI.CU$IU . INDIllfi 'Holdv 1' 0 do 01 Q. o o .10, o / 'lllltll O o. l O I 0...“. leIJ’V-h // . . . . .l../r JV Io. 0. con 0 o 1/r/ A I"" 0 0 V0 0. O T / d ’I’I f C t. O . ’lg a on Ill] 0 r . II Ir h 7' / . 1,5,, I j A/ J H! 1 [...-III I + I l/ V. I o n“ ’1’] I f/ g [ILr/ I / I / / ;. X .2 / / g I oi... £- / / .3 n . .... It / w Lu. ..ICTQ "UP: A g 00.0. o I..." I.‘ 5.033 3.4 3:: / :2 030. lb Oh 30.3.... 258-... n W 'urm 'u (olomov dOIO mu It", onoo mu o1 A1IO 3M '13 nu 'I' (01001?!) mo um rum onoo nu o4 Id“ ‘0 1001 IN 00“ Ilflfllld 3“!” 100‘ UN.“IO 3800.184 Ammo 63 The first point which warrants discussion is the degree of accu— racy with which the theoretical curves, shown in Figs. 25, 26, 27, and 28, match the experimentally determined points. As was previously men- tioned, the experimental points in Fig. 25 were used as a basis for de- termining the solids' friction factor (f8) which was in turn used to calculate the remaining curves for various pipe inclinations. For this reason, Fig. 25 can not be used as a basis for comparison. Also it should be noted that five throughputs were analyzed in Fig. 25, but that only four were considered in the remaining three figures. The reason for this is as follows: With a blower of the type used on the test apparatus, which is similar to ones used in actual practice, the throughput is limited by the pressure drop within the pipe line. It will be noticed that as the pipe angle was increased, the pressure drcp per foot of pipe increased rapidly. ‘While the blower could handle 7b.h0 lb./min. with the pipe in a horizontal position, it could not sup- ply the additional energy needed when the pipe angle was increased. Thus, when a throughput of 7h.h0 lb./min. was attempted, at any angle other than 0°, very inconsistent pressure drop readings were recorded, indicating intermittent particle flow. For this reason, these results were not recorded. Also, it will be noticed that the velocity range possible with the blower used becomes smaller as the throughput increa- ses. The experimental points in Figs. 26, 27, and 28 agree reasonably well with the calculated curves. The largest deviation occured in Fig. 28, with a throughput of 57.82 lb./min. As the velocity was de- creased from 100 ft./sec. to 90 ft./ sec., the experimental points fell 6h directly on the curve, but with a further decrease to 70 ft./sec., the points failed to follow the changing slope of the theoretical curve. This one test was duplicated five times with similar results in each case. The maximum deviation of these points from.the theoretical curve was 9.1 per cent, but since this deviation was not evident at the other three throughputs, it was neglected. By inepection of equation 6, it can be seen that the static head component of pressure drop varies from zero for horizontal pipes to a maximum for vertical pipes. This same phenomenon is evident in Figs. 25, 26, 27, and 28. For a change in pipe angle from O0 to 90°, there is an accompanying increase in the pressure drop, for a constant throughput, of over 100 per cent. There is a drcp in particle velocity of approx- imately 20 per cent over this same range; thus it can be argued that the drop due to the friction of the solid phase could not account for the increase in pressure drop. Since the drop due to the air friction does not change for a given velocity, the only other component which could have increased was the drcp due to the solids' static head. This is analogous to water flowing through a pipe line. Neglecting fluid friction, the static head is zero if the pipe is horizontal and in- creases as a function of the sine of "£9" as the inclination increases. In a pneumatic conveying system, the total increase in static head is composed of two components. The first is due to the phenonenon men- tioned above. The second is common only to systems which have solid particles suspended in a fluid of low specific gravity, In such a system, as the pipe angle increases, the velocity of the particles de- crease. This decrease in velocity causes the density of the dispersed 65 solids to increase, thus increasing the static head. This is illustrated in Fig. 33. It should be understood that even though the curve repre- senting a variable particle velocity seems to have a greater effect on "(3%" than the curve representing pipe inclination, such is not the case. While the curves in Fig. 33 are illustrative, they do not represent an actual situation. If a pipe were varied from 00 to 90°, thus transver- sing the entire pipe inclination curve, the particle velocity would de- crease, but only over a small portion of the particle velocity curve. Thus the direct increase in pipe inclination accounts for the largest part of the increase in the density of the diSpersed solids. The continual decrease in the slope of the curve, from a pipe angle of 00 to 90° in Figs. 25, 26, 27, and 28, is also due to the static head component of pressure loss. At a pipe angle of 0°, the pressure loss and air velocity possess a linear relationship, which is compatible with the theory developed. As the pipe angle increases, the pressure loss increases at a faster rate for low air velocities than it does for high air velocities. Fig. 3h represents the two components of pressure loss which, when added, give the second curve from the t0p, represented in Fig. 28. It can be seen from this figure that the static head component of the total pressure drop due to the solids is much larger at low air velocities. The reason for this is as follows: For a given throughput, the density of the particles within the pipe (Fae) 18 directly related to the air velocity. At low air velocities, the density of the dispersed solids would be high. For high air velocities, the opposite would be true. This is represented graphically in Fig. 3h. Since the static head loss is directly proportional to the weight of n mm .mwe case so m.se\a A,p V meadow steepness he apnmeen (>6 .0 0.0 m.o .... podnwsoé n cams on m oanuw§> b .0 .3. 0H. «hm omuqduo “ovum :mwem u on eH 09E MS. emu 0 5. 39.36 has: mm as consanna> :00 Moo N00 H00 000 .eazxa me.ms pseewaoeee oom\.pm 05 n sufioeao> nfi< pageants me soaafieq (e) noun-{foul sci-pd OH ON 0 o o °oes / '13 (8A) AQIOOIGA 9I011J3d 67 omega smash the co consonpe use: seesaw .ephaom madam vHHom on can moan ensemoum Hupoa pm-p.e «when =mw.m .q .H ease com eases seam .cezxw mo.m: mo and Inmsouna a now noun onsmaonm Hdpoa on» mo upocodeoo 0m 3m .man .oem\.pe spacefles the ow .-m .1... 