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By Arthur F. Taggart

The major portion of the work described in this paper was performed by R. W. Young, † a graduate student in the department of Mining and Metallurgy, Sheffield Scientific School, Yale University, working under a cooperative agreement between the Hardinge Conical Mill Co., the Sheffield Scientific School, and himself. Since this cooperative scheme is at present in effect in the case of a considerable number of other students in the department and since it is the hope of the school that the privilege thus extended may be utilized even more freely in the future by mining and manufacturing companies, it may not be amiss at this point to give a summary of the general plan. Briefly it is as follows: A graduate student, whose undergraduate work in this or other universities shows promise of ability to handle research work, is chosen by conference between the company and instructor involved. The aim of the company in the agreement then entered into is to obtain the solution of one or more of the technical problems with which it may be confronted, or, at the end of 1 or 2 years, to obtain as an employee a man especially trained in its work. As a means to accomplish one or both of these ends, the company furnishes the machine, apparatus, or material to be tested and pays the student during his graduate work a small salary, usually just sufficient to cover his living expenses, tuition and fees. The aim of the student is special training along a line in which he is particularly interested, the attainment of his advanced degree, and the chance to show to his future employer ability to handle such problems as may be presented to him. In return for the financial aid which he receives he agrees to devote at least half of his working time to the special problem submitted by his company. The other half is devoted to study of the collateral subjects required by the department for the granting of the degree which the student seeks. The student further agrees to enter the employ of the company in question at a wage not greater than that paid in like positions to recent graduates not specially trained and to remain with his employer at such wage for at east 1 year. If the student is to obtain a degree, the special work forming the basis of his investigation must be such as will involve real research and not mere routine manipulation. The subject is chosen by conference between the three parties to the agreement. The work is carried on under the direct supervision of the instructor involved. The school furnishes the general laboratory and library equipment essential to the pursuit of any extended investigation. In

Jan 1, 1918

By W. E. D. Stokes

The application of aviation to mining and petroleum operations, on the basis of economy and attainment, has become a demonstrated fact. According to Dominion Government rccords, 30 Canadian companies engaged in air transportation with northland mining camps, carried 13,000 tons of freight in 1935, and in 1936 carried 16,000 tons. In addition, many mining companies used planes to transport prospectors with canoes, outboard motors, gasoline drums and supplies to remote locations, and one company maintained a plane to take radium-bearing ore from its mine on Great Bear Lake nearly 1000 miles south to the railway at Waterways, Alberta. Heavy pieces of mining machinery weighing 2 tons are being carried by Ford trimotor planes over the Andes, at an altitude of not less than 15,000 feet. At Bulolo, New Guinea, 17,500 tons of disassembled gold-dredging equipment has been flown over inaccessible terrain, while supplies and building materials for a community of 1000 whites have been transported by airplane. A 31/2-ton shaft was carried on one notable trip, while at another time an automobile, 2 tons of rice and a large safe went over the mountains in one plane. Fig. 1 shows an electric generator that was carried by plane to Bulolo. Many large American oil companies operated fleets of planes during 1936, ranging from fast, luxurious air liners for executives to elaborate geological prospecting units, ambulance planes, freight carriers and pipe-line repair crews. According to the U. S. Geological Survey, commercial firms photographed 16,291 square miles during 1935, while the Government compiled from aerial photographs by the Geological Survey in the United States 85,544 square miles. It was found that information could be determined in a fraction of the time required by surface methods. However, sounding a word of caution, a Commonwealth of Australia government report on aerial survey operations had this to say: It is necessary to repeat ad nauseam that aerial photographic survey is in no sense a substitute for geological investigation, though it is a very valuable adjunct thereto, and greatly facilitates and aceeleratcs geological mapping. There are many details

Jan 1, 1937

By G. J. W. Kor, F. D. Richardson

The sulfide capacities a1 1500°C of slags in the systern CaO + CaF, +Al2O3 have been measured by bringing samples into equilibrium with gas mixtures made from CO + CO2 + SO, + N2. The capacities are negligzble both JOY CaF, and CaF, + Al2O3 melts but when lime is present even at 20 wt pct capacilies as high as 30 x lom3 can be obtained. The results have yielded information concerning the liquidus at 1500°C and fluoride-oxide melts in general. The slags used in electroslag refining contain substantial amounts of calcium fluoride. Robinson and Grainger' report that good results can be obtained by using slags of the approximate composition 70 wt pct CaF2 + 30 pct Al2O3. It has also been reported2 that a mixture of 50 pct CaF2 + 30 pct A12O3 + 20 pct CaO makes a good slag for general use. In view of the fact that very low sulfur contents are claimed for ingots produced by the electroslag process. studies have been made of the sulfide capacities [c, = wt pct S (PO2/Ps2)1/2 at 1500°C. of slags consisting of pure calcium fluoride, and of its mixtures with lime and/or alumina. These studies have also provided information on the phase diagrams. The slags were brought into equilibrium with gas mixtures prepared from NZ + CO + CO2 + SO2. Because CaFz is volatile and also easily hydrolyzed. measurements were made of its loss in weight in various flowing gas mixtures. EXPERIMENTAL Procedure. The apparatus and procedure were the same as described previously. Both platinum and iridium crucibles were used (height and inner diameter about 1 cm), but those made from iridium were stronger and able to withstand a greater number of experiments. In each experiment two crucibles were set in an alumina support and 1 g of slag mixture was divided between them. The materials from each crucible were analyzed separately after being brought to equilibrium with the gas, and then quenched in the water-cooled end of the reaction tube. Materials. Alumina and lime were prepared as de-scribed previously.4 Calcium fluoride was obtained by igniting Analar calcium fluoride in a platinum boat at about 800°C in a stream of pure dry nitrogen: the product was cooled in a desiccator. The slags were produced from mixtures of the powdered constituents, these being melted together in the course of each equilibrium experiment. The sulfur analyses and the X-ray diffraction meas- urements on the solidified slags were made as described previously.4 From the latter it appears that the CaF2 contained less than 0.5 mol pct CaO. RESULTS Values of (ps2/po2) for the Gas Mixtures. The re-sults have been represented in terms of (ps, /Po,)"? for the various gas mixtures used. The va1;es of this function at 1500°C are listed in Table I: they were calculated from the data cited previously for calculations at 1350°C 4 Weight Losses with CaF, and CaF, + CaO. The re-sults of the weight loss measurements* at 1500°C for

