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Do not write until you have something to say. Think first; then write. In order to be understood, you must know what you wish to say. Clear writing is the consequence of clear thinking. Therefore consider your subject well before you begin to write; ruminate on it; marshal the salient facts in your mind; saturate yourself with the ideas you wish to express and with cognate ideas; then express yourself deliberately. If you are bubbling over with your subject the words will come, but you might as well expect to sail without a breeze as hope to give life to words without the living thought. Here I may advert to the fact that among the uneducated it is a common expectation to acquire the knack of writing without taking the trouble to study the art of literature. I overheard a woman in a suburban train remark to her neighbor: "I'd like to be able to write well without stopping to think about it". She was one of many that would like to do a thing well without the trouble of thinking; but it cannot be done in respect of anything to which thought is essential. The possession of a good voice does not justify a person in expecting to sing successfully to a large audience; before singing in public one has to master the technique of singing; one has to learn first how to breathe properly, how to enunciate, and many other things. The successful singer is an artist, not a megaphone. Most of us would regard a man or a woman without any training in the art of singing as a fool or an impostor if he or she were to give a public concert, yet we do not recognize the equal foolishness and imposture of persons that write books before they have studied the technique of writing. That is why so many books are unreadable, and why many books by clever men are difficult to read. They start to write books before

Jan 1, 1931

By Arnold Hoffman

A RESPONSIBLE steel executive recently declared that scrap shortages, despite fantastic prices reaching up to $50 per ton, are responsible for the loss of 140,000 tons of steel a month and that in March 1947 alone 25 more steel furnaces could have been operating were it not for scrap scarcities. His answer to this serious situation was to ask for a speedier flow of scrap and also abolition of Government control over pig iron distribution. It would be more logical, perhaps, if an answer to this growing problem of scrap deficiency were sought within the steel industry itself. As long ago as 1933, L. B. Lindemuth, a consulting steel metallurgist, warned the steel industry that a shortage of scrap was inevitable and that beyond 1938, adequate supplies for open-hearth furnaces could not be expected. The outbreak of war, with consequent phenomenal demands on the industry, accelerated production of steel and further worsened the scrap situation. Today we are suffering from a condition which could have been prevented had the industry been more far-seeing and provided for an inevitable contingency. However, better late than never, and measures can now be taken to alleviate permanently scrap shortages in the future. This can be done by greater utilization of heavy sinter which experience proved is an excellent substitute for scrao and lump ore.

Jan 1, 1947

This discussion of the paper of Chester W. Washburne should have been printed following the remarks of H. A. Wheeler, in Bulletin No. 100, April, 1915, pp. 835 and 836, but was inadvertently omitted. ROSWELL H. JOHNSON:-There is one reason why the hydrostatic interpretation of gas pressure is not wholly acceptable. As we go clown in the sands we seem to get excesses of gas. Particularly in this field it becomes excessive in quantity relative to the amount of water in the sand. If this holds in other fields as well it must mean that there has been an ascension of water, because these sedimentaries when laid down, were filled with connate water. If we do get an ascension of connate water, produced by some such phenomena as its expansion by heat or by the formation of new gas by pressure upon organic materials at great depth, we can hardly expect the pressure to be controlled merely hydrostatically. * In reply to Mr. Wheeler's inquiry as to gas wells with pressure higher than hydrostatic pressure, I would cite the original wells given by Orton on which he based the hydrostatic theory. He used in his calculation a head of 600 ft. above tide, assuming the outcrop of the Manitoulin Islands to be in Lake Superior, whereas the Trenton does not outcrop at Lake Superior. The Manitoulin Islands are in Lake Huron, the level of which is 580 ft. above tide. No allowance is made for the lower density of the fresher water near the outcrop, the weight taken for the whole column being the water of high density found at the wells.