0 >hso O. wH. O H O °qg/'u1 (qvo edrd JO qoog Jed dexq exnssemd solids per unit volume of pipe, the head loss would be greater at low air velocities, as is indicated in Fig. 3h. Theoretically, curve "B" in Fig. Bh'would approach the abscissa asymptoticly as the air velocity approached infinity. Thur far in this discussion, the reasons for the results which are presented in Figs. 25, 26, 27, and 28 have been discussed. The fol- lowing paragraphs will deal with the data presented in Figs. 29, 30, 31, and 32, which were obtained directly from Figs. 25, 26, 27 and 28. The graphs of throughput versus pressure drop emphasize several points which are not obvious at first glance in Figs. 25, 26, 27, and 28. If it were desired to specify an air velocity from'Fig. 29 for a given throughput, which would result in a minimum.pressure drop, the lower curve, representing an air velocity of 60 ft./sec. would be chosen. If the same thing were desired, but Fig. 32 were used, the curve representing an air velocity of 110 ft./sec. would be chosen. This points out that the trend of these curves is completely reversed in changing the pipe inclination from 00 to 90°. This reversal is caused by change in the slope from.positive, in Fig. 25, to negative, in Fig. 28. It should be noticed that at the two smaller pipe incli- nations, the pressure drop for a given throughput does not vary exces- sively with air velocity. However, at the two larger pipe angles, the pressure drop is significantly dependent upon the air velocity. ‘ It can be observed from.Figs. 29, 30, 31, and 32 that the slope of the curves increase as the pipe inclination varies from 00 to 90°. This is caused by the increase in the pressure drop differential, be- tween any two constant throughput curves, as the pipe angle increases. This cause is evident if a comparison is made between Fig. 25 and Fig. 28. 69 Another point which is very well illustrated by Fig. 32 is that the slape of the individual curves, for one pipe angle, increases as air velocity decreases. This can be explained by the use of Fig. 28. As the air velocity increases, the pressure differential, between any two of the constant throughput curves, decreases, thus causing the slope of the lines in Fig. 32 to increase. The reason fer this increase can be traced directly to the increase in the static head loss as the air velocity decreases. This trend, of course, reverses direction at some angle between 00 and 32.730 where the slope.of the curves in Fig. 25 reach zero and become negative as it is in Fig. 26. An analysis of Figs. 30, 31, and 32 gives the impression that it is more economical, from a power standpoint, to maintain a very high air velocity. ‘While it is not the object of this research to discuss power requirements, the above statement warrants a brief explanation. The statement is true only from the standpoint of head loss due to the presence of the solid phase. ‘When the entire power requirement is con- sidered, the situation reverses direction. The explanation of this re- versal lies in the fact that the horseepower required to move air alone is proportional to the cube of the fan R.P.M. Thus, while it is advan- tageous to Operative at high velocities from the standpoint of energy loss due to the presence of the solid phase, this advantage is more than offset by the additional power input required to increase the air veloc- ity. Another argument for operating at low air velocities is that less damage will result from impact of the particles with the pipe wall as they round corners in the pipe line, or are deflected at the pipe out- let. 70 This concludes the discussion of the results presented in the eight graphs on pages 61 and 62. The next two items to be discussed are the two tables in Fig. 35 and 36. These two tables, one representing the lowest and the other the highest throughput tested, are presented to give a quick comparison of the inter-relation between throughput, pipe inclination and air velocity. From either Fig. 35 or 36, it is possible to make the following pressure drop comparisons for soft white winter wheat being conveyed, at a constant rate, through a 3.89 inch I.D. tube. 1. Hold air velocity constant and vary the pipe angle. 2. Hold pipe angle constant and vary the air velocity. 3. Vary both air velocity and pipe inclination. In addition, by varying the throughput, a comparison of the effect of this variable on the resultant pressure drop can be made. A h3 (in./ft.) For a throughput of 25.93 #/min. Air Velocity' Pipe Inclination ft-/3°°° 0.0o 32.73° 62.S° 90.0° 60 0.0190 0.0369 0.0570 0.06h5 70 0.0200 0.0333 0.0h70 0.0522 80 0.0208 0.0320 0.0820 0.0h58 90 0.0213 0.0312 0.0390 0.0h21 100 0.0220 0.0310 0.037h 0.0h00 110 0.0228 0.0310 0.0363 0.0385 Fig. 35. Effect of pipe inclination and air velocity on pressure drcp due to the solid phase (air drop excluded). Aha (in./ft.) For a throughput of 57.82 #/m1n. Air Velocity' Pipe Inclination ft./sec. 0.0° 32.73° 62.5° 90.0° 60 0.01433 0.0826 0.1256 0.11.36 70 0.01.50 0.0751; 0.10h5 0.1168 A 80 0.01169 0.0711 0.0930 0.1030 1 90 0.0h8h 0.0696 0.086h 0.0935 100 0.0500 0.0697 0.0832 0.0881: A; 110 0.0519 0.0698 0.0816 0.0856 Figs. 36. Effect of pipe inclination and air velocity on pressure dr0p due to the solid phase (air drop excluded). 72 SUMMARY‘AND'CONCLUSIONS Equations have been derived which enable the design engineer to calculate the pressure drop, due to the conveyance of solid particles, for any pneumatic conveying system. For any Specific condition, the equations depend only on the experimentally determined friction fac- tor (fa). These equations were presented under the Theory Section and were derived in the Appendix. The design and construction of the test apparatus is illustrated under the Apparatus Section. The procedure followed during the tests and the results of these tests are given in the next two sections. The figures on pages 59, 61, and 62 represent the most important data presented. Fig. 23 represents the experimental friction factor (f,) which was used to calculate the graphs shown on pages 61 and 62. These graphs represent a comparison between the experimental and theoretical results. It is felt that these two agree closely enough to assume that the equations developed are valid, over the range tested, for wheat flowing in a 3.89 inch pipe. As previously mentioned, these equations were developed on the basis of initial assumptions set forth by Hariu and Molstad (20) and Pinkus (30). While the equations developed have proved valid for various throughputs, pipe inclinations, and air veloc- ities, they can not be assumed generally applicable until their validity is proved in a larger diameter pipe. §29cific equations for soft white winter wheat The two equations which are of most use to the design engineer are 6 and 8. Restating these equations: 16 a -" 263 (8) Cz’flza' ‘4CIC: 73 Where: 6: 0.2.9,”: _ g i In? .20 c _ -o.04 fipgv; 205,42“ ‘2' mg mga’ 0.2/9/0v'z 20/9/62 C3 = P a. a. + P a”; _ 9530/79 my de And: f‘U’L 6 6 L f L 13-50 AH—5595+5”5m9+°‘”““’ (6) 203/710 ”3’2. 209010 Now with "f8" known from Fig. 23 and "v8" calculated from equa- tion 8, it is possible to predict the pressure loss by the use of equa- tion 6 for steady state flow, in feet of water. These equations can be considerably simplified for any one type of particle and atmospheric condition. By making use of the physical prop- erties of the soft white winter wheat used in this study and by assundng dry air at a temperature of 50° F., equation 6 and 8 become: *2 C: 3 62" J51: " 4053 (80') Where 2 ‘9, J C‘ — 0.02.27 - 6‘, —0.0454 7/; — 0.02858 63 = 0.0.2.2774" + 0.028.787}; — 32.2 5m 9 And: ir‘trtS <3 -51? Z 29" AH = (2.49)]0'4 ’ :7 51" +0.0/604 Viz, Sm a-Hzaha .2521}. (6a.) 5 The assumptions which limit the use of equations 8(‘) and 9(‘) are as follows: 1. The particles being conveyed must be wheat with physical prop- erties similar to those of the wheat used in this experiment. 