Jan 1, 1970

By N. M. Levine, W. M. Fassell

In this laboratory study the problem of aerative conditioning to separate chalcopyrite and pyrite from cobaltite was simply effected with a sulfy-drate collector and pH by proper choice of mixing variables. It was shown that for a given impeller type and geometry, selectivity is governed by a relation between the Froude number and a modified power number multiplied by impeller tank-diameter ratio wherein the power factor is expressed as power intensity or horsepower per unit volume of contained pulp. In applying this approach to other systems, other criteria would be used in place of selectivity. The purpose of this paper is to show how solutions to problems of aerative conditioning of pulps may be enhanced by development of mixing parameters in a given system through application of a fundamental approach to agitation. The term aerative conditioning refers to a combination of processes which include mechanical gas dispersion, gas solution in the liquid phase, transport of dissolved gases and other reactants to the reaction zone, physico-chemico interaction within the liquid phase and/or at the solid surface, and, finally transport of products away from the reaction zone. Important elements of these processes are: 1) Air-Liquid Contact Area: This area limits the rate at which a given gas may dissolve in a given liquid. Thus, an aerative conditioning system should be designed for optimum gas dispersion. 2) Diffusional Factors: Such factors as concentration gradient, diffusion film thickness, and diffusivity may govern the rate at which dissolved constituents are transferred to the zone of interaction at a particle surface and the rate at which reaction products are transported therefrom. Thus, such systems would be designed for maximum turbulence to effect good mixing and to minimize diffusion film thickness. 3) Solids-Turbulent Liquid Contact Time: Sufficient time should be provided for interactions to take place at solid-liquid interfaces. The region of maximum turbulence for mechanical systems being in the impeller zone, it is important that the number of passes through this zone be optimized. This means that a proper balance should be struck be- tween flow and turbulent power to achieve optimum conditioning time. Too high a flow rate and insufficient turbulence may be improper if the reactions are diffusion limited. On the other hand, too much turbulent power and too little time in the reaction zone due to insufficient flow power may also be limiting. 4) Geometry and Impeller Design: The design of the conditioning vessel and the type of impeller employed are important factors in determining the relative distribution between flow and turbulent power and the degree of gas dispersion. Maximization of power input would be to no avail if the distribution between flow and turbulent power were improper or gas dispersion insufficient. 5. Physical Chemistry: The reactions between dissolved gases and solid surfaces may be limiting if gas solubility, activation energies and/or free energies are not favorable. J. H. Rushton, E. W. Costich, and H. J. Everett' have summarized the mechanical elements of the combination of processes listed in a fundamental mixing equation. This equation was derived by dimensional analysis and relates the physical variables for a single impeller, centered in a cylindrical, vertical axis, flat-bottomed tank. It is, where T is tank diameter in feet; H is liquid depth in feet; C is height of impeller off tank bottom in feet; S is pitch of impeller; L is length of impeller blades; W is width of impeller blades; R is number of baffles; D is impeller diameter in feet; Np is the power number, pg/dN3D5; P is power in foot-pounds per second; g is the gravitational constant, feet per second; J is width of baffles; B is number of im-

Jan 1, 1961

By C. D. Woodward

THE Anaconda Copper Mining Co. purchases 25,000 kw. of electric power for its mining operations at Butte Mont. This power is delivered, over duplicate feeders, in the form of 60-cycle, 2400-volt, three-phase current, to five compressor plants, where most of the energy is used for driving air compressors. At the compressor plants are located the switching apparatus for controlling the 2400-volt power and distributing it to the various mines. At these points, also, there are a number of motor-generator sets for converting the alternating current to 275-volt. direct current for the haulage systems. Pole lines convey the power from the compressor plants to outdoor transformer substations at most of the mines. When it is not economical to distribute the power at the lower voltages in the mines, transformers and motor-generator sets are placed at strategic points .underground. All power is purchased on a maximum-demand basis, therefore there is installed at one of the compressor plants an eight-element totalizing graphic wattmeter. This instrument records simultaneously the value of all power taken at the numerous points of delivery, which not only eliminates the diversity factor but permits load dispatching between compressor and pumping plants, and thus materially reduces the maximum demand from the power system. As most of the mine hoisting is done, by 90-lb. compressed-air winding engines, the air-compressor equipment for the winding engines and mining operations is quite extensive. The standard air compressor has a rating of 7500 cu. ft. per min. of free air, and most of the compressors are directly connected to synchronous motors. The synchronous motors are designed for 80 per cent. leading power factor, thus facilitating power-factor correction of total mine load. Consequently by cooperation with the power company, the voltage of the power received at the compressor plants is constant.