Jan 5, 1915

Discussion of the paper of E.. C. LEE, presented at the St. Louis meeting, October, 1917, and printed in Bulletin-No. 130, October, 1917, pp. 1825 to 1832. H. M. WILSON, Pittsburgh, Pa.-The statement ill the paper of T. T. Read, "Increasing Dividends Through Personnel Work;" that the offering of substantial money rewards for avoidance of accidents is much more effective than mere propaganda or education respecting accident prevention, is a, point fully substantiated in the experience of insurance inspection under workmen's compensation acts. The first year under the Workmen's Compensation Law in Pennsylvania, during which over 2000 mines were tinder the observation and protection of the inspectors of the insurance companies, has resulted in several inspections of each mine, a splendid cooperation .between the operators, the State mine inspectors and the insurance inspectors, and an average reduction in premium rate for insurance from $3.83 to $2.77, a reduction of more than $1 per $100 of payroll, on an average payroll of nearly $100,000,000, In other words, the insurance companies have

Jan 1, 1918

By R. S. Wagner, H. Brown

Criteria for nucleation with the aid of twin planes during crystal growth from the melt are discussed. It is shown experimentally that bismuth crystals can grow from a subercooled melt in a twinned bismdtic form. A mechanism of growth based on the presence of at least me twin plane is proposed. It is well known that faceted growth can be observed in crystals grown from the vapor phase, dilute solutions, or from the melt. Faceted growth, in which the crystal is bounded by its slowest growing faces, will occur if the growth rate is strongly orientation dependent. The addition of atom layers on a facet plane can only occur by two-dimensional surface nucleation or with the aid of an imperfection. Nucleation with the aid of dislocations was proposed by rank' and observed to be of particular importance in crystal growth from the vapor phase. Nucleation with the aid of two-dimensional imperfections, notably twin planes, was suggested by stranski2,3 and Frank.4 A twin plane, terminating at the growth interface, can form a reentrant step at which nucleation can occur at a much smaller super-saturation (or supercooling) than required for two-dimensional surface nucleation. Nucleation by a twin plane usually results in a fast growth rate along a crystallographic direction parallel to the twin plane. Such a nucleation mechanism, based on the presence of a twin plane, has been used by Dawson5 to explain the growth and morphology of sheet-like crystals of paraffin n-hectane. In recent years more evidence was found that nucleation by twin planes occurs frequently in crystal growth from the vapor phase and from dilute solutions, for example, in cadmium,' barium titanate,7 silver,8 silicon9 and gallium arsenide.10 In crystal growth from a supercooled melt, however, nucleation by twin planes has so far only been observed in materials with the diamond or zinc blende structure. Bennett and Longini11 were the first to recognize the important role a single twin plane plays in the growth of germanium dendrites. Subsequently, it was found that a prerequisite for continued propagation of germanium dendrites is the presence of two parallel twin planes which form a self-perpetuating system of nucleation sites.12 Sili- con and some III-V compounds such as InSb also grow dendritically by twin plane nucleation. It appears that the following criteria must be satisfied in order that nucleation with the aid of twin planes can occur: A) The growth form of the material must be faceted." B) The formation of twin boundaries, by a fault in layer sequence during growth, by plastic deformation, or by an accidental meeting of properly oriented crystals, must be possible. C) Twinning must form a reentrant step where the twin boundary terminates at the faceted growth interface. D) These three conditions are necessary, but in certain cases not sufficient for continued crystal growth with the aid of a twin plane. Depending on interface morphology, a combination of more twin planes is sometimes required to form a self-perpetuating system of nucleation sites. This investigation was carried out with the idea in mind that nucleation with the aid of twin planes is a more general phenomenon and should occur in those materials, grown from a supercooled melt, which satisfy the criteria outlined above. It has been found that crystals of high-purity bismuth grown from a supercooled melt can grow by the aid of a twin plane. In the first two sections the faceted growth form and the twinning elements of bismuth are discussed. In the last section prismatic crystals of bismuth, which appear to grow with the aid of a deformation twin are discussed.