2. Dry air at a temperature of 50° F. 3. An atmospheric pressure of 1h.7 pounds per square inch. 8. The solids' friction factor (is) is as given in Fig. 23. The variation of head loss with changing atmospheric conditions is small, however, if extreme accuracy is desired, the origional equations 6 and 8 should be used. It should also be remembered that the head loss in feet of water, as calculated from equation 6 or 6(‘) is only one of three of the major pressure losses encountered in an actual pneumatic conveying system. Either of these equations give the pressure drcp which results after steady state conditions prevail. By this, it is implied that the particles no longer have any appreciable acceleration. In this experiment, this point occurred approximately 2h feet beyond the 1800 bend for all pipe inclinations. There was a 8light increase in this distance as the inclination increased. However, since the exact point at which particle acceleration ended was not 75 important, the values were not recorded. Any one of the pressure drops observed were valid as long as they were recorded beyond this point. The other two types of pressure losses which, while very important, were not investigated in this study are: 1. Pressure loss due to the acceleration of the particles to their steady state velocity. 2. Pressure loss due to any bends or elbows in the pipe line. An actual example will now be given to illustrate the use of equations 6 and 8. It should be remembered that while the following example assumes that "fa" is valid for any pipe diameter, this has not been experimentally verified. ‘Wheat is being conveyed at a rate of 5,500 #/hr., with an air velocity of 75 feet per second, through a six inch diameter tube at an inclination of hOO with the horizontal. Calculate the pressure drop in 60 feet of this tube after steady state conditions prevail (particle acceleration equals zero). The atmospheric conditions under which the system will operate are: 1. Air temperature of 600 F. 2. Air pressure of 1h.7 p.s.i. 3 . Relative humidity of 50%. Since these conditions differ from those upon which equations 6(a) and 8(a)'were based, it is necessary to use equations 6 and 8. Solution: The method of attack is as follows: 1. Solve equation 8 for the average particle velocity (v8). 2. Use this value in equation 6 to determine the pressure dr0p in feet of water. 76 To solve these equations, the following constants will be needed: 1. Physical properties of the wheat are as given on page 52. 2. vg = 75 ft./sec. 3. f8. - 0.028 (From Reference 6) h. f _ 0.0102 (From Fig.23) S 5°14. _-_ 12.2 x 10‘6 #/ft. sec. 6. Pa -.-.- 0.0763 #/ft.3 7. D e 0.5 ft. Be In : 60 fte 90 GS 1' 55m X We, 00 = 7.775 #/rt.2 Calculation of ”v8" from equation 8: ".203 4/5, :: c, - /C,’-—4c_,c, Where: 6 __ 0.26,“: 52': ’ 4h7:7 .2119 _ (o.2)(z20.5'x/0“) (0.0763) _ 3.0/02 ’ 82.6 x/o" 2(0.:) .5; - 0. (DUB! 77 0-4flp7/ar9. zeapui] C2: " + ITO-QUZOJNO‘QWI) (0.0763) (20 ) (A20. 5x/0")(/2. 2 x/o'é) C = - + Z L 82.6 x /0“ (82.6 x/0")(/2,39 x xo-3) c, s —-3.3// 0'2'7’0’3 “0.2 zoflp/‘(a‘ul . C3: + "" 95/776 (0-2)(/20.5’x/0“) (0.0763)(7.5')2' C = + 3 82.6 x/O" (2.0) (may x/a'6)(/2.2 no“) (75') “‘32.2 .31» 40. = /06.46 (82. 6 X/O")(/Z-39 x/o-J) So: -62) 006- {Q —3.3// - /(—3.3//)z’ -(4)(/06. 4s)(o.0//85- «3 1x; = 37. 9 F7'/.S.¢='c'. NOW calculate A H from equation 6: - :- fviloék + 6:10 5M9+ £1.11; ’3. 2036.0 Elia 2096p AH: 78 (0.0/02) (37. 9) (60) (z 77:) (7. 775’) (e o) 5;» 40° (2)(0o5'>(32-z)(6a.4.) (37.9) (62.4) (0'028)¢0)(75)2(0.0763) (2)(0-5')(32. 2)(c.2.4) 111* = C7.C>é?é?é§ 'f'C9./AZ£§.5' 1r C?..3257£? 25H : 0.5731 feet of water for 60 feet of pipe. This is the pressure drop which would result after steady state conditions prevail. If an actual systerm were to be designed, the other two types of losses, mentioned earlier, would have to be added to the above figure to obtain the total head loss. As was brought out in the Review of Literature, very few inves— tigators have studied pressure losses in farm.pneumatic systems. Segler (32) does set up an equation which can be used to predict the pressure loss in a horizontal pipe, provided the appropriate friction factor is used. Pressure drops were calculated using,Segler's equations for the throughputs shown in Fig. 25, and the values thus obtained were then compared with the theoretical values shown in the figure. The deviation between the two values ranged from 1.7 per cent to 10.1 per cent with the present investigator's values being consistently lower. This is the only check which could be made on the experimental and theoretical results obtained in this experiment, as no reference could be found in which the pressure drop due to solid particles had been investigated at various pipe inclinations between 00 and 90°. 79 The data presented in the graphs on pages 61 and 62 were completely discussed in the previous section; however, a more condensed discussion will now be presented. The principal objective of Figs. 25, 26, 27, and 28 was to com? pare the experimentally determined points. A small consistent devi- ation is evident at the two highest throughputs in Fig. 26, 27, and 28. At these throughputs, the experimental points seem to fall slightly below the experimental curves. As was mentioned earlier, this devia- tion is insignificant from a practical standpoint but from a theoretical point of view, an explanation should be offered. .This explanation is as follows: The solids' friction factor (f8) was based on pressure drops Observed with the pipe in a horizontal position and then was in turn.used to calculate the theoretical curves at the other inclinations. Since the component of pressure drop which "fa" represents is that of the particles sliding on the pipe wall, it is possible that there was more sliding when the pipe was horizontal than when it was vertical. If this were true, this component of head loss would be less at larger pipe angles than was indicated by "f8". This explanation seems feasible; however, there is a possibility that it may be incorrect. Actual obser- vation of the flow of particles with the pipe in the horizontal and ver- tical positions indicated no difference in the uniformity of the density of the dispersed solids. It should be remembered that this was only a ' visual observation and that there may have been a difference which was not evident to the naked eye. The two trends which are illustrated in Figs. 25, 26, 27, and 28 should be again emphasized. The first is that the pressure dr0p 0U increases as pipe inclination increases. This is due directly to the increasing static head component of pressure loss which is a function of the sine of the pipe angle. The second trend is an increase in pres- sure drop as the air velocity decreases and the pipe angle increases. This is due to increased density of the solids within the pipe as the air velocity decreases. This in itself would have no effect on the static head component if the pipe were horizontal, since the static head is, by definition, zero. However, it can be seen that if the pipe were at some angle other than 0°, this increased weight of solids per unit volume of pipe would appreciably increase the static head. This same argument can be presented to explain the pressure drop increasing, with an increasing rate, at large pipe angles and low air velocities. If it were possible to increase the air velocity to infinity, the curves in Figs. 26, 27, and 28 would reach a point at which they became linear and possessed a slope equal to the curve in Fig. 25 for any given throughput. This is most evident in Fig. 26 where at high air veloc- ities the curves are again becoming linear. Figs. 29, 30, 31, and 32 illustrate that there is a linear re- lationship between pressure drop and flow rate for a given air velocity. As would be expected, the pressure drop increases as flow rate increases for any given air velocity; .Also, due to the static head component, the pressure drop is less at higher velocities for pipe angles of 32.73° or greater. A more thorough explanation of this phenomenon is given in the previous section. Fig. 3b shows the two components which make up the total pressure drcp due to the presence of solid particles in the air stream. Fig. 37 showns this curve combined with the pressure drop due to the air alone. 