Jan 2, 1922

By R. T. DeHoff, F. N. Rhines

The problem of determining the number of particles of a phase distributed randomly in unit volume c an opaque matrix from measurements made on random plane sections is closely investigated. A formalized derivation for the general case is presented. Applications of this formal result are made to specific types of aggregates dispersed in a matrix; circles, particles with flat circular ends, cylinders, and constant shape aggregates of ellipsoids of revolution. Quantitative measurements of the average geometric properties of these aggregates are developed. In 1953 R L. ullman' developed a technique for determining, from measurements made on random plane sections, the number per unit volume, Nv, of particles imbedded in an opaque matrix. Using meas urements previously developed for volume fraction, vV,' and surface area per unit volume, .SV,= he was able to determine average volume, average surface area, and average dimensions of particles, independent of size distribution, for spheres and circular disks,' as well as for uniformly sized cylinders of any axial ratio.4 The technique is mathematically rigorous for the cases studied. Recent studies of this problem have yielded rigorous solutions for the general case of cylinders, permitting evaluation of NV independent of size distribution and with all axial ratios intermixed. Generalization to shapes having flat, circular ends has been deduced. A solution has also been obtained for the ellipsoid of revolution, independent of size distribution, but requiring a constant axial ratio in the generating ellipses. In the following derivations, as in Fullman's work, it is assumed that the problem is purely a combination of geometry and probability theory,that is,eithe the particles to be measured are imbedded randomly in the matrix, or a sufficient number of random plane sections are taken to make the sample representative. A relationship exists between the number of par- ticles of a given size and shape that may be situated in unit volume (Ny) and the number of intersections a random plane can be expected to make with these particles (Na). It is the purpose of the following section to derive this relationship. The probability of Intersecting Convex Bodies. Consider a convex, closed surface, that is, one for which no two surface normals point in the same direction, situated at some arbitrary position and orientation in a cube of material that is one unit long at each edge. It is not necessary to assume that this surface is symmetrical. Let planes be constructed in the cube parallel to the top face and at random distances from it. Those planes which lie between the two planes which are just tangent to the top and bottom of the surface will intersect it. The probability that a plane will intersect the body may be defined as the limit of the fraction of planes that lie between the two tangent planes as the total number of planes constructed becomes infinite. This fraction, in the limit, is equal to the distance between the two tangent planes, DV, divided by the total length over which planes are constructed, which has been taken as unity. If the body is now rotated to a new orientation, applying the same argument, the probability of intersection is again numerically equal to the distance between tangent planes. Let DV ($, 0) be defined as the distance between tangent planes of a convex body as a function of orientation, Fig. 1. The probability, Pr, of intersecting the body with a randomly oriented and randomly positioned plane, is then equal to the average value of DV (0, $) over all possible orientations. It may be easily shown that for a system of spherical coordinates the probability of finding an orientation between Q and Q + de, $ and $ + d$ is (1/4n) sin $ dB d$, so that This relationship may be applied to each body in an aggregate of convex bodies. In particular, if the bodies in an aggregate are classified according to size and shape, and the ithsuch class is considered, Eq. 111 may be applied to this entire class, the probability of intersecting any body in this class being

Jan 1, 1962

By H. A. Stacy

THE ability of galvanized sheet steel to withstand severe bending is of very great importance as relates to all such sheet material which, in service, is not used in the flat condition in which it is purchased. A "bend-test" clause is found in, all specifications for material of this kind. In the attempt to draw up a specification for galvanized sheet steel the subcommittee of the Federal Specifications Board having this work in charge, soon found that there was a surprising lack of published data and apparently very little available from manufacturing sources upon which to sustain or reject the various requirements embodied in the tentative specification which, in turn, had been based largely upon other specifications submitted to the subcommittee for this class of material. Specifications from 25 sources were received; 10 Government specifications, 10 from private users of such material, and five from manufacturers. The main points raised were: (1) The minimum mandrel thickness, expressed in terms of the thickness of the sheet tested, over which sheets with different weights of coating can be bent 180°, without serious damage to the coating; (2) the minimum radius of curvature on the inside of the angle in 90°-bends in such material; (3) effect of double seaming on the coating; (4) uniformity in the thickness of coating over a sheet, particularly as relates to the results of bend tests. In view of the uncertainty existing, it was considered very desirable for the subcommittee to conduct a series of tests in order to secure reliable information.

Jan 10, 1926

By Charles B. Dudley

THEO. N. ELY, Esq., Superintendent of Motive Power. DEAR SIR: It is now nearly three years since my first report to you on the subject of steel rails was written. That report, as you will remember, dealt principally with the question of the relation between the chemical composition and physical properties of steel rails and their power to resist crushing and fracture in actual service. Other matters were referred to or touched upon in that report, but the main question was, Why do some rails crush or break in service while others do not? You will doubtless remember that the principal conclusion arrived at was, that the softer rails are less liable to crush or break in service than the hard ones. Or, in other words, so far as conclusions could be drawn from the chemical analysis and physical test of 25 samples of steel rails which had actually been in service, these conclusions were that those rails which have the smaller amounts of carbon, phosphorus, silicon, and manganese are less liable to crush or break in service than those which have larger amounts of these elements. Or, again, looked at in the light * At the Lake George meeting of the Institute in October, 1878, I had the honor of presenting to the Institute, through the kind permission of the officers of. the Pennsylvania Railroad Company, the results of a study of twenty-five samples of steel rails, which had all been in actual service. Considerable discussion followed the publication of that paper, and there seemed to be a strong disinclination, especially on the part of the steel-rail manufacturers, to accept the conclusions presented. One of the principal objections urged against the conclusions drawn was, that they were based on too few samples; in other words, that no conclusions safe to act upon could be drawn from the examination of twenty-five rails. In view of this criticism it was decided to repeat the investigation with a larger number of samples, and with the aid of the experience gained in the first investigation. The results of this second study of steel rails are, by the permission of the officers of 'the Pennsylvania. Railroad Company, herewith presented to the Institute, with the sincere desire that they may aid in adding to our knowledge of this most important product. Like the previous paper, this is in the form of a report to one of the officers of the company, which will account for the style, and the manner of presenting the data

Jan 1, 1881

By R. E. Goodman, M. A. Mahtab

The, state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore, is considered an axisymmetrier body with axisymmetric loading. The initial vertcal and borizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-uise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses tire now reintroduced along with tile changed moduli and original boundary constraints. This procedure is repeatrd until convergent stresses are reached. The effect of nonlinearity on streases is examined for a 6,000-ft wellbore in a scbistose gnezss and Berea sandstone using results of laborratory triaxial compression tests. The results sbou that the effect is restrited to one well radius from the bottom periphery of the bole. Beyond a distance of one-quarter radius, the elfect of nonlinearity on stresscs IS almost always less than percent for the cases conszdered, The consideration of a static pressure inside the well does not magnify the effect of monlinearity on borehole stresscs. INTRODUCTION The terms " wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding (1) the behavior of the lined or unlined hole, (2) hydraulic fracture response, and (3) the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Toppingl and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (ol -o3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for tile gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (v) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of v with deviator stress application, but the rate of increase diminishes with confinement. The ET and v curves for the two rock types are tabulated in Tables 1A and 1A for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation. STATEMENT OF THE PROBLEM Given a state of stress in the ground prior to drilling a hole (initial stresses), we assume that

