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By R. T. Mishler

I wish to express my keen appreciation of the article on the above subject by Coe and C1evenger.l It has been doubly interesting to me, for the reason that the experience recorded and the principles evolved practically parallel the results of similar investigations made by myself and others at The Lucky Tiger Mine, El Tigre, Sonora, Mex. An outline of the work at El Tigre may aid in confirming the principles expressed by Coe and Clevenger. El Tigre has the unenviable distinction of possessing a slime with a much lower settling rate than any recorded in the article discussed. Under most favorable conditions the settling rate is about one-third that reported for the Liberty Bell mill, and one-tenth that reported for the Nipissing, Golden Cycle, and Presidio mills. This slow settling characteristic of Tigre ore has necessitated careful investigation of settling phenomena throughout the various evolutions of the plant. Previous Settling Investigation at Tigre During construction work at the mill, the metallurgical engineer in charge, D. L. H. Forbes, ran a series of experiments on settling. His tests proved that deep settling tanks were not ordinarily necessary. The use of tanks 2 or 3 ft. in depth was suggested.2 Later experiments demonstrated that the following principles of settling applied to Tigre pulp.3 1. In settling dilute pulp, settling rates are independent of pulp depth. 2. In settling thick pulp, settling rates are approximately proportional to pulp depth.4

Jan 1, 1918

By William G. Pariseau

A design procedure for the quantitative estimation of support load requirements in underground mines is presented. The central problem in the design of mine support is one of es¬timating a maximum load that the ground will exert on the support in the coarse of mining. The distribution of stress around mine openings changes as mining progresses. At the time of support installation, the support load is essentially zero. With the passage of time and advance of the face, ground motion loads the support. The finite element method of analysis provides a simple quantitative technique for simulating the effects of mining and face advance on support load requirements. In particular, the maximum support load can be estimated by the proposed design procedure.

Jan 1, 1978

By James J. Bean

F. M. Lewis—I believe that density recorders are a prerequisite to all well operated ore concentrators. Well designed density instruments are very accurate and give an excellent record of the steadiness of the operation. Controlling the density of a pulp with an instrument, as described by Mr. Bean, is new and the experiences in developing this controller at the American Cyanimid Co.'s Mineral Dressing Laboratory are very interesting and should be extremely helpful to others who are planning on designing or installing controlling density instruments. Instruments for recording the density of the classifier overflow or flotation feed are rather common in ore concentrators, but there are a number of profitable uses for these instruments that are not too well known. Density recorders with bubble tubes submerged to different depth in a classifier pool give an excellent record of the classifier operation. The loading and unloading of the machine, that is so easily masked in the density of the overflow, can be easily recorded if the instrument is installed at some depth in the classifier pool. On some occasions, two instruments with bubble tubes at different depths give a more candid picture of the irregularities in the classifier operation. When cleaner machines are operated in closed circuit with roughers, a record of the density of the cleaner tails will indicate the circulating load in the circuit and is very helpful in coordinating different operators, because quite often the circulating load will be increasing for some time before the analyses of the products will change. Density recorders are used to record the variations in the dilution of the underflow from thickening tanks and in at least one plant the instrument controls the underflow.

Jan 1, 1951

By James J. Bean

F. M. Lewis—I believe that density recorders are a prerequisite to all well operated ore concentrators. Well designed density instruments are very accurate and give an excellent record of the steadiness of the operation. Controlling the density of a pulp with an instrument, as described by Mr. Bean, is new and the experiences in developing this controller at the American Cyanimid Co.'s Mineral Dressing Laboratory are very interesting and should be extremely helpful to others who are planning on designing or installing controlling density instruments. Instruments for recording the density of the classifier overflow or flotation feed are rather common in ore concentrators, but there are a number of profitable uses for these instruments that are not too well known. Density recorders with bubble tubes submerged to different depth in a classifier pool give an excellent record of the classifier operation. The loading and unloading of the machine, that is so easily masked in the density of the overflow, can be easily recorded if the instrument is installed at some depth in the classifier pool. On some occasions, two instruments with bubble tubes at different depths give a more candid picture of the irregularities in the classifier operation. When cleaner machines are operated in closed circuit with roughers, a record of the density of the cleaner tails will indicate the circulating load in the circuit and is very helpful in coordinating different operators, because quite often the circulating load will be increasing for some time before the analyses of the products will change. Density recorders are used to record the variations in the dilution of the underflow from thickening tanks and in at least one plant the instrument controls the underflow.