81 The combined curve represents the total drop which would be present in an actual system.under a specific set of conditions. It is evident that there is an optimum velocity at which the total head loss will be a minimum. From a power input standpoint, this still would not be the most economical velocity at which to operate. This velocity can be determined from the H.P. curve in the same figure. In this particular case, an air velocity of approximately 62 feet per second required a minimum H.P. The point of minimum H.P. will always occur near the lowest, if not at the lowest, air velocity which will convey the parti- cles. If the exact point is desired, a graph similar to Fig. 37 can be determined for any specific design requirement by the use of Fig. 23 and equations 6 and 8. Practical_gperating range As was just shown, it is generally desirable to keep the air velocity as low as possible to reduce the power required for operation at a given capacity. In this experiment, the minimum air velocity pos- sible ranged from approximately 65 feet per second for a horizontal pipe to 70 feet per second for a vertical pipe. These figures agree very well with those given by Segler (32) and Kleis (22). It was stated by both Segler (32) and Kleis (22) that the max- immm.throughput is almost entirely dependent upon weight, rather than volume. In other words, a given size pipe would convey a greater vol- ume of oats per hour than wheat, the pounds per hour remaining con- stant. Kleis (22) found that an upper limit for a four inch horizon- tal.pipe was 58.h pounds per minute. The results of this experiment indicate that it is possible to exceed this value, but the system.0pera- tedmuch more smoothly when the throughput was kept below this limit. ONH OHH o. o.m 0.: O O 0 °dId :0 4005 mi '8 ’H (£01) 'd ‘H O m 0.0H emam Qua tom Amos OOH .00” R .mE .ps speeches the 0m 0» 00 o .o .3 .1. :8 3.8.6 325 com .. cause 8.8 ea} u .a .H 3.2 3.3 so schemata. a n3 :5 no soon are season .m .m one 9385 does no 38850 oo. ”Li/"II (uv) odm JO zoos Jed dean mung om. II.I|."I 82 an .mE oomph...” .3832, 0. 8H 0: 02 ca 8. ea oo o oo. :3 o.m . , w ,2 , .. . so. mcwaom 0» csoq "Li/"II (u v) odtd J0 zoos area down Owens 0. 0. ~o ‘3de 30 zoos ”J 'J ‘H (£01) 'd ’H 0 e (I) .o .3 ._. rs omvomvo .33 com 9&5 code 0.3 O N e .22 .q .H 31E 5 no.3 no passage a sou 2?. no soon hem season .a .m on. no.5 enseeehm H.309 Ho Swazi roam tom Anocd .m o.NH 83 The number of feet of pipe which could be included in an actual system depends upon the following: 1. Capacity of the blower. 2. Size of pipe used. 3. Throughput desired. h. Pipe inclination. 5. Number of elbows and bends. To determine this value for any specific situation, it is nec- essary to add the steady state drop, as determined from equation 6, to the inlet drop and the drop due to any elbows which are present. The latter two losses were not investigated during this research. Possible analysis of silgggnparticles. If the theoretical analysis, as presented to date, can be proved valid for all common types of farm.grains, the next step would be to investigate the possibility of applying the theory to the flow of for- ages in a truly pneumatic system. This presents many problems, both theoretical and practical. From a theoretical stand point, it would be almost impossible to determine a true solid's velocity since the parti- cles are not uniform. The best method of attack would be to determine a representative "v8” from the pressure drop data obtained. This method of obtaining "v8" was completely discussed earlier in this report. The value obtained might be interpreted to represent an average velocity of all the particles in the pipe. The range which this average velocity represents would vary considerably from light to heavy particles. 'While most grains approach the shape of a Sphere, particles of forages are more closely represented by'a cylinder. Since the value 8b of the coefficient of resistance (0), as used to calculate "£8” for wheat, was determined from true spheres, it would be necessary to obtain such a graph for cylinders when the analysis is applied to for- ages. ‘A serious practical problem, which makes it difficult to obtain experimental results, is the method by which the particles could be introduced into the air stream. Due to the low density of the material, it is necessary that the pipe have a minimum diameter of seven inches. It appears doubtful that the bucket wheel feeder used with grains would 'work satisfactorily with forages. There is a possibility that with the larger pipe, the injector feeder might operate effectively. However, the most promising possibility seems, at the present time, to be some type of auger-feeder. From the previous remarks, it can be seen that the problem.of truly pneumatic transportation of forages is much more complicated to analyze, both theoretically and practically, than the flow of grains. Another point which should be remembered is that, to data, forages have been transported almost entirely in impeller systems. However, the work of Kleis (22) indicates that in a system where particle damage is not important, thus allowing the blower to operate at a high R.P.M., the particles do receive appreciable energy from the air stream. This indi- cates that the analysis as presented for truly pneumatic systems, may have some application in impeller systems which use high speed blowers and convey material long distances. Summary of conclusions 1 l. The experimental data obtained, to date, indicates the theoret- ical analysis was valid. 2. 3. 7. 9. 10. Pressure drop due to the solids increased as pipe inclination increased. Pressure drop due to the solids increased as the air velocity decreased and the pipe angle increased. A linear relationship existed between the pressure drop due to the solids and the flow rate, for any given velocity; Pressure drop due to the solids increased as flow rate increased for any given air velocity and pipe inclination. The static head component of pressure drop decreased as air velocity increased. The sliding component of pressure drop increased linearly as air velocity increased. The horse power input to the system was a minimum when the air velocity was as low as possible, this value being determined by the point at which the air ceased to convey the particles. The minimum air velocity which will carry wheat particles in a horizontal pipe was 65 feet per second. In a vertical pipe this velocity was 70 feet per second. The maximum throughput of wheat in the 3.89 inch diameter pipe, which allowed smooth operation, was 57.82 pounds per minute. :1... RECOMMENDATIONS FOR FUTURE STUDY Check the equations, which were developed, with pipe of varying diameters. To date, the theoretical equations have been proved for wheat flowing through a 3.89 inch diameter pipe of varying inclinations. The next logical step is to test the validity of