Jan 1, 1969

By R. W. Fountain, W. D. Forgeng, G. M. Faulring

Precipitation of the phase Co3Ti (Cu3Au type) from a Co-5 pct Ti a11oy has been investigated using single-crystal X-ray diffraction techniques. Oscillation and transmission Laue patterns of specimens aged for short-time periods at 600" C indicate the formation of titanium-rich and titanium-poor zones coherent with the {100} matrix planes. Longer aging times at 600° C establish that the equilibrium phase also forms on the {100} matrix planes as platelets. These observations are corroborated by electron metallography; electron diffraction studies show the phase Co3Ti to be ordered. A probable sequence of the precipitation reaction is discussed. A previous publication by two of the present authors reported on the phase relations and precipitation in Co-Ti alloys containing up to 30 pct Ti.1 The results of this investigation established the existence of a new face-centered cubic inter metallic phase, ranging in composition from about 17.0 to 21.7 pct Ti at temperatures below 1000° C The decomposition of the fcc supersaturated solid solution was studied employing hardness and electrical resistivity measurements. The changes in hardness upon precipitation in alloys containing 3, 6, and 9 pct* Ti were found to be associated with an initial increase in hardness followed by a plateau and then a second, more pronounced hardness increase. Investigation of this behavior by electrical resistivity measurements suggested that two different kinetic processes were involved, which, when interpreted in terms of the kinetic relation,2-4 indicated that initial precipitation was in the form of thin plates. On continued aging, the plates impinged during the growth process. The general features of these findings have been confirmed by Bibring and Manenc,5 while, in addition, they report the phase to be ordered. The present investigation was undertaken to provide more definite information on the structural relationships between the precipitate and the matrix. EXPERIMENTAL PROCEDURE Single crystals of a (20-5 pct Ti alloy were prepared from the melt employing the Bridgman technique. Poly crystalline rod, 1/2 in. in diam, prepared from vacuum-melted material, was machined to 3/8- in. diam to remove any surface contamination that may have resulted from hot-working. The crystals were grown under a purified hydrogen atmosphere in high-purity alumina crucibles heated by induction. Considerable difficulty was encountered in attempting to grow monocrystals because of the high melting point of the alloy and the high solute concentration. However, one crystal about 6 in. long was obtained which was essentially a single crystal except for one or two very small grains around the periphery. The as-grown crystal was solution heat-treated for 24 hr at 1200°Cin a purified argon atmosphere and water-quenched. One-quarter-in. slices were taken from each end of the solution heat-treated crystal for chemical analyses, and the remainder of the crystal was mounted and oriented by the back reflection Laue Method. The chemical analysis of the crystal was as follows: Pct Ti Pct 0 Pct C Pct N Pct H Pet CO 5.29 0.08 0.004 0.002 0.0003 Balance By proper tilting of the crystal, it was possible to obtain slices 1/32 in. thick of [loo] and [110] orientation. The solution heat-treated crystal slices were sealed in silica capsules for the aging treatments, with titanium sponge placed at one end of the capsule to act as a getter. All slices were water-quenched from the aging temperatures, the capsules being broken under the water to ensure a rapid quench. Thinning of the slices for transmission X-ray studies was accomplished by a combination of mechanical and electrolytic techniques, the final thickness being about 0.1 mm. Laue patterns of the solution heat-treated crystal indicated that no strain was introduced by the thinning technique. ELECTRON METALLOGRAPHY After X-ray examination, the structural changes attending the precipitation were followed by examination of direct carbon replicas of polished and etched surfaces of the single-crystal slices and extracted phases. The earliest indication of significant structural change was observed after aging at 600°C The structure of a heavily etched, solution-treated crystal is shown in Fig. l(a). Aside from the etch pit pattern, no regularity of background structure is observed. On the other hand, in the background of the specimen heated for 500 hr at 600°C, the etching pattern shows a directionality indicating the influence of minute precipitate particles, Fig. l(b). On electrolytic dissolution of this specimen in 10 pct HC1 in alcohol, a large volume of very small, flattened cubes

Jan 1, 1962

By J. C. Savins

The practical analysis of the hydrodynamics of the wellbore has long been a subject of interest to engineers. This paper presents a simplified solution to the problem of computing the pressure drop for the flow of drilling mud in the annulus of the wellbore. This solution is, however, an exact and rigorous solution under the assumptions which have been imposed. These assumptions are that the drilling fluid is a Bingham plastic fluid* and that the annulus is formed by two concentric, stationary, cylindrical pipes. It is further assumed that the fluid is incompressible and that its motion is isothermal and in a steady state. This problem under the same assumptions has been attacked by previous authors. Beck, Nuss and Dunn' proposed that the equation for the flow of a Bingham plastic fluid in a cylindrical pipe could be applied to an annulus if the pipe radius were replaced in the equation by the hydraulic radius. This equation, known as the Buckingham-Reiner equation' (see Appendix 1), was also used in an approximate form. Van Olphen pointed out that even for a simple or Newtonian- fluid the pipe equation (Poiseuille's law) could not be converted to the Lamb equation escriptive of flow in an annulus (see Appendix 1) by using the hydraulic radius. Van Olphen further attempted to give a solution for the annular flow of a Bingham plastic fluid by introducing approximations similar to those which have been used in the case of the Buckingham-Reiner equation. Other attempts to provide approximate or exact solutions have been made by Grodde' and by Mori and Ototakeq. The present authors some years ago in unpublished work derived the correct expressions relating the pressure drop and flow rate for this problem. It was found that the solution consisted of two simultaneous equations, one of which contained a logarithmic term. Thus, obtaining numerical results for any particular case of interest involves very tedious trial-and-error computations. Very recently Laird presented the correct derivation of the two equations which are given in full detail in Appendix 1. In order to reduce the amount of calculation time which would be involved in providing a complete tabular or graphical solution to the problem, a high-speed electronic digital computer has been utilized. For this purpose the two simultaneous equations were transformed into more compact expressions by introducing reduced variables. These expressions are given in the following theoretical section. A similar procedure in this problem has been developed by Fredrickson and Bird1" Their tabular results, however, are very incomplete in the range of practical interest for problems of wellbore hydrodynamics. We have furthermore been able to express our graphical results in terms of convenient and familiar dimensionless groups. THEORETICAL DEVELOPMENT Use of Reduced Variables In terms of reduced variables the two simultaneous equations just discussed take the following form, The reduced variables q, x, a and z are defined in terms of the various measured quantities, where Q is volumetric flow rate, AP/L is pressure gradient, Dl is OD of inner pipe, D, is ID of outer pipe, is plastic viscosity, and is yield point. Thus, we have a dimensionless volume flux, a dimensionless reciprocal pressure gradient, and the ratio of the pipe diameters Before introducing the fourth reduced variable, z, it is of interest to consider the physical significance of the parameter x. As may 'be seen from the velocity profile of Fig. 1 the Bingham plastic fluid has the interesting property that a portion of the stream flows at a uniform velocity without shearing action. This section of the stream is situated approximately in the center of the conduit and is known as the "plug flow" region. Its existence is due to the fact that the shearing stresses within the region do not exceed the yield point, which is one of the two flow properties characterizing the fluid. The parameter x then turns out to be the ratio of the