Jan 1, 1962

By R. B. Schluter, M. M. Fine

A process for winning copper from pelletized chalcocite concentrate without matte smelting and converting is under development at the Twin Cities Metallurgy Research Center of the U.S. Bureau of Mines. The new procedure includes a two-stage fluid-bed treatment in which the pelletized concentrate with 33% Cu and 7% S is first desulfurized to about 0.5% S in an oxidizing atmosphere, and then metallized by reduction with hydrogen. The reduced product is melted with flux to separate metallic copper from the gangue. The metal must be refined to remove residual sulfur and iron. The pelletizing of the fine concentrate into mini-pellets prior to fluid-bed treatment is an important feature of the process, because it permits shorter reaction time, decreases dusting, and facilitates subsequent processing.

Jan 1, 1972

By David D. Rabb

Under the auspices of the Atomic Energy Commission, the Lawrence Radiation Laboratory of the University of California analyzed an experiment to provide information as to whether the chimney of broken rock produced by a deeply buried nuclear explosive could be "drawn" by conventional techniques. Since many low-grade disseminated ore-bodies occur in a granite media, the experiment took place in a granodiorite-quartz monzonite intrusive porphyry in the Nevada Test Site as a follow-up to the Department of Defense's Hardhat detonation in February 1962. For emplacement of the nuclear device, a 12 ¼ - in. pilot hole was reamed to a diameter of 44 in. and a depth of 950 ft in one pass using a Hughes multiple-cluster rotary bit. It was then cased to 36 in. ID. The center of the explosive device was located 938.85 ft below the collar. The yield of the device was predicted to be 5 kilotons, or an equivalent of 5000 tons of TNT; the yield was later confirmed by chemical means to be 5.4 kilotons.

Jan 3, 1964

By Robert A. Haney, Stephen J. Gigliotti, James L. Banfield

A series of investigations were made by the Mine Safety and Health Administration to evaluate the performance of various face ventilation systems as part of a program to reduce frictional ignitions of methane and to develop face ventilation systems that could be used with the line brattice more than 10 feet from the face. Tests were conducted in a full-scale laboratory model of a face area. Systems tested included unassisted blowing and exhaust line brattice, diffuser fan and spray fan systems. Systems were evaluated at air quantities ranging from 1.4 to 7.0 m3/s (3,000 to 15,000 cfm), and brattice-to-face distances from 1.5 to 9 meters (5 to 30 feet.). Tests were designed so that systems could be evaluated for the location of the high-point methane concentration in the face area, methane dilution capacity, and face ventilation index. The methane dilution capacity is the total amount of methane a system can dilute to 1.0 volume-percent. The face ventilation index is the efficiency at which the available face air volume is being used.

Jan 1, 1982

By H. I. Aaronson, S. M. Kaufman, G. M. Pound

WHETHER the carbides associated with bainite precipitate from the ferritic component of bainite, as originally suggested by Davenport and Bain, or from the adjacent austenite at aus-tenite:ferrite boundaries, as proposed by Hultgren, 2 remains in dispute.3-5 A recent metallographic investigation in this laboratory has shown that the bainitic carbides formed in a plain carbon hypo-eutectoid steel nucleate entirely within ferrite at higher reaction temperatures3 and in both ferrite and austenite at lower temperatures." The present investigation was undertaken to ascertain the effects of alloying elements on the nucleation sites selected by bainitic carbides. The compositions of the steels studied were as shown in Table I. Specimens of these steels were