these equations for a larger pipe. If they hold for the latter case, they can be assumed applicable to any farm grain. This leads to the next step which is to calculate friction factors for various other types of grain. Determine "f5" values for different grains. After the validity of the equations has been proved for larger diameter pipes, friction factors can be calculated for other types of grain. These values could be computed directly from pressure drop data obtained with either the large or small pipe, since the equations have proved valid for any pipe diameter. It is suggested that the smaller pipe be used because of ease of handling, etc. Actually, only one pipe inclination is needed to obtain enough data to plot a "f8" curve; however, it is recommended that the data thus obtained be checked at some other pipe inclination. Investigate pressure losses due to forages. As was mentioned earlier, this is a very difficult problem.since forage particles not only vary in size, but also in density, within any one lot. Then if various lots are considered, the length of cut ‘will vary, thus introducing another variable. It is felt that if a ;friction factor were determined, it would be at best only an approx- imtiono Li.. §3tudy the design of an inlet which could be used to introduce forage :particles into the air stream of a truly pneumatic system. It was mentioned earlier that the best possibility, to date, was the use of an auger-feeder. This, however, requires additional construction and extra power source, both of which are undesirable. A.method is needed by which the desired capacity could be efficiently handled. Study the relationship between pressure drOp in a high Speed impeller system and a truly pneumatic system. In a low Speed impeller system of the type discussed in the Introduction of this study, the particles receive most of their energy directly from the impeller wheel; therefore, pressure drop is not an important parameter in the design of such a system. In a high Speed impeller system, the particles still.receive appreci- able energy from the impeller wheel, but they also can obtain energy :from.the air stream to replenish that lost throughout the piping .system. This indicates that the pressure loss, per foot of pipe, 1would have a direct effect upon the distance the particles could be conveyed for a given blower. It is possible that after a reasonable length of pipe, this pressure loss could be calculated from the equa- tions developed in this report. Establish an exact method of determining particle velocity. Determining the particle velocity has been a major problem con- fronting all who have investigated pressure losses due to the pneumatic conveyance of solid particles. Since it is an important parameter in the deve10pment of any type of theoretical pressure loss equation, its value must be determined. Three possible methods of idetermining "v8" were discussed in the Apparatus section of this study. The shut-off gates finally decided upon proved rather inac- curate. This made it necessary to calculate "v3" from the pressure drop values, which is perfectly valid, but cuts down the number of variables left to check the theoretical equations from two to one. If it would have been possible to experimentally determine "vs" at one inclination, the value for any other inclination could have been calculated and compared with the experimental results. Some method is needed which would permit the determination of an average "v ” without interruption of the flow within the pipe. This 'would allo: the readings to be taken much faster and also more ac- curately. Investigate losses with various elbow radii. Segler (32) has made a brief study of this subject, however, the jpossibilities are by no means completely exhausted. Segler (32) discusses the paths followed by the individual particles as they travel around 90° bends of various radii. He presented the inter- nal wear of the pipe wall as proof of his statements. It would seem advantageous to obtain a glass elbow and run these same tests while recording the motion of the particles with a high speed camera. From these observations, perhaps further theoretical 'work could be accomplished. Study acceleration losses immediately following bends. Segler (32) gives data which allows the pressure drop in certain size elbows to be represented by the drop in an equivalent length of straight pipe. After expressing a given elbow in terms of equiv- alent feet of pipe, equation 6 and 8 can be used to predict the pres- sure loss. 9. Since the data that Segler (32) presents is limited, it is felt that more work is needed for elbows of other configurations. Data of this kind is essential in the actual design of a pneumatic system since equation 6 and 8 are not valid for sections of pipe in which the particles are being accelerated. Determine a method by which inlet losses could be reduced. Segler (32) gives a very thorough coverage to the subject of pressure losses with various types of inlets. He expresses these losses, as he did for elbows, in terms of equivalent feet of straight pipe. His data shows that these losses are an appreciable percentage of the total pressure loss. It is therefore felt that it would be advantageous to design an inlet which would reduce these losses. The principal inlet loss occurs because the particles have no initial velocity, parallel to the pipe wall, at the instant they enter the air stream. If a small impeller could be used to accel- erate the particles to their terminal velocity, before they enter the air stream, the inlet acceleration drcp could be neglected, thus reducing the total head required considerably. 90 APPENDIX So that the body of this report may be kept as clear as possible, the derivations of the principal equations have been omitted in the theoretical analysis and presented in this Appendix. The first three sections will be devoted to the derivation of the pressure drOp equations. Due to the complex nature of the system to be analyzed, it was necessary to make the following simplifying assumptions before proceed— ing with the pressure drop analysis: 1. The component of velocity perpendicular to the pipe wall will be small relative to that parallel to the wall. 2. The total pressure drcp along any section of pipe, after steady state conditions are reached (ap = 0), is made up of three come ponents, these being: a. That due to the air alone. This is assumed to remain con- stant with or without particles in the air stream. b. That due to the particles striking each other and the pipe wall. c. That due to the solids' static head. 3. The coefficient of resistance, as applied to freely falling bodies, can be applied to particles moving in an air stream. h. A friction equation of the Fanning or Darcyeweisbadkptype will account for the energy loss due to impadt between the individ- ual particles and the pipe wall. The equation of motion will be developed from.the following free body diamgram of a single particle. This particle is experiencing an up- ‘ward acceleration due to an air stream, whose direction is tangent to the path of motion at the instant considered. Y . l. I z /" r a? 3 § ,er L» gaffij; path of particle ; V1; /‘/I «\Q’ fix 9 x \ u - ' \a \ \l / ’ r VV ’ «I; ’l i i - E w; 7 .1 .2 Fig. jfl3. Free body diagram of a single particle experiencing an upward acceleration due to an air stream, whose direction is tangent to the path of motion. Section I Derivations of equations 5 and 6 are as follows: Applying Newton's Law (Efsmq) to the system in Fig. 38, and summing the forces in the tangential direction gives: 542..., = F5 - Whit-’3") “ °°’ F Expressing oc in terms of 9 z 90 - e co; (90 - e) COAQ: :51". 