By George Stern

THE purpose of this investigation has been to study one method for making ordinary carbon steel by the powder metallurgy technique. This method con- [ ] sists of pressing and subsequently sintering an intimate mixture of iron powder and graphite in a suitable atmosphere to produce a steel. Two types of iron powder have been studied, electrolytic and reduced. The sintering of mixtures of loose carbonyl iron and carbon black for several hours at 1000° to 1100°C. (1830° to 2010°F.), followed by forging of the resultant ingots to bars, has been studied by Offermann.1 Trail' has reported on the properties of hydrogen-reduced and electrolytic iron powders, both containing 0.5 per cent carbon. Methods for making steel bodies by powder metallurgy have also been sug- [ ] gested by Goetzel,3 who recommends the addition of steel powder of well-defined carbon content to pure iron powder, and Volterra,4 who suggests compaction and subsequent sintering of a mixture of steel powder, iron oxide and iron powder. Additional methods for making steel bodies by powder metallurgy have been reported in the literature by Koehring,5 Allen,6 Balke,7 Wulff,8 Boegehold,9 and others. 10,11,12 It is felt that the method of pressing iron powder and graphite, as described herein, lends itself best to production because of the lubricating action of the

Jan 1, 1946

By H. C. Chao, L. H. Van Vlack

Small MnS inclusions with known crystallographic orientations were placed inside powder compacts of low-carbon steel. After the metal was axially campressed with negligible end friction, the deformstions for the metal and the inclusions were compared. The MnS inclusions deformed more when the [100] direction was aligned with the compression axis than when the [111] direction was parallel to this axis. The deformations of the inclusions in the two principal radial directions were equal for each of the above orientations. Inclusions with [110] compression alignments did not deform with radial symmetry. The relative deformation of the inclusion and metal was closely dependent upon the relatiue hardness of the two phases. The relative deformation of the two phases was not sensitive to the rate of deformation. RECENT studies by the authors1.&apos; suggested that the plastic deformation of MnS in steel would probably be highly sensitive to the orientation of the inclusions and to the temperature of the metal. This paper reports an investigation of these factors upon MnS behavior within steel. Manganese sulfide (MnS) possesses an NaCl-type structure and typically has extensive (l10) {110} slip as a separate (noninclusion) crystal.&apos; A secondary slip system, ( l 10) { l l l}, has also been observed where the major slip system is restricted. In general, MnS inclusions must be rated as a highly deformable second phase.3 The amount of sulfide deformation varies, however, with several composition and processing factors. Some of these have been only partially assigned. For example, it is known that minor amounts (<0.01 pct) of silicon within free-machining steels will increase the amount of MnS deformation,4 but the mechanism of the added deformation can only be surmised at the present. Manganese sulfide and steel have sufficiently comparable deformation characteristics so that slip which is started in steel may be continued through the sulfide inclusions and back into the steel if the crystal orientations are favorable.5 A more detailed discussion of previous work on the plastic deformation of NaC1-type crystals and on the plastic deformation of inclusions within a metal is given in Chao&apos;s work.6 EXPERIMENTAL PROCEDURE The manganese sulfide which was used in this study was prepared by previously described methods.&apos; Single crystals of MnS, both as cleavage cubes and as spheres, were oriented within steel powder compacts so that the desired crystal directions were parallel to the direction of axial compression. A four-stage hydrostatic compaction procedure was used and involved the following steps. In the first stage part of the powder was placed in a metal die 1 in. in diameter with a thick (1 in. OD, 5/8 in. ID) rubber liner which had one end plugged. The steel powder was hand-rammed, making it as dense as possible before placing a carefully sized MnS crystal (either as a sphere or as a cube) near the center. The crystal was oriented with the chosen direction vertical; viz., [001], [011], or [111], with the aid of a X10 microscope. A pair of tungsten wire threads 0.020 in. in diameter was inserted along the side of this (&apos;core compact" to locate the desired plane after the compression tests. After the crystal was positioned in the center of the die, more powder was added and carefully rammed by hand. The die was then capped with a rubber plug of the same hardness and thickness as that of the liner. The whole assembly as shown in Fig. 1 was compacted by a ram load of 54,000 lb (about 70,000 psi). In the second stage a smaller, 3/4-in, rubber-lined die was used to give a stress of approximately 120,000 psi. The above process was repeated with the initial compact serving as a core for a larger compact. The final product after sintering was a cylinder 1 cm long and 1 cm in diameter, having a density of 7.54 g per cu cm. This was close to the theoretical density since the metal contained a non-metallic phase. There was no evidence of MnS deformation during the hydrostatic compaction or subsequent sintering. Elevated-temperature hardness data were obtained by procedures previously described.2 Compression tests for inclusion deformation utilized the cylinders which were described above. The critical problem in these tests was the lubri-