Jan 1, 1958

By E. D. Peters

It frequently occurs in the establishment of reduction works, in an entirely new and untried mining district, that the metallurgist in charge finds considerable difficulty in determining the process best adapted to the ores which he receives for treatment. At the first glance it would seem easy enough to decide what style of furnace is best adapted for beneficiating any one class of minerals. If the ore possessed a quartzose gangue and was comparatively free from base metals, while salt could be obtained at a reasonable price, one would naturally resort to a chloridizing roasting, and pan or barrel amalgamation for the extraction of its silver contents. If galena or carbonate of lead was the prevailing mineral, and charcoal could be obtained at moderate figures, the blast-furnace would beneficiate the ores most advantageously. But if, as is usually the case in Colorado, the ores consisted of an intimate mixture of galena, zinc-blende, copper-pyrites, and noble silver minerals, associated with an overwhelming mass of siliceous heavy spar, or limestone gangue, the common reverberatory furnace can be used to the greatest advantage ; and, although the product is only a copper matte, I do not hesitate to affirm that it can be treated, and the silver, gold, and copper produced at nearly the same price for which silver and lead can be separated. In Germany, blast-furnaces are frequently used for this same purpose, both for argentiferous and non-argeutiferous copper ores; but any one who will take the trouble to examine the statistics of smelting at Fahlun, the Oberharz, and other Continental works of this description, will see that the expenses are far too great, and the production much too small to think of employing this method in our mining districts, where only the softest and most miserable kind of charcoal is obtainable. I propose in this paper to give an accurate account of the expenses incurred at the Mount Lincoln Smelting Works in treating the same kind of ore, and producing the same end-product in both blast and reverberatory furnaces. I have taken for comparison a favorable campaign of the blast-furnace, and a good average month's running of the reverberatory. In the blast-furnace estimate I have included the calcining and concentration of the matte produced during that campaign, as I always, when possible, concentrated the regulus made

COLUMBIA SECTION S. S. FOWLER, Chairman., J. C. HAAS, Vice-chairman, LYNDON K. ARMSTRONG, Secretary-Treasurer, 720 Peyton Bldg., Spokane, Wash. W. H. LINNEY. J. F. MCCARTHY. On July 15, 16, and 17, 1918, through the good offices of Secretary Stoughton, and the courtesy of War Department officials, Columbia Section was able to secure a series of moving pictures which were presented under the auspices of the Spokane Engineering and Technical Association.. The title was "The Way Out," representing the activities of individuals who had lost an arm, a leg, or both, yet whose apparent misfortunes were made the stepping stones to advancement in various human activities. The exhibitions were given at Natatorium Park in the evening, each of the three performances being attended by 1000 per-sons. Later the films were shipped to Kellogg, Idaho, where they were shown in the principal playhouse one evening to a full house. On July 31, 1918, the Columbia Section participated in the luncheon and other entertainment in honor of Alfred D. Flinn, Secretary of the Engineering Council, who made a trip through the country to meet different classes of engineers, members of the National Societies, for whom he had a message. The entertainment was under the auspices of the Spokane Engineering and Technical Association, Mr. Peter Mogensen presiding. The luncheon was held in the Elizabethan Room, Davenport Hotel, at noon, 35 engineers being present, of whom about one-third were our members.