9 0C fetid; Giving: a? F” = /Z'- Vt'tfizv:~fii> \Szrr £9 = Ivoca, 00 [(72.0) Y ‘ F 1' ,,,/' 0 i ‘ ,, 0? /-l i x r“? gtf' """"" ath of article i ,. , r 11"» F. P P ‘v’L /" \ Pf 9 \5 \ \l” r VV T at." i A! 1!; 7 '1']; 2 I i ‘1” fl __ -_ w w- -_._,..,_ .-_,._.M.,_.A._...,. . .--.i..-,,.,._._ -_ _, A Fig. jflB. Free body diagram of a single particle experiencing an upward acceleration due to an air stream, whose direction is tangent to the path of motion. Section I Derivations of equations 5 and 6 are as follows: Applying Newton's Law (8. {rs/724) to the system in Fig. 38, and summing the forces in the tangential direction gives: .. » ’0”f‘5’. ‘5 r 55..,- FZ“W<’L,2““)C“~* °C p Expressing oc in terms of 9: 0C -= 30 - e (‘05 0. = 605 (‘90- 9) (0.5.0:. -5/n 5 Giving: 1p - f2 r _ __ m: J,._......:._ 5 :: E.-(7‘.$n) ‘ f; V/(\ ’9 > tn. 9 n) a. U) 92 ED, as defined by Coldstein for free falling spheres, is equal to [0 v‘Cfi G- This will also apply to a s stem vhore the air is moving, 29 as well as the particle, if the relative velociigr 14;3;;(ua-fiug) is sub- . N ‘\ . . eiituted for v. Equation 1 now becomes: 0/ U5 r77¢?—;7- his equation wouli hold for one parti ole in an air stream, but am- W)CaP-m9(’o,g 61);”,9 (2; 29 if several particles ero simultaneously in the stream, an additional term must be included to accoxr nt for energy lost due to collisions with other particles. In addition, if the particles are enclosed in a pipe, this term must account for losses due to sliding on the pine wall. FOlIOWing the sursestions of other investigators, the Darcy- "J .i ?bisback friction equation will be added to account for these extra losses encountered in actual gxmumetic transporting systems. alrz H fi 10 3 2217:? Rearranging this so it will re Lpr sent tlw force exerted per particle (F): .. is [07/32 AP“ 209 65‘ how multiplying both sides by AP gives: 1 2 (A PM. = 52 5’9"" e5 9,» [0,3 = pounds of solids per square foot of pipe cross-secti on. This 5 multiplied by the area of one particle gives weirht "h" of that particle. Therefore, the above equation can be written as: flaw 0?— II at F M N D 3 93 I Adding this term to those of equation 2 gives the complete differential equation of motion for the system. 0’7}? €(1/OZ" {5:2 [‘0‘ ,0 f ”U“: . . Q = -..- ---~-. -.-—3.. Cflp .. (g; a: 5"”.9 _, 5 (r1 d 7' gm 9 3 ,3 ) ---"-2 0 J) When steady state conditions prevail (g%;§h:(9), equation 3 can be re- written in the following form: 2 1v " 1,- [/0— 2 \ ”2‘29 J) ero=M3(J/;J €j4/n0+-%:i; (4) Since for grains and forages the term ( 12~7;—§: ) is very nearly 4‘ unity, it will be neglected in the remaining pressure drcp calculations. It can be seen from this force balance that the energy loss due to solids' friction plus that due to the static head will be equal to that supplied by the drag correlation. Converting each of the force terms in equation h. into equivalent expressions for pressure drcp per unit of mass flow results in the fol- lowing expressions: 1. For the impact between particles and the tube wall the Darcy- weisback friction equation gives: A H. :: i [Q .1512 “10‘" .5 ’5 2 0 9 8.20 Expressing this as drcp per unit of mass flow by using gay ,3: 14 gives: AHfs : f; "J; 1. e, 2 age to A //;5 is in terms of feet of H20. 2. For the static head expression: IO -—‘-’-’ Lsme ES 1 Expresli,g this as drcp per unit of mass flow gives: All/("h = ' Aflgé = Sing [65 ago '14 From the two previous expressions, it can be seen that the pres- sure drOp is a linear function of both the solids' velocity and flow rate. The validity of this expression will be tested by analyzing the experi- mental data. 3. From the drag correlation: €C/7p (35" mfg-)2, [gee-r Parnr/(a) : 2 3I-M_1N— The number of particles present in "L" feet of pipe'will be equal to: N = 7072M W ___ H5 Vb _ 6: Halo W/Pf'” flr/1C/C V111: V; is)“ 615/11”) [—0 N_ 739963 So the total force exerted on the solids in "L“ feet of pipe is: F _ {EC/it (VI/a.’ 1;)2 /6:,' ’9‘; L0 (’07:) — 2 9 7/} VP '0‘? Changing to drcp per unit of mass flow: 5.7:? 7") _ a? 3 “65p CVZ.‘ V3.22 (1”; 69:95; £0 £75 £7.21")? 1]}! = QCT/7P ( 1f ‘* 15?.)2 [‘06: 012029 Jig/Pf?" Substituting these equivalent expressions into the force equation.h gives: ,. - z .flgfiai’w :33? ... £5.17. + ...fLZ "2,0 429-er 6: 217363,, Solving this equation for"f“ gives: 2' fiC‘Fpfi/‘f 1*")2 =g~123 31591» 337132 onm’29vvfl’o .12 209K€uo 053(15):? (5.3-75)? == VF 632 [73 5",» 6+ gags/52. 9S r‘r , F _4_ \2 _ f. ‘ \ 0m ..‘5’4 f"- ’3 5‘ ‘76.-_’E_:;:-1J_ (5) J3 ’ ""”' ' ';;,}6g'ggézz““” This expression will be used to experimentally determine'fg'from the ob- served data. As previously mentioned, the total head loss for a given length of pipe (assuming steady state flow exists) is made up of threeparts. AH = AH” +AHM + AHQ If the steady state condition has not been attained, another term must be added to account for the pressure loss during the acceleration period. This term will amount to an appreciable percentage of the total drop near the inlet. . an. 6 67 A flax/”(F A f’ = "f‘ méww£_ i + ...—J... 10 5": 9 + /&_'Ji (1 ’A, 6 209 6;. “”3610 4U? ”i U (AH is in feet of H20). "f8" is the experimentally determined value of the solids' fricé tion. 'féfis the value of DarcyeWeisbach friction factor for the flow of air through pipes. The equivalent Fanning friction factors would be one fourth as large as those used in the Darcyfifleisbackkequation. Section II The derivation of equation '7 is as follows: Restating equation 3 : o’v; 1°{za-Lr~)z ,o,,o .c «Ll-2 - .. : J “"4”" (7/71 ... (Lima: 5"}? 9 __ .5 .5. This differential equation will now be solved for'v; in terms of the other variables. Letting: 1:: (a I” - x filrr>v V 96 Vo r 3 *g'zW" 4);)“.14 .1) 3 Z J Substituting into 3 gives: .g/V . _ A J};- = Mug-3:.) .- ,2 -—y:x_;~ Separating variables yields: y; z , -d?C._-_-_...._ . .....-“ X‘/;4-,2x1r:/;+O(~ y)’z/_;‘<—z Since'g;'is constant during the acceleration period, the following sub- stitutions can be made: K2. 3 Z X 1'; x13, = (A ~ // Substituting these expressions into the above equation: 01 7 _ n... [guy-3.- -..-..“ K3? "' K2 1}: “f ’1', Integrating both sides yields: / C —- neg/QT :KK'V 4:51-“,3 f K52; ‘f - ~—w—~»—- ““*° -.4;;-+ C ‘4K/f5f/Tzz 2K31ffK2+/4KI<,+K, Replacing the second set of constants with the first gives: M- ‘4’. -..- ~4/< K + K” =V— 4(x uglzxxl-Y) + 4x2 7;} =2/Icsz'2‘ Vs; 2;“: n V z y) + x2 V -..... ...-Mw-o-_ .... =Z/zx + yx 7/332 2y The expression for "t" now becomés: 97 / 7“ = ~33: ______ 2 ZX + 2’X‘2 03-22 /n im'.“ (_X_—_>’) J- -ZX_2;3 mfg/7X77} 7X74? ~Z>J +6 21,— _J’: 2 IX " 2" . _- 2"”; 7‘sz X*/X-v"-z/ Since the initial conditions are vs: 0 when t: O, the constant of inte- gration (c) is equal to: ———-—-——-- ...-..— __ 3.- ..- .....— --.—.---—_‘..o —/' *2/323—22X +y2< "fa? 72/, .... A--. -3 ___... ——-——-.—..‘ Q-h- -. nu... w'.‘ I-O'Q"- ~~w 2 «smo-UV. -d-.r.--lv- —.—---.— --— - - » - .. ...-u--- -. ~«~.—v—---¢ ___... ZJ‘ZX-XJ. J3"—22’ ' 22X 23: +2/2X+‘2X 1"" ~22? Replacing “C" with its equivalent expression yields: .— ' _.__‘,. -.M - ...“ ”...—-.- ~u -!---—._..-_ E2/’Z>< + YX‘zaz— "22’ 1" -- _ 3.- //7 Z 137-3117."1.5.3.5313,“ " //‘ . _ {721 . “if /-... 