Jan 1, 1965

By E. A. von Hahn, T. R. lngraham

The rates of cementation of pd11 on electropolislzed copper cylinders were studied in aqueous perchloric acid solutions at pdII concentrations from 0.02 to 0.1 mM. The cylinders were rotated at various high speeds to reduce the diffusion layer to a minimum thickness. In 0.1 M HClO4 solutions, the cemented palladium is dense, adherent, and shiny. The rate data indicate that there are two stages in the deposition. In the initial stage, the rate of cementation is first order with respect to the pd11 concentration. The second stage is much slower. The first stage is consistent with rate control by the diffusion of pd11 ions to the copper surface, and/or chemical reaction at the surface, and the second stage is consistent with rate control by the diffusion of copper ions from the cop-per surface through the deposit of cemented palladium, out to the main body of solution. In 0.001 M HClO4 solution, only the first stage is evident and the rate is more rapid than at higher acidities. This rate enhancement is attributed to PdOH+ ions that predominate at low acidity and aye more reactive than unhydrolyzed pdII. The deposit is porous and loose. All of the cemented deposits are Pd-Cu alloys rather than pure palladium. Activation energies are 9.5 kcal per mole in 0.1 M HClO4 and 7.4 kcal per mole in 0.001 M HClO4. CEMENTATION or displacement reactions occur between aqueous solutions of metal salts and immersed metals according to the general equation: where M1 is electrochemically the more noble metal. Although these reactions find considerable application in metals recovery processes (e.g., the cementation of copper192 or gold3), in electrorefining processes (e.g., solution purification before electrolysis4,5), and in plating and metal finishing processes,6 few studies have been made of the kinetics of such reactions.7-9 The rates of cementation reactions will depend on one or more of the following factors: a) chemical reactions at the metal-solution interface; b) ionic transport to or away from the interface;&apos;-&apos; and c) the character and adherence of the cemented deposit on the substrate metal,6a,10 because the deposit will inhibit the rate of transport of dissolving ions (M2m+) into the solution. In this investigation, the kinetics of the early stages of cementation were studied to obtain an understanding of the reaction mechanism under conditions in which the deposit was sufficiently thin that its inhibiting effect could be disregarded. To achieve this, very dilute solutions in Mn+ were used. Cementation rates are often fast in the initial stages and transport-contr01led.9 To find conditions under which transport control would shift to chemical control, very high stirring velocities were used to minimize the diffusion-layer thickness. Of the many possible cementation reaction systems, the palladous perchlorate-copper system was chosen for this investigation because it was believed to involve simple ion-for-ion exchange. In addition, there are no interfering side reactions, such as the reduction of hydrogen ions, and anion effects are usually absent in perchlorate solutions. EXPERIMENTAL Materials. Reagent-grade chemicals and redistilled water were used in all experiments. Palladous perchlorate stock solutions (0.02 M) were prepared by dissolving 99.5 pct Pd sponge (Johnson Matthey and Mallory Ltd.) in concentrated nitric acid, adding concentrated perchloric acid, evaporating twice slowly (to prevent PdO precipitation) to a small volume, and diluting in a volumetric flask. To prevent gradual hydrolysis of PdII, the stock solutions were made 0.4 M in HC104. Tests for pdIV (Ref. 11) and C1- were negative. Copper strips were cut accurately from 0.025-in. electrolytic tough pitch sheet, Sample 1 (Mines Branch stock or Canadian Copper Refineries Ltd., Montreal), or from oxygen-free, high-conductivity sheet, Sample 2 (American Metal Climax O.F.H.C. brand, sold by Utility Brass and Copper Corp., Brooklyn). The strips were annealed for 1 hr at 335°C in a stream of purified nitrogen (Union Carbide, Linde Division) which had

Jan 1, 1967

By H. l. Burghoff, A. I. Blank

The state of knowledge bearing on the stability of copper under stress at elevated temperatures is generally known to be in need of revision and extension. The present investigation, dealing with the creep characteristics of a deoxidized copper of low residual phosphorus content, is intended to contribute in some small measure toward this end. The experimental data presented herein have been correlated by methods of evaluation and interpretation familiar to those who are concerned with crecp of metals. In practice it is common, if not requisite, to use structurally stable materials at elevated temperatures. It is frequently desirable, however, to test materials under conditions that produce structural change, in order to determine the extent of such change and its effect on physical properties, thus making it possible to establish accurately the limiting conditions to which such materials may be safely exposed. The creep characteristics of the drawn copper wire of this investigation arc directly associated with its structural instability at elevated temperatures. Complete realization of this fact is essential to the evaluation of its creep resistance under various conditions. Creep results should apply to steady deformation under equilibrium conditions, but these are seldom attained in only one or two thousand hours. It will be shown that steady creep rate for copper at useful stresses does not usually begin until considerably more time has elapsed. A wholly satisfactory substitute or shortcut for extensive creep testing does not appear to be evident in the application of mathematical analyses to limited experimental data. Material A single lot of phosphorized copper wire was drawn down to 0.125-i11. diameter with a final reduction of 84 per cent. After mechanical straightening, a portion of this wire was annealed to an average grain size of 0.013 mm. in a controlled-atmosphere furnace. The composition and initial properties of the copper in these two conditions are listed in Table I. Photomicrographs of the original structure are shown in Fig. I.