Jan 9, 1918

By Nicholas J. Grant, Bill C. Giessen

The phase diagram Ta-Ni has been treated repeatedly; investigations up to 1958 are summed up in Ref. 1. Since then, an equilibrium diagram has been presented by Kornilov and Pylaeva.2 They found the following intermediate phases: Ta2N; (CuA12 type),3 "TaNi" (p phase, Mo8Co7 type), TaNiz, and TaNi3 (Ticus type).5 Of these, the crystal structure of TaNin remained unknown, and no further literature reference was found. According to Kornilov and pylaeva,&apos; TaNil melts peri-tectically at 1420°C. A 5-g alloy of Ta + 66.7 at. pct Ni was prepared by inert-gas arc melting using 99.95 pct Ta rod (NRC-MG) and 99.9 pct Ni shot (Fisher). The weight loss after three melts was <2 mg; a microscopically homogeneous ingot resulted. As shown in Ref. 6, no oxygen or impurity pickup needed to be considered under these conditions. Specimens were annealed for 15 hr at 1350°C, 15 hr at 1205oC, and 15 hr at 875°C with subsequent powdering and stress relief for 10 min at 1350°C, 15 min at 1205oC, and 1 hr at 875oC, respectively. Micrographs and X-ray analysis (114.6 mm Norelco camera, filtered CuK, radiation) showed homogeneous one-phase alloys in the as-cast state and at all three temperatures, all having the same powder pattern except for broad lines in the as-cast state. From this it is concluded that either TaNi, melts congruently or its melting behavior is a transition between the eutectic and peritectic cases. Since it was found that very slight surface contamination on stress relieving can considerably alter the structure of similar phases (e.g.,TaPt3),7 patterns before and after stress relief were also compared; they were identical except for line broadening in the non-stressrelieved condition, and two faint impurity lines in the stress-relieved samples. The powder pattern is presented in Table I. All lines were accounted for by indexing with a tetragonal lattice, 0Yh- I4/mmm , with a, = 3.154 ± 0.001A, co = 7.905 * 0.002i and c/a = 2.506. The atomic positions are: 1000; 1/2, 1/2, 1/2] + 2Ta(a): 000; + 4Ni(e): *(002); z = 0.333 * 0.002 This proves TaNi2 to be a representative of the MoSiz (Cllb) type. The variable parameter was determined by grouping the visually estimated intensi- ties according to their 2 indices, plotting their F values, and varying z for best fit, which was obtained at z = 0.333= 1/3. Since absorption was not considered, only the relative intensities with similar 28 can be expected to agree. The interatomic distances are presented in Table 11; the standard error is *o.o2A, resulting chiefly from the uncertainty in z. These distances indicate a coordination number 10 for both kinds of atoms and show that the pseudohexagonal layers along (110) are rather un-distorted. The mean atomic volume of 13.1A3 is close to the Vegard&apos;s law value of 13.3A3, showing

Jan 1, 1964

Jan 1, 1934

By Roger M. Nendick

The recovery of precious metals from heap leach solutions can be accomplished by two processes: 1. The Carbon Adsorption Process 2. The Merrill-Crowe Zinc Precipitation Process A brief review of the relative process economics is made. Each process presents certain design considerations that must be addressed during the evaluation and engineering design for the project. Discussion is presented on the design criteria for each process.

Jan 1, 1984

By Basil B. Zavoico

During 1938 the Russian oil industry, while able to increase its production 4.69 per cent above the preceding year, was not successful in correcting some of its basic difficulties, and the industry&apos;s position as it entered 1939 was unsatisfactory. The internal political difficulties of 1937 and 1938 took a toll in the oil industry as they did elsewhere in the U. S. S. R., further complicating the solution of the problems facing it, most important of which still remain: lack of experienced and responsible leadership, able to make quick decisions; undisciplined and migratory labor; and insufficient and often unsatisfactory quality of the various equipment needed by the industry and its ineffective distribution. Recent developments in the U. S. S. R. suggest that during 1939 the management will be granted more latitude and hence somewhat better results may be anticipated from the executive branch, provided, however, the "purges" do not recur. The labor should be better disciplined and should not shift as easily, owing to the introduction, at the close of 1938, of individual labor passports to all workers in the country, the principal purpose of which is to correct those two deficiencies. It is not anticipated, however, that the service of supply will show any appreciable improvement in 1939, partly because of inherent difficulties and partly because the manufacturers of heavy machinery are working primarily and necessarily for munitions. Production Production of crude oil during 1938 is estimated at 224,714,000 bbl., as compared with 212,742,000 bbl. in 1937, an increase of 4.69 per cent but 12.76 per cent below the planned output. While there were no major readjustments in the source of supply of crude oil, both the older districts, Baku and Grozny, were barely able to maintain their 1937 levels of production, the increased output being supplied primarily by the fields of Maikop and Ural Permian Basin districts. While exploration work was outstandingly successful in 1937, in 1938 no discoveries of any