3 23--222; 2 3 22222.3 g £ng - (fo-X-Xxg‘f-f'fj /” ...-__.....,..__.._.-..3. (___... ..-- ~2Xf JZZXfYXV —Z.‘2__§ Making use of .the following logarithmic idenity (1n A - In B =11: é) the equation for "t" becomes: 7 - — ‘1‘“-..v-h‘... ~ . ,, ,~.,‘.-‘ -_‘._ ,. ‘,— m-. ..--..— —.—..~ m‘m‘ -mw Ex / Xx'zrz -‘Z‘2’ ’_ _1. " co-..“ XXV/X71?“ZX:&~Z‘/ZX*‘//t/;f,_zy ! - ,_ .. .__-__. i 9 i Z(2<—-— 2’)"/.;- 2M +2sz+y ("w/2’ /n f: .7 XJ3—2/zx+>JX J3: -2y 477 t-ZX‘WJ. +2;sz + 2 ,2 } 1 i To facilitate the simplification of the previous expression, let: 2’— - / ' ‘ ' ' ~ ' - ,;,-—~,-,— /n x»- .— 5 ... A‘/‘6 L/T4 ~/~5‘ 7.x; 1715—1 L. I I 2 I x '0 I / “I __ " - . ‘( +0 ‘2’ /: ... ’r' l/ :1 + /k.4 ’3’] .6 4 K6 1 I if 2' = '"T""‘"‘ r2 --- : -- - , » 3 2" ’ —.~«’ ; -; $3752,“ ./ "f, u I 'h 1’; 2 . " ._ I 5— 9 , .4 , .. Clearing this expression of Kb and K”: _ / a A ’. 2 .3' \ _f I .-. f“ 2- f ,. ‘ ._ - 7" ... ‘r -. "- ‘ 4‘. '2" “J 5 f, _'. . :1" 7 ,._ I\,(‘ "‘ it I 7/ ["lf . .- .- ’5-7 ’l/I ,—7 . --- ,__ -' ' s», /,. 2 ~ ‘ 7 '1 "“ . . ' "' 2"." —~ "- “ ,, ' A 7.1- ' ' '7' " l 6 / 'k 7 \ / / 3. "v o: 7;. L- ' ' I, " k .1 I“ - 1r /) f . fl '- .r ’7' |.’ > ‘. ! 2 u— p- 4 _,, . _ \ ‘1 . a .43 J- ~ 2 x ,. — 3. 2 + .2 3 « 23" ,3, ,2 r. _. 131‘,“ 1. - ._ _ / )‘ 7/“ ' 7 ’7 7X 7 fl 2' ,2 CS‘ ,9 /K “ML; / .3 My) 5 :42 min/s .J.-Z_O<- 2’) 2 22—22» «233 ‘—v‘--—.._.-_ _ — -——-4-.. . 2 __ 6 '(7/ — - "‘ —- ’ —-“/‘ I’v-‘ " I' ‘ (X ”K6 W U)7 a], ’ZM'P/ +{X-~2')1/5_2;< C) H 0 91’ H- :3 CQ 6" :37 Ho 0) C. 23? ’1 0 03 U] H. O :3 g CL Solving for“ vs '3 K6 ‘ any 2 qr.(—:f' 415’ “_2,‘TTqu‘H,;)~—_ZJ T+‘-M7+7/0_A— -zrs — r< 7‘ 1 .. r. 7 H .3. 2r 6' Xbfl-Kgc‘? 6 x4; K6 2 :r: x+cz VQA-i 5 f-M’n " e-ngr -. K 7" 4.!" T -_ Z-—__é:‘x 1 r31 6 mix - z “ 5' “ a -. ” if” F Xfic "“7 K: 2”" XV: K6 Simplifying this expression: X r / ~25}, _ ~ZKgT . xC .... 7: . a. i:-.17.—.1);.Z.---<-s_...... , / “ e ""’(X‘f’*’f/-Xl/’ Kg 'Vz. -2KRT\ -£"k7 «(MAO—e j’Z'f'ff Z J :‘ _. ~2F~g7 .. f ~[x v H: - e (x r.-— :3)? lim. vs 1’31 X ' Z _ .--.“ ... V”) X’l«";+y”—27"% /X1/a_-1---Z‘/ Removing the constants : Val/3 CA7: J. I -" a“; 51") (‘9 2mg , ji— :t) Ad; : ---.- Fifflpv‘ Fffipg ,0- fifififfi} r‘Z-l‘i fr - ,3 ___-___:_1+ ”...... “37"? PSInQ [‘3 ... 3 —'=€:;th(. As mentioned in the development of the pressure drcp equations, the value of (.f§%;:;) will be almost unity and hence will be neglected in E the remaining calculations. —-~--4'----—- - 5,-,, e ,2 ”‘3 a 9 -03.: ___“- -..- ___ _2 -..---_- . .. 7 l - - ,. —‘~ - ~ Jf/lfya' I/iC/yp tat-”é :C/7p 9 Tg 53/,” + w \a In I) 100 13’- ,F: (x2.- —- 2 m 325, H (.9 42103.7 U" : ...—.....- .m--.-..-...... .. .- .. -... . ..-... .4..-.......-..,.... ....._........---.... "Ham"... 5 p (K'Af ' If. ..._...... K“ - ~ -,. p—‘TMN -"“" “3".“ j 'r‘," .7. ~ F 0- +V12 j are (H .- ,. :7 + V5; f. If“... M: ~2mj‘f: war? 2 m J' ___..-“ ‘ — ‘_‘:_____:‘" _. MW ‘- Z ‘/ m 3 0 VOL {5; 6‘3; -- 2 f)'“) ."I 2b,”, r.‘ CI; C4914: fl/rn , JZJL r (H 3:» i‘r-f oqflfii (I // ~2an f r ,2 r7: :3 D flv'lg’fjc/ijb‘ ‘1‘.“2’} "2' Sin 0) ’.\ _______, ___,__ _-..____ __,,,________, ..__ _ .1" .-..__,_ ___” I r“_ 7/; : ....-- \// 81:7,; 3; 404me //€CH (21L 5,. 9+; Lr )__Zm9 3.5:” Derived assuming "C" equals a constant. Valid for RN between 103 and 10""5 . Section III The derivation of equation 8, in which "C", as a function of "RN", equals 0 4 r 575,18 as follows: Restating equation 3: "' " - 9" ' I! III- F \‘ 0' “E - 6’52. ,7..a(-s;a-x-;>‘ ,5”: a... C __ j; 4;"- T‘“ - ‘ ‘ "" 571——-—--— ~ «n.1, m, 1.9/2 0 7. ,2 ’77 A) v \ I? IC. (.4 LBtRN’X W/swhere X .-: a”: 101 Substituting this into the expression for "C" yields: dIcfi X ( Va.“ 1:3} C 3 it). 4 I‘" Now replacing the terms in equation 3 with these notations: 1 (7’11; 4L6? * ‘2 -514 .' 2‘~v:"—- r‘—-—"’ dr f X41" . WA r g) y - 4 d7; F . H ..-: = o 4 My. ... + +4.4: (7 - .,r:‘-- :‘—.7 dr ‘ ‘) 2< * “j '“' ——-= = 0.4 r-u:;f'°~ 0.8 by w + 0 4 r7/3 + 41402,;— V I’ a 7 4 0 ’L-I: .... y, ‘15:; 6 _ Z "’ '~'-' 2: -z/;"(a4 r ~7) + 7/;(- 9.9% 75,-f4.:))+ 0.40“ 145.2% {no v; --z Simplifying this expression by letting: " U" 4 r v ’y" 3 L4, 7 .y "" I” .- 9‘ ”'flérvk—‘dr/‘X’ .9 L2 adf‘f J94J£ a “3:353 The above equation now becomes: dug q .‘f L 7f" , ' “ . ' . cf f- / 5 i “o “ 3 Separating variables: 'J/ M- cf 7' = P , -1”--.Lmn.__mfi- ‘ - ,‘ " /_'_ ‘ ’ , . - (5 .- ’ ' ' I _, . f a“- .1 Integrating both sides: 74. __ / / ’9 4:} . '1 ' if " /f"":," A bf“ ”'26 "' ” /* 2“ Q ' --‘ .1 + . U ‘2‘. r r ,' :‘ 102 Where: 2 ... Q : CZ " 4‘ («1 Cl Since the initial conditions are v; = 0 when 7‘ = 0 , the constant of integration (0) is equal to: C: —-{-—/h 02-. Q n 7": / /hCZCM3+CZ—~fa)ffz+/5)7 ”7:“ (26‘v:+6‘2+/a)(6‘ WU ‘2‘? ... + "if“. ‘ 7‘: ___”,7/ (:2 Q 46 V5 ..-- VIQ 36,6271; —0 25, “IL/3m“ +313 Transposing this into eXponential form: .. 2 ... 2 63;)(926 .:*Q ZQVZM+Cz)—cz - Q 7" 46/7/13 “/2?— Solving for"v;: lécfi '5 ‘_ Q __ ZCSDZ/T +£Z:—-—C2f0_ 5’- -7/(I$ e" a"; 6‘ 7/5 6.7/22— 2 48/7/31/5 :0 75(26162'261F)+€£’Q 7C2 8_TW:_E£.C ffiA4L/Wfiem :0 e 7V? -T .. r? V5. +4T,‘VZVQ e 7/: fi.. M--—*“.-"‘-w-filim_fl-*' ‘w— I 2 1'"; “Ti/_- Q'Q 7'“; C W‘Qe ... F" In 103 Determine the terminal velocity vhich the :nrticles will reach by letting t—-’00 2, [InL‘Ug : (Q —.<:@ f—eoo ZC€2~2CZVW “LI" €22,461? C, — C22 5 2652 ‘24/622 -45‘, C3 The constants for the above equations are: _ 0.25;:63; __ fs‘ ~ mg 2.0 O ‘3: m9 ”790/ .2 ‘3' = (9.}? Ififit/€;,1{E}1f_J229/i#”(4ik ~Lc;- __ E? :E;,, 69 M9 "290’ ' H .25 Derived assauninf 'C =O-4+g-’—8-Valid for "PM" between 100°5 and 104 . Section IV This section of the Appendix will deal mdth the development of the orifice equations. Fig. 39 will be used as a basis for the development of equations 11; and 15 . fl/R’ Q‘ —> FLOW Fig» 39. Crossection of conveyor pipe near the orifice. lOu Writing the energy balance betwe‘n points "1" and "2" (see Fig. 39) gives: v2 )9 “ll—2' P ’ _ .2 2. + ’ +2, - —— +—-—— +22 (9) 23 G 29 & Since the pipe lies in the horizontal plane, 31::22. Collectinv terns and assuming that Alvlzzszzs z #2 2. jag—71’; 23 H/“Hz This expression is valid only for pressure differertiels less than ten inches of water, as was nrovicusly mentioned. Solvinr this equation for "v2" rivesz zamrfil 1Q : / — '92)2' fl Since the actual velocity at point "2" will never reach the above theo- retical value due to frictional losses, it is necesserf to introduce a velocity correction factor (Cv)' 2 3 (HI _H1) ’0 142 :: CTmr- I .— ‘12? 43 ( ) 0,) Substituting Q/l? for v2 in equetirv: 10 "ields an expression for the flow rate in fts/soc. Q=/92C‘ 29(f6_fi2) ’ (0, However, due to the reduced area of the stream at the pressure tar, anoth- er correction factor (CA) must be included in the above equation. For con- "n H venience, "CV" and 99 will be lumped into one coefficient - "C". 2 9 (HI " H2) (:0 / — (ea-)4 To reduce the number of steps required to calculate "Q", the pressure dif- 62= n72 ferential will now be converted from feet of air to inches of water. fi/‘i Afw 6.2.38 "h" equals head in inches of water Z: From the equation of a perfect nae: 9 3 \1 So; :7 6 6Zo387-53.3_ T H nap - 276.8735 Hm" L In this expression, and "P" are, respectively, the absolute temperature and nressure of the surrounding air. Substituting this value of "H" into equatimu 11 Fives: 024 ’ “of (226/? This equation can be further simplified by assuminr the pressure and tangereture of the surroundinc air to be, respectively, 29.92 inches of Hg and 50° F. Therefore: T absolute 460-+50 =-510° absolute. P absolute 3.11.3.3. 