Jan 1, 1945

By G. R. Leverant, C. P. Sullivan

To evaluate the effect of a dispersion of nondeform-able, incoherent, second-phase particles on high-strain cyclic deformation and fracture, recrystallized TD-nickel (Ni-2ThO2) and a commercially pure nickel, Ni-200, were fatigued under strain control at total strain ranges varying from 0.009 to 0.036. Relative to the Ni-200, the slip at the surface of the TD-nickel was more wavy and discontinuous due to the presence of the thoria particles. This made crevice formation (incipient cracking) within slip bands more difficult in TD-nickel than in Ni-200. Both materials cyclically hardened to a constant (saturation) flow stress which increased with increasing plastic strain amplitude. Cellular substructures were developed in both materials during cycling. The cell size in TD-nickel was controlled by the thoria particle distribution and was independent of plastic strain amplitude over the range investigated. The cell size in Ni-ZOO was larger than that in TD-nickel at similar plastic strain amplitudes and was a function of plastic strain amplitude. These results, together with the cyclic stress-strain curves for both materials, are discussed in terms of a model for fatigue strain accommodation at saturation recently proposed by Feltner and Laird. NUMEROUS fatigue investigations have considered the interrelation of slip character, dislocation substructure, and cracking in pure metals and solid-solution alloys. However, except for the studies of the low-strain fatigue of internally oxidized copper alloys1 and cast, dispersion-strengthened lead,&apos; little is known about the effects which small, incoherent, nondeform-able, second-phase particles have on cyclic deformation and cracking processes. Effects due to the particles alone are often obscured by a dislocation substructure introduced during thermomechanical processing of dispersion-strengthened metals. In the present study, recrystallized TD-nickel and a commercially pure nickel, Ni-200, were employed to evaluate the effect of a thoria dispersion on high-strai fatigue deformation and cracking at room temperature. I) MATERIAL AND EXPERIMENTAL PROCEDURE The TD-nickel was supplied by DuPont as a 5/8-in.-thick stress-relieved plate which had been subjected to a proprietary schedule of thermomechanical treatments, and the Ni-200 as 3/4-in. bar which was subsequently annealed for 2 hr at 850°C in argon resulting in an average grain diameter of 0.05 mm. The compositions of these materials are given in Table I. The microstructure of the TD-nickel consisted of elongated grains parallel to the primary working direction with an average width of 0.16 mm, Fig. l(a). Many fine annealing twins were present indicating that the starting material was in a recrystallized condition; this supposition was confirmed by the absence of of any extensive dislocation substructure, Fig. l(b). Sheetlike stringers parallel to the rolling direction were occasionally seen both within grains and at grain boundaries. Some approximately spherical particles about 2 in diam, which may correspond to exceptionally large thoria particle aggregates, were also present. The average Young&apos;s modulus of the plate material in the rolling direction was 21.8 X 106 psi which is consistent with a {100}<001>recrystalliza-tion texture3&apos;* being prominent. In transmission microscopy, the 2.3 vol pct of thoria particles generally appeared to be uniformly distributed although some clusters, 0.1 to 0.3 in diam, of larger particles were observed as previously reported for TD-nickel sheet,5 and stringering of particles was present in some areas as welt. The average diameter of the thoria particles was 450A with a calculated mean planar center-to-center spacing of 2100A, as determined by quantitative metallographic analysis.= The 0.2 pct offset yield stress was 36,000 psi which agrees with the value predicted by the modified Orowan relation7 for edge dislocations bowing between thoria particles of the size and spacing observed in the present investigation. Fig. 2 illustrates the specimen design employed for the axial high-strain fatigue testing. Adapters were screwed onto the threaded portions of each specimen so that testing could be performed in the same manner as that reported for buttonhead specimens.8 Stressing was coincident with the working direction for both materials. The gage section of each specimen was electropolished and lightly etched prior to testing. The total strain was controlled, being varied between zero and a maximum tensile strain ranging from 0.009 to 0.036. In addition to these tests, a circum-ferentially notched TD-nickel specimen was cycled over a total strain range of 0.0075. The same strain

Jan 1, 1969

By Louis Huber

THE Liberty tunnels extend through a very steep hill in Pittsburgh (locally called Mount Washington) for a distance of slightly over a mile. The two tunnels parallel each other and are 59 ft. apart, center to center (Fig. 1). They are for vehicular traffic, and in each there is ample space for two lines of vehicles. Northbound traffic, towards downtown Pitts- FIG. I.-NORTH PORTAL OF LIBERTY TUNNELS. NOTE THE WINDBREAK AT END OFEAST TUNNEL. burgh, is confined to the east tunnel and southbound traffic to the west tunnel. The South Hills residential district is separated from downtown Pittsburgh by Mount Washington, a steeply rising escarpment south of and adjacent to the Monongahela River. The Mount Washington district immediately south of the Monongahela River has been reached, for many

Jan 1, 1927

By G. Donald Emigh

Nothing is more important to life-plant and animal-than phosphate. Its compounds are essential to the energy functions of all living systems and for the formation of bones and teeth. Animals get their phosphate from eating plants and other animals, or domestically from feed supplements. Plants get their phosphates from the soil. Man&apos;s most important use of phosphate is for fertilizer; approximately 95% of the world&apos;s phosphate rock production is consumed by fertilizers. Most of the balance is processed in electric furnaces into elemental phosphorus, the important raw material for making industrial phosphates. Recovery of uranium from phosphates has been possible but not widely used. However, recent significant developments have generated interest in such recovery in the US and elsewhere. Phosphate occurs in all igneous and sedimentary rocks, and in all fresh and salt water. However, economical recovery is limited to deposits where natural concentration of the phosphate mineral has occurred. Occasionally natural concentration is great enough that the material can be used as mined; generally, however, the ore is low grade_ and must be concentrated. Phosphate rock is produced in 31 countries. Fig. 1 shows the location of major phosphate rock producers as well as some of the known phosphate deposits not yet in production. In the last decade the world phosphate industry has experienced steady growth. World production rose from 98 Mt of phosphate rock in 1973 to 140 Mt in 1982. Fig. 2 shows the growth curve of rock production and graphically illustrates the almost straight-line rise since 1945 in both US and world production. Table 1 gives the breakdown, by countries, of world rock production, 1974 through 1979. Table 2 shows US rock production by producing areas. Definitions of Terms Used in the Phosphate Industry Phosphate Rock: Commonly called rock in sedimentary deposits and apatite in igneous deposits. Those expressions generally include any mined, or mined and beneficiated, fluorine-containing calcium phosphate used as the raw material for the next stage of manufacturing. The average phosphate content in rocks is 0.1 to 0.2% P2O5, as documented by McKelvey (1973). About 200 minerals contain more than 1 % P2O5. However, the important mineral in igneous rocks is fluorapatite, [Ca5 (PO4),3 F], containing about 42% P205 and 3.8% F2; in sedimentary rocks the important mineral is francolite, a carbonate fluorapatite containing up to 2% molecular CO2. Both are in the apatite family of minerals. Most phosphate rock, whether beneficiated or not, is a fine-grained material. The expression phosphate rock has no relation to its phosphate content. For example, phosphate rock from Idaho used in the production of phosphorus may contain about 24% P205, whereas rock from Morocco may contain 36.6% P2O5. Phosphorite: A deposit of phosphate directly or indirectly of sedimentary origin, which is of economic interest. Grade of Phosphate Rock: The calcium phosphate content of phosphate rock is expressed in different world areas by one of the following terms: BPL (bone phosphate of lime) TPL (triphosphate of lime) P2O5 (phosphorus pentoxide) P (phosphorus-not commonly used) An illustration of relationship is: 80% BPL = 80% TPL = 36.6% P5O2 = 16% P