Jan 1, 1951

By George G. Griswold

The Parkes process of lead refining is based on the fact that when zinc isemixed with molten lead bullion, it forms an alloy with the silver and gold. This alloy freezes at a higher temperature and is of a lower specific gravity than the lead. With proper regulation of the temperature, the alloy solidifies and floats on top of the lead bath, from which it is removed and the silver, gold, and zinc recovered. The alloy should contain the maximum amount of silver (Ag2Zn,). The usual practice is to make two additions of the zinc. The first addition gives an alloy, or zinc crust, the zinc of which is saturated and is treated for the recovery of its zinc and silver; the crust from the second addition contains an excess of zinc and is used for the first addition on the following kettle. The crust produced depends on a number of items: purity of bullion, temperature, care with which kettle work is performed, addition of zinc, pressure used in expelling lead from crust, etc. It is desirable to make the concentration of silver in the zinc crust as high as possible; otherwise an undue amount of byproducts is produced, which greatly increases the cost of refining. It was formerly considered good practice to make a concentration of 20 :1. That is to say, if the lead bullion assayed 150 oz. dorê per ton, the assay of the retort bullion recovered from the zinc crust should be 3000 oz. per ton. As a matter of fact, the concentration should never, except on bullion assaying over 300 oz., be so low, and with low-grade bullion it should be 50:1. In one lead refinery where, ordinarily, the work was good, on a bullion averaging about 200 oz. per ton, a concentration of 24:1 was common; but how it was obtained was known only to the foremen. Changes occurred, and under new foremen the kettle work fell off badly; the problem then was to bring about this greater concentration. As is customary, the refincry had a "schedule" for its 60-ton kettles, which gave the number of pounds of zinc required for all possible assays, on both the first and the second zincing. Using this schedule, high temperatures

Jan 1, 1924

By Edward K. Landis

Our Transactions contain so many suggestions of apparently trivial, yet really important, contrivances for the saving of time and

Jan 1, 1893

By H. A. Schwartz, Wolfram Ruff

The spheroidal form of the temper carbon nodules in malleable cast iron and of the graphite mottles of "mottled" cast iron suggests that in both all the graphite in a given mottle or nodule grew from a single center of crystallization or nucleus. $ There is, however, a distinct metallo-graphic difference between the mottle and the nodule; the area of mother metal impoverished in combined carbon by the crystallization of graphite in a mottle is practically coextensive with the ramifications of the graphite, while the impoverished zone of metal corresponding to a given nodule is always larger, and usually much larger, than the approximately spherical mass of graphite crystals forming the nodules. Furthermore, the mottle probably is formed during freezing and the nodule almost always at a considerably lower temperature. Assuming that the nodules or mottles can be used as a measure of the existing nuclei (capable of germination) we propose to record certain observations as to the graphitizing reaction in the light of the number and habits of growth of these nuclei. The present authors, in cooperation with others'-', have reported upon various cognate aspects of the problem. The fact that temper carbon is a mass of flakes and not a solid granule has become well recognized since the introduction of an improved polishing technique8, 9, 10 for cast iron. The problem of deriving from the circular planar intercepts of a mass of spheres of varying sizes their number and size distribution in space has also been satisfactorily solved12, 13 Growth of Nuclei in White Cast Iron It has already been shown1, 3 that the progress of graphitization with time is usual1y consistent with the assumption that nodules grow in size

Jan 1, 1936

By Wolfram Ruff, H. A. Schwartz

The spheroidal form of the temper carbon nodules in malleable cast iron and of the graphite mottles of "mottled" cast iron suggests that in both all the graphite in a given mottle or nodule grew from a single center of crystallization or nucleus. $ There is, however, a distinct metallo-graphic difference between the mottle and the nodule; the area of mother metal impoverished in combined carbon by the crystallization of graphite in a mottle is practically coextensive with the ramifications of the graphite, while the impoverished zone of metal corresponding to a given nodule is always larger, and usually much larger, than the approximately spherical mass of graphite crystals forming the nodules. Furthermore, the mottle probably is formed during freezing and the nodule almost always at a considerably lower temperature. Assuming that the nodules or mottles can be used as a measure of the existing nuclei (capable of germination) we propose to record certain observations as to the graphitizing reaction in the light of the number and habits of growth of these nuclei. The present authors, in cooperation with others'-', have reported upon various cognate aspects of the problem. The fact that temper carbon is a mass of flakes and not a solid granule has become well recognized since the introduction of an improved polishing technique8, 9, 10 for cast iron. The problem of deriving from the circular planar intercepts of a mass of spheres of varying sizes their number and size distribution in space has also been satisfactorily solved12, 13 Growth of Nuclei in White Cast Iron It has already been shown1, 3 that the progress of graphitization with time is usual1y consistent with the assumption that nodules grow in size