Jan 1, 1939

By Basil B. Zavoico

During 1938 the Russian oil industry, while able to increase its production 4.69 per cent above the preceding year, was not successful in correcting some of its basic difficulties, and the industry&apos;s position as it entered 1939 was unsatisfactory. The internal political difficulties of 1937 and 1938 took a toll in the oil industry as they did elsewhere in the U. S. S. R., further complicating the solution of the problems facing it, most important of which still remain: lack of experienced and responsible leadership, able to make quick decisions; undisciplined and migratory labor; and insufficient and often unsatisfactory quality of the various equipment needed by the industry and its ineffective distribution. Recent developments in the U. S. S. R. suggest that during 1939 the management will be granted more latitude and hence somewhat better results may be anticipated from the executive branch, provided, however, the "purges" do not recur. The labor should be better disciplined and should not shift as easily, owing to the introduction, at the close of 1938, of individual labor passports to all workers in the country, the principal purpose of which is to correct those two deficiencies. It is not anticipated, however, that the service of supply will show any appreciable improvement in 1939, partly because of inherent difficulties and partly because the manufacturers of heavy machinery are working primarily and necessarily for munitions. Production Production of crude oil during 1938 is estimated at 224,714,000 bbl., as compared with 212,742,000 bbl. in 1937, an increase of 4.69 per cent but 12.76 per cent below the planned output. While there were no major readjustments in the source of supply of crude oil, both the older districts, Baku and Grozny, were barely able to maintain their 1937 levels of production, the increased output being supplied primarily by the fields of Maikop and Ural Permian Basin districts. While exploration work was outstandingly successful in 1937, in 1938 no discoveries of any

Jan 1, 1939

By AIME AIME

UNTIL recently, practically all geophysical prospecting in Australia was conducted by government departments, either by the Aerial, Geological and Geophysical Survey of Northern Australia or the New South Wales Department of Mines. At present, in addition, the Shell company is carrying out an extensive geophysical campaign in South West Queensland. The Northern Australia Survey has now been in operation for over six years, its work being carried out principally in the northern and central parts of Australia over an area of about a million square miles. At present this Survey is being brought to a conclusion but it appears certain that the geophysical section will be transferred to a Commonwealth Government department on a permanent basis. At present the officers of the Geophysical Section are preparing or have issued some 150 reports on their field work and also a special technical report on the geophysical practice of the Survey.

Jan 1, 1942

By A. S. Nowick, E. S. Machlin

ONE of the main criteria used to rate the heat-resisting properties of alloys is stress rupture.1 During a stress-rupture test a tensile specimen is held under a constant load at a constant temperature until it fractures. The chief measurement made during this test is the time required for rupture at the specific test stress and temperature. It was found empirically from a series of stress-rupture tests at a constant temperature that when the logarithm of the time for rupture is plotted against the logarithm of stress a straight line is obtained within experimental error.2~3 This method of showing stress-rupture data has been adopted by many investigators and the KACA.4 By interpolation and extrapolation from these plots, values of the stresses required to rupture the specimens (the rupture strengths) in 10, 100, and 1000 hr are obtained for specific temperatures. Alloys are then rated for a particular application on the basis of their rupture strengths at the rupture life that most nearly represents the application. Inasmuch as stress rupture is an important criterion in rating heat-resisting alloys, it would be advantageous to know the quantitative dependence of the time for rupture on stress, temperature, com- position, and structure. In order to obtain this information, an investigation was made at the KACA Cleveland laboratory during the spring of 1945. The theory of rate processes was used because it has been found to apply to certain processes such as chemical reactions, viscous flow, and creep that occur at a definite rate for given conditions. It was thought that stress rupture was such a process. An equation was derived that gives, for a given com- position and structure, the dependence of the time for rupture on stress and temperature. The investigation is part of a general program to provide information that will lead ultimately to the development of better alloys in order that the efficiency and power output of gas turbines used in aircraft propulsion can be increased. THEORY The theory of rate processes will first be discussed as a general theory. It will then be shown that if stress rupture of heat-resisting alloys can be treated as a rate process, certain equations must be satisfied. Later sections will then show that these equations are satisfied. General Theory of Rate Processes The theory of rate processes5 eveloped by Eyring and others has been applied to chemical reactions as well as to other processes such as viscosity of liquids and diffusion. In every case in which rate- process theory can be applied, there is a small subdivision, so that the macroscopic process is the net effect of all the small processes. This smallest subdivision is called the "unit process.&apos;&apos; For example, in a chemical reaction the unit process is