Jan 1, 1983

By E. W. Engle

For several years the Fansteel Products Co. has been engaged in e production and development of various of the rarer metals. It is at present engaged in the commercial production of tantalum, tungsten, and molybdenum in a very high state of purity. The information contained in this paper is partly a general compilation from various sources and partly information obtained as a result of recent years of work in the laboratory of this company. Tantalum, tungsten, and molybdenum form a group peculiar to themselves among the commercially available metals. Their very high melting points (tantalum 2770&apos; C., tungsten 3350&apos; C., and molybdenum 2550" C.) set them apart so far as the metallurgical processes for their production are concerned. Further, when properly prepared and treated they will stand a somewhat unusual degree of cold work, that is work below the temperature at which marked crystal growth takes place. Such cold-worked metal may show a high tensile strength; tantalum to 130,000 lb. per sq. in., tungsten to 490,000 lb., and molybdenum to 260,000 lb., in the form of fine wire. In physical appearance, these metals are not unlike some steels; they may be better described by saying that polished tantalum somewhat resembles lead; polished tungsten, iron; and polished molybdenum, nickel. The polished surfaces of all three remain untarnished in ordinary air. Air containing corrosion-producing impurities will, in general, show molybdenum the least resistant to corrosion and tantalum the most resistant. Molybdenum has, however, a high degree of resistance to corrosion by hydrochloric acid, a property that should render it of commercial interest. On the other hand, it is markedly attacked by some of the weaker organic acids. The three metals oxidize rapidly when heated at or above a dull red in air. This feature limits their use in many applications where their high melting point and strength make them appear usable. Tungsten and molybdenum, at red heat, are quite inert to hydrogen and nitrogen; while tantalum has a rather remarkable affinity for all the ordinary gases, which results in its becoming embrittled in their presence. This

Jan 1, 1925

By S. R. Balajee, I. Iwasaki

The interaction between British gum 9084 and dode-cylammonium chloride (DAC) at quartz and hematite surfaces was established from coadsorption studies and streaming potential measurements. The cationic DAC interacts with the somewhat anionic British gum 9084, leading to the formation and adsorption of a binary complex of DAC-British Gum 9084 at the interface. The parallel ability to depress quartz along with hematite as a result of the interaction between DAC and British gum appears to be the main reason for the ineffective depressant action of starches and starch derivatives in the cationic flotation of iron ores. Amines are not particularly selective collectors for the flotation&apos; of siliceous gangue from iron ores and, therefore, a suitable iron oxide depressant is needed for a satisfactory separation. Various starches and their derivatives have been extensively tested with oxidized iron ores,&apos;-3 and it has been empirically established that British gums and dextrins are preferable. However, for the flotation upgrading of magnetite-taconite concentrates from 8 or 8.5% Si O2 to about 5% Si 02, British gums, which have been used so successfully on oxidized iron ores, have been found to have no effect and oftentimes are actually deleterious.4 In previous articles,5-7, starches were shown by adsorption measurements, flotation tests, and floccula-tion tests to interact with calcium ions in solution, and it was thought that a study on the interaction between starches and dodecylammonium ions would be able to shed some light on the anomalous flotation behavior described above. In fact, starches are known to interact markedly with paraffin-chain-type surface active agents and, thereby, to precipitate the starch or inhibit the iodine-starch reaction.8 From X-ray diffraction studies and viscosity measurements, the formation of a helical complex between mylose and a surface active agent has been postulated.9 The interaction with other types of hydrophilic colloids, such as synthetic polymers and proteins, has also been investigated and is usually explained in terms of van der Waals&apos; force interaction and/or ion-ion interaction. In the present investigation, the interaction of British gum and dode cylammonium chloride on quartz and hematite was studied by adsorption and streaming potential measurements in an attempt to establish the mutual adsorption behavior of British gum and dode-cylammonium chloride on mineral surfaces and to clarify the anomalous depressant activity of British gum in the cationic flotation of iron ores. All the measurements were carried out at a natural pH of near 7 because dodecylammonium chloride gives maximum selectivity of flotation separation at this pH2 and to avoid any third parameter in the system. EXPERIMENTAL MATERIALS AND METHODS Minerals: The quartz and hematite samples used for the adsorption tests were prepared as described in a previous paper,"J except that the specific surfaces of the samples were increased to 5,860 and 16,000 Sq cm per gm, respectively. For the streaming potential measurements, the 48165-mesh fractions screened out of the original samples were etched with hydrochloric acid, washed repeatedly with water, and stored under water in Pyrex bottles. Reagents:DodecyIammonium chloride (DAC) was prepared1 1 by bubbling dry hydrogen chloride gas through a benzene solution of high-purity dodecylamine supplied by Armour and Co. British gum 9084, received from Corn Products Co., was solubilized by first dispersing it in water to produce a 0.05% solution and then homogenizing it in a blender for 5 min. Distilled water was used in the preparation of the samples and the solutions and for all test work. Adsorption Measurements: The procedure for the adsorption density determinations was also the same as that described in the previous paper.1° The residual concentrations of the British gum and the DAC in the supernatant solution were analyzed colorimetrically by the phenol-sulf uric-acid and amine-picrate methods, respectively. The validity of the mine-picrate method for the colorimetric analysis of DAC in the presence of British gum and the analysis of British gum in presence of DAC were checked by establishing calibration curves between optical density and concentration. Streaming Potential Measurements: The cell assembly for the streaming potential measurements was similar to that described by Fuerstenau.&apos; The streaming potential

Jan 1, 1970