13.6 x 62.38 2117 ;f?:,/rt.2. .LW . . . i 2 . . assum;ng T==SlOO absolute ard P==Pll7 fi/ft. , equation 11 can be written 853 Q: 6‘56 ("1‘72 543—24 of air can be found by substitutins vlfil for Q in equation f6,- h, (73) "he velocity 13. This substitution yields: 65.6292C =fl//_(0 £2 M—hz ?implif7ing3 656C W/(Ogy / 0,-51 {/4) Var any given pipe and orifice, equation 1h “U,” = If x/ZM There Kl 3’ 67‘5Té;<: and 04 .. _ /‘0§)’/ Ah—h,hz The value of "C" riven by Ref. 29 reduces to: is 0.80. For this specific installation, 01::3.99 inches ard 022:3.l?5 inches, thus 8 6.516 x 0.80 .3 . 25' (3.89 4_, 44 3125- Equation 1h rmm'becomcsz V,” = 44.25%}, 05) The limitations on equation 15 are: 1. Valid only for this installation. 4. Cerchd assuminu T 3 500 F. 2117 fl/rt.?. v. Derived assuming P Section V The possibility of error due to the compressibility of the air in a long pipe will be examined assuming a pipe to be 150 feet long with steady state conditions existing. The static pressure loss along this pipe, and thus the head differential, will be assumed to be 15 inches of water. If the temperature is assumed to remain acrstant, the following can be written: 1 .. D . f? /' ‘ ’2 /; Where "P " will be assumed to equal LBl in hos cf water. This fixes l u n f, (C 4, .0 ‘r‘ .a' P2 (at Ll! .lnpllLs.) CL Water. This gives a volume ratio of: V, F? 4/6 , -—-- = —— = ---- : ayes V2, «to {\E/ - Since volume is proportional to area for a given length of pipe: /7 I r .. '. / ’ 7 :5 0, 3 hi {’3 [1" ”’ (1' C" K" 6 ”2 tow since Q = VA: (2 _ (9.5%») = o. 966 v,’ I; I H J t/ _ C? 2 f9 1 so V = c.9oo V1 with _;h equal to 15 inches of water. Section VI The possibility of error due to the loss of air through the bucket wheel feeder air vent: will now be considervfi. The volume of one chamber in the cuzket wheel feeder is 0.9353 ft.3. Since the paddle wheel rotates at to R.F.V., the air loss r‘r minute is as follows: fl air loss (#/min.) : .0“63 x x L0 3 9.71 ft.3/min. C This aetounts for the loss due to the rotation of the naddles. An ad- I ditional loss of 3 ft. /min. will be added to actount for any additional loss due to air leakage by the iadiles. ihis Liv~s a total loss of ll.7l ft. /min. by assuming the air valoxity within the pipe to be ."1 ‘ .i ,-:..4‘ ,. . ‘fi " ,3 - lei 1t./sec., the dll iljw rate would oe /00 ft. /mih. {‘ .203 % loss 2 11.71 X 100 = 2.95% 300 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 109 RE PERENCES Albright, C. W., and others. "Pneumtic Feeder for Finely Divided Solids." Chemical Engineering. 56: 108-111. June, 1949. Allen, J. R., and others. Heating and Air Conditioning. 6th ed., McGraw-Hill Book Company, N.Y., 1946. Belden, D. 8.. and Kosscl, L. S. "Prusure Drops." Industrial and Engineering Chemistry. 41: 1174-1178. June, 1949. Barge, O. I. "Design and Performance Characteristics of tho Flywheel Type Forage Hamster Cotterhoad." Agricultural Engineering Journal. 328 85.910 beruary, 19510 Bcsley, H. E., and ‘Humphrios, W. R. "Machines Designed for Harvest- ing and Storing Grass Silage ." Agricultural Engineering Journal. 228 125-1260 April, 1941. Brown, A. I., and Harko, S. M. Introduction to Heat Transfer. 2nd ed., McGraw-Hill Book Company, N.Y., 1951. Bryson, A. E. "An Experimental Investigation of Transonic Flow Past Two-Dimensional Wedge and Circular-Arc Sections." National Advisory Comaittee for Acrnatuics. Technical Note 2560, Washingtm, November, 1951. Challsy, B. "The Pumping of Granular Solids in Fluid Suspension." Engineering. 149: 230-231. March, 1940. Cramps, W. "Pneumatic Transport Plants ." Chemistry and Industry. 44. 207-213. 1925. Dallavalle, J. M. Micromeritics. 2nd cd., Pitman Publishing Corporation, N. Y., 1948. Davis, R. F. "The Conveyance of Solid Particles by Fluid Suspension." Engineering. 140: 1-3. July 5, 1935. Davis, R. F. "The Conveyance of Solid Particles by Fluid Suspension." Engineering. 140: 124-125. August 2, 1935. Duffcc, F. W. "Efficiently Filling the Silo." Agricultural Engineer- ing Journal. 6: 4-12. January, 1925. Duffso, F. W. "A Study of Factors Involved in Ensilago Cutter Design." Agricultural Engineering Journal. 7: 84-87. March, 1926. Duffcc, F. W. "Mochanizing Forage Crop Handling." Agricultural Engi- neering Journal. 20: 47-49. February, 1939. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 110 Duffee, F. W. "New Developments in Forage Harvesting." Agricultural Engineering Journal. 24: 182-183. June, 1943. thning, J. T. A Treatise on Hydraulic and Water Supply_Engineering. 4th ed., D. Van Hostrand Publishers, N.Y., 1884.' "Fluid Mechanics." The Encyclopedia Americana. 11: 40lb-401d. Goldstein, S. ‘ggdern Develgpments in Fluid Mechanics. University Press, Oxford, England, 1938. Harin, O. H., and Molstad, M. C. "Pressure DrOp in Vertical Tubes in Transport of Solids by Gases." Industrial and Engineering_Chemistry. 41: 1148-1160. 1949. Jennings, M. "Pneumatic Conveying in Theory and Practice." Engineer- ing. 1508 361’363. 194C. Kleis, R.W. "Moving Feed From Storage to Feeding Point." Agricultural Engineering Journal. 35: 655. September, l95h. Lapple, 3. 2., and Shepherd, C. 5. "Calculation of Particle Traject- ories." Industrial and engineering Chemistry. 32: 605-616. May, 1940. ‘ Lees, A. "Crop Moving by Air Force." Farmer and Stock Breeder. 52: 1493. 1948 Longhouse, A. D., and others. "The Application of Fluidization to Conveying Grain." Agricultural Engineering_Journa1. 31: 349 Jilly, 19500 Longhouse, A. D. "Performance Characterisitcs of Long Hay Blowers." Agricultural Engineering Journal. 30: 439-441. September, 1949. Hatheson, G. L., and others. "Dynamics of Fluid-Solid Systems." Industrial and Engineering_Chemistgy. 41: 1099-1104. 1949. Miller, J. T. A Course in Industrial Instrument Technology. United Trade Press, London. Over, E. The Measurement of Air FIOW. Chapman and Hall, Limited, London, 1927. Pinkus, 0. "Pressure Drops in the Pneumatic Conveyance of Solids." Journal of Applied Mechanics. 19: 425-431. December, 1952. Rhodes, T. J. Industrial Instruments for Measurement and Control. McGraw-Hill Book Company, N.Y., 1941. 33. 34. 35. 36. 37. 38. 40. 111 Segler, G. Pneumatic Grain Conveyin . National Institute of Agri- cultural Engineering, Wrest Park, England, 1951. Segler, G. "Calculation and Design of Cutterhead and Silo Blower." Agricultural Engineering Journal. 32: 661-663. December, 1951. Sternbruegge, G. W. "Air Flow in the Main Duct of a Barn Hay-Drying System." gAgricultural Engineering Journal. 27: 217-218. May, 1946. Stewart, E. A. "Cutting Ensilage With Electric Motors." Agricultural Engineering_Journa1. 9: 175-179. June, 1928. "The Pneumatic Transport of Grain." Engineering. 111: 205. Febr- mry, 19210 Vogt, E. G., and White, R. R. "Friction in the Flow of Suspensions." Industrial and EngineeringiChemistry. 40: 1731-1738. 1948. Whisler, P. A. "The Field Forage Harvester." Agricultural Engineer- ing Journal. 28: 497-499. November, 1947. Whisler, P. A., and Frushour, G. V. "Engineer Advance Art of Making Grass Silage." Aggdgyltural Engineering Journal. 34: 315-318. May, 195:5. W Zink, F. J. "Specific Gravity and Air Space of Grains and Seeds." Agricultural Egggneering_dournal. 16: 439-440. November, 1935. goon use cm :3 n, («a 5:!)th SD53? - ' ,v ' Int/1 f {3 Vi? . ‘. .7124." JUN z 6 AUGll Demco—293 MICHIGAN STATE UNIVERSITY LIBRARIES 03046 9J32 3 1293