Jan 1, 1947

By R. D. Vaughn

The analysis of laminar flow of power-law non-Newtonian fluids in narrow, eccentric annuli is employed in this paper to discuss the problems of lubricant flow in journa! bearings and of errors introduced by eccentricity in experimental studies with concentric annuli on extruders and wellbore annuli. The velocity profile and pressure loss-flow rate equations are developed for the laminar flow region. In addition, the expected error in flow rate and pressure-loss measurements for concentric annuli as a result of eccentricity is determined. For example, a 10 per cent displacement of the core of an almost concentric annul us would cause a 1.8 per cent decrease in the observed pressure loss for a fluid with a power-law exponent n of 0.25. The corresponding increase in the observed volumetric flow rate would be 7. 5 per cent. INTRODUCTION Non-Newtonianism and eccentricity occur simultaneously in two engineering problems: (1) flow of lubricants in journal-bearings and pressure-reducing bushings, and (2) flow of non-Newtonian fluids in plastic extruders and wellbore annuli. The lubricants used for moving parts are often non-Newtonian in character — often they are plastic in behavior. A solution to the problem of flow of non-Newtonian fluids in narrow eccentric annuli is particularly pertinent to this problem. In all experimental studies of laminar flow of fluids in concentric annuli, such as in extruders and well casings, the error due to eccentricity must be estimated or studied. A number of publicationsl-4,6,7 have dealt with this problem for Newtonian fluids; however, I am not aware of work for non-Newtonian fluids. This work is directed to the non-Newtonian problem. Before the solution to the problem is given, the pertinent conclusions from the work on Newtonian fluids will be reviewed. Heyda 1 and Redberger and Charles 2 have published general solutions to the problem of the laminar flow of Newtonian fluids in eccentric annuli, apparently without knowing of the earlier work of Ca ld well 3 and Bairstow and Berry,4 which is reported by Dryden, et al. 5 Although several mathematical routes are encompassed by the work of these authors, the results appear to be equivalent. Redberger and Charles2 show that the error caused by eccentricity in concentric annuli is negligible for small diameter ratios (k < 0.5); however, for large diameter ratios (k + l), the error in the predicted flow rate can be as great as 100 per cent or more. Partial solutions to the problem are available from the work of Dryden,5 Tao and Donovan6 and Piercy, et a1.7 Tao and Donovan examined the case of flow in narrow, eccentric annuli (k + 1) with and without rotation of the annular core. These authors also reviewed previous work on this subject and verified their approach with experimental data. Dryden gives the solution for the limiting case of complete eccentricity or tangency. Piercy, et a l. published an early solution to the problem of narrow eccentric annular flow. The conclusions of Redberger and Charles2 and the experimental proof of Tao and Donovan6 both suggest that the region of large diameter ratios (k + 1) is of main interest and that the parallel planes approximation to the solution in this region is satisfactory. This method will now be extended to the laminar flow of non-Newtonian fluids in narrow eccentric annuli. THEORETICAL SOLUTION The geometrical aspects of the problem are illustrated in Fig. 1. To represent the non-Newtonian fluid the power-law model was selected. This model has many disadvantages which have been pointed out; nevertheless, its simplicity, its frequent and wide applicability justify its use in this work. Fredrickson and Bird8 and Savins9 have used it as a basis for a theoretical study of laminar flow of non-Newtonian fluids in concentric annuli.

Jan 1, 1966

Jan 1, 1928