Jan 1, 1936

By C. R. Hayward

CARLE R. HAYWARD.-I do not want it understood that I think that the conclusion that the time of tempering temperature is immaterial has been definitely proven, but since these are the first definite figures put out, I thought before continuing on more work ourselves, it would be well to present them as progress and for information. J. A. MATHEWS, Syracuse, N. Y.-I think that if Prof. Hayward would consult the paper of Profs. Barus and Strouhal,1 1885, he would find about 250 pages, mostly figures, on this subject, in which they investigated the tempering effect by electrical and magnetic methods. There are so many figures in the paper that it is very difficult reading. One point particularly brought out was that even at a low temperature, such as the boiling point of alcohol, about 60° C., there is a tempering effect, increasing up to 4 hr. One reason they obtained those results, with which the present authors are at variance, was that they started with a high-carbon steel which hardens thoroughly, whereas the steel Prof. Hayward and his collaborator used was a comparatively mild steel which does not take a great deal of hardening. About 3 years ago Mr. Stagg and I published 2 a few figures bearing on the same subject, but we used .a low-carbon alloy steel of high tempering qualities and found a great deal of improvement, particularly in ductility, by continuing the drawing up to 4 hr. We used a chrome-vanadium steel showing after heat treatment 250,000 tensile strength. On short drawing, we got almost no ductility, but by continuing to 4 hr., we raised it to 12 per cent. I believe Prof. Hayward's results are due to using comparatively mild steel, whereas Prof. Barus used drill rod and carried out a, wonderfully exhaustive

Jan 4, 1917

By M. B. Kasen

eralized strain equation appear quite different they are really identical. This identity can be shown in a simple mathematical rearrangement. Referring to Eq. [I], the substitution of ln(1 +?E) for ? (where ?E is the engineering strain) yields: a =s8- (s8?so)e?1/?c) ln(1 +s8??E) [4] or s =s8?(s8?so)(l +?E)-1 [5] Replacing (1 + cE) with its equivalent, (l/lo): s=s8?(s8?so)l/€c [6] Adding and subtracting the quantity (s8 - so) yields: s=s8?(s8?so)+ (s8-so) l-(^)l/£c [7] = s0+(s8?so)ri-(^0)1/^l [8] Letting n = 1/?c it follows that: This equation will be seen to be identical to the generalized strain expression in Eq. [3], the coefficients a and b being equal to so and (s8?so)/?c or n(s8?so), respectively. Confirmation of the relationship noted above was provided by fitting experimental stress-strain data5 for 304 stainless steel (total strain from 0.072 to 1.15) at room temperature at a true total strain rate of 4 x 10-3 sec-1 to Eqs. [I] and [3]. In this study nonlinear regression analyses were used to evaluate the equation constants. The results of this evaluation are presented in Table I. When these constants are used in Eqs. [I] and [3] the curves obtained are coincident. It will also be noted that the value of n is equal to YE,, the value of a is equal to so, and the value of b is equal to (s8 - so)/Ec. These equalities are illustrated in Table I where the Voce constants in parentheses were calculated from a, b, and n values. Excellent agreement is seen to exist. It is concluded, therefore, that the Voce equation is, indeed, identical to the linear expression involving generalized strain. In applying the generalized strain concept to stress-strain data, it has been noted3 that data within what was termed the transition region (first few points in the plastic flow region) must be excluded from the analysis in order to obtain the linearity in Eq. [3]. A similar exclusion applies in the use of the Voce equation since an expression which would describe the strain-hardening region would usually be found to be not too effective in the elastic-plastic fillet2 which connects the elastic line to the strain-hardening region. These considerations further substantiate that Eqs. [I] and [3] do indeed describe identical behavior. Note added in proof. Since this manuscript was submitted for publication, correspondence with Professor S. R. Davies, University of Edinburgh, (of Ref. 3) indicated that his associates have also confirmed the identity between the Voce equation and the generalized strain concept. It is sometimes desirable to obtain a small grain size in super-purity metals. Unfortunately, the absence of impurities, the low recrystallization temperatures, and the low activation energies for boundary motion result in rapid growth of relatively few grains when conventional recrystallization practices are used. For example, Arajs et al.1 were unable to obtain a mean grain diameter less than about 0.4 mm in iron containing 38 at. ppm of impurity. The <1 at. ppm purity range in many modern superpurity metals results in yet larger limiting grain sizes. It is the purpose of this communication to describe a technique by which mean grain diameters as small as 30 µ have been produced in aluminum having an impurity content < 0.5 at. ppm. The technique should be applicable to superpurity metals other than aluminum and has potential applications to grain refinement of commercial alloys. The necessary and sufficient requirements for production of a small grain size are as follows: a) a large number of potential nucleating sites must be created randomly within the cold worked material, b) sufficient thermal energy must be provided at a rate that will simultaneously activate a large fraction of the potential nuclei, and c) the grain growth must be stopped shortly after grain impingement.&apos; A high density of potential grain nuclei may be cre-

Jan 1, 1970

By H. V. Winchell

It seems to me that uniformity of mining law in North America must of necessity start with uniformity in each country. I understand that the Provinces of Canada have the right to make their own individual laws and conditions, to prescribe the terms under which the prospector or the applicant for mineral titles may secure the same. That is not true of the states in the United States. In this country, the Federal Mining Law was made applicable to the public domain, which, at the time of the adoption of this Act in 1872, was chiefly west of the Missouri River; it is impossible to locate a mining claim in most of our eastern states. It is true, however, that there are certain holdover rights, mostly obsolete, arising from the fact that at the time of the formation of the Confederation of States, the land that belonged to each state became the property of the Federal Government. I am not quite correc-t in that, it was sometime after the adoption of our Constitution, I think it was 1778, but those rights were largely, by agreement, surrendered to the Federal Government; but it is a fact that the great acquisitions of territory in the West, with the single exception of Texas, were of domain that came into the possession of the Federal Government and our Federal Mining Law applies to that territory. No state has the right to (by legislative enactment) enlarge upon the rights given by the Federal Mining Law, governing the acquisition of mining claims in its territory, within its boundaries. Each state, however, may, and some of them do, limit somewhat the rights given to the prospector. For instance, the Federal Mining Law provides that a claim may be taken, staked upon the public domain, of 600 ft. in width and 1500 ft. in length. Some of the states, like South Dakota and Colorado, have at times said "that is an excessive amount of land for a single mining claim; we will therefore limit it to 300 ft. or 200 ft. in width." There is, therefore, not any direct and immediate need for uniformity of mining laws in the United States, such as there might possibly be if it were considered at all desirable upon the whole in Canada. The initiation of mining rights under the Federal Mining Act is the act of discovery of valuable mineral in place, referring now to the lode mining claims, but the same is true of the placer claim. It is true that the emphasis has never been laid upon the word valuable and that

Jan 1, 1920

By S. Katz, M. E. Nicholson, J. J. Kelly, D. R. Curran

A series of wedges of 1020 steel (2 1/2 by 6 by 8 in.) were explosively loaded, as shown in Fig. 1. A slab of explosive on the surface of the steel wedge was initiated simultaneously along one edge, producing an essentially two-dimensional oblique shock in the metal. Pressure and density in the metal were measured as a function of distance from the explosive-metal interface by a method described elsewhere.&apos; While for pressures below 130 .kbars the technique produces accurate results, for greater pressures the presence of two shock waves in the metalzy3 makes interpretation of the data uncertain. However, the location of the transition in pressure at 130 kbars can be readily identified from the data. The assumption of a single shock in the region above 130 kbars overestimates the pressure computed on a multiple-shock model. After firing, the wedges were sectioned, lapped, and etched with 2 pct Nital. A photograph of an etched specimen is shown in Fig. 2. The specimens were examined metallographically. The dark region, at the top of the specimen, was heavily banded, Fig. 3, while the lighter area was comparatively free from banding, Fig. 4, the boundary between the two regions being quite abrupt. The very light regions at an angle of about 45 deg to the explosive-metal interface show virtually no banding. The origin of these light regions, which are not Luder&apos;s bands, is not yet explained. The thickness of the heavily banded area was measured and compared with the pressure at the boundary between the heavily and lightly banded regions. The results of these measurements and calculations are given in Table I. For all shots, the pressure at the boundary is approximately the same

Jan 1, 1960

By Leonard C. Grimshaw

The idea of bonding two dissimilar ferrous metals, and making use of both, is an old one. Tips have been brazed onto tool shanks for many years. The bonding of larger pieces to form whole bars and sheets has also been accomplished, but has received little attention in the technical literature, although a number of patents have been issued covering various methods for its accomplishment. There are three main motives behind the manufacture of composite steels. One is that the physical properties of one steel may supplement those of another; a useful, but at the same time, hard, brittle steel may be backed by a soft ductile one, or a stainless steel may be backed by a steel possessing greater strength. Another motive is direct lowering of cost; an expensive steel may be backed by a less expensive one, bringing down the cost of the piece as a whole. The third motive is an indirect lowering of cost, as when a useful steel is backed by a steel that is easier to machine, so that machining cost on a finished product is lowered considerably. Often more than one of these motives lead to a decision to use a composite steel. Previous Methods There are two methods in use that result in tolerably good bonds between ferrous metals: (1) the casting method, and (2) what we shall call the "heat-pressure" method. This "heat-pressure" method covers processes in which the bond is made between two prepared surfaces by heating them and then applying pressure. Usually sufficient pressure must be used to produce appreciable spread and elongation, or else we arc merely brazing and not truly welding. Casting methods for welding together ferrous metals have been used more than 74 years, and are described in the technical literature as applied

Jan 1, 1936

By Leonard C. Grimshaw

The idea of bonding two dissimilar ferrous metals, and making use of both, is an old one. Tips have been brazed onto tool shanks for many years. The bonding of larger pieces to form whole bars and sheets has also been accomplished, but has received little attention in the technical literature, although a number of patents have been issued covering various methods for its accomplishment. There are three main motives behind the manufacture of composite steels. One is that the physical properties of one steel may supplement those of another; a useful, but at the same time, hard, brittle steel may be backed by a soft ductile one, or a stainless steel may be backed by a steel possessing greater strength. Another motive is direct lowering of cost; an expensive steel may be backed by a less expensive one, bringing down the cost of the piece as a whole. The third motive is an indirect lowering of cost, as when a useful steel is backed by a steel that is easier to machine, so that machining cost on a finished product is lowered considerably. Often more than one of these motives lead to a decision to use a composite steel. Previous Methods There are two methods in use that result in tolerably good bonds between ferrous metals: (1) the casting method, and (2) what we shall call the "heat-pressure" method. This "heat-pressure" method covers processes in which the bond is made between two prepared surfaces by heating them and then applying pressure. Usually sufficient pressure must be used to produce appreciable spread and elongation, or else we arc merely brazing and not truly welding. Casting methods for welding together ferrous metals have been used more than 74 years, and are described in the technical literature as applied

Jan 1, 1936

By Edgar G. Tuttle

The accompanying figures show a jig arranged for separating the middle product or middlings obtained in the concentration of certain ores, minerals, coal, etc. In the preparation for sizing, prior to jigging, of ore-bearing minerals, coal, etc., with their impurities, it is generally desirable to avoid reducing them to unnecessarily small sizes. Where the impurities adhere to the mineral particles or are disseminated through its mass, it is generally necessary to crush to such a fineness as will unlock the minerals from the gangue. If a considerable proportion of the material consists of mixtures of the minerals and gangue, each in large size, and a lesser proportion consists of a mixture of the two, in smaller sizes of various dimensions, it is not always desirable to reduce the whole to such size as would be required to liberate completely the pieces of ore and gangue in the finest mixtures. In such a case it is preferable to reduce all the material to such an

Jan 1, 1897

By S. Weinig, E. S. Machlin

THE mechanism of the martensitic transformation has been the subject of a remarkable number of papers in recent years.&apos; Because the task of evaluating all the available theories is a formidable one, the authors will confine themselves merely to the presentation of results of an experimental investigation of the habit orientation, lattice relations, magnitude and direction of average transformation shear strain, and orientation of subband markings for a single variant of the possible habit systems in an 11 pct Mo-Ti alloy. It is hoped that these data will assist in the establishment of a rigorous theory for the mechanism of the martensitic transformation. Experimental Procedure Specimen Preparation: A sample, approximately 1/2 x 1/4 x 1/4 in., was cut from a double arc-melted ingot composed of commercial-process A titanium and high purity molybdenum (nominally, 11 pct Mo). It was capsuled in evacuated Vycor at 10.-3 mm Hg subsequent to a double argon wash and homogenized for 48 hr at 1100°C. After a direct quench into H2O at room temperature, a large-grained specimen resulted, which, by X-ray diffraction and metallographic means, was subsequently shown to be in the body-centered-cubic phase, ß. Two adjacent, approximately perpendicular faces were polished and the ends of the specimen were ground parallel in a V-block. Fiducial lines were inscribed at 45" to the common edge of the polished surfaces in order that they would be perpendicular to the habit traces of the subsequently formed a plates.2 The specimen was then compressed between the ground ends in a Buehler press to stress induce the transformation ß to a&apos;. Experimental Measurements: The habit-plane orientation, the orientation of subband markings, the orientation relation between the parent ß and the product a&apos;, and the transformation strain for the same plate were determined. To further establish the nature of the subbands, one surface was repol-ished and etched. The bands in the a&apos; were still visible and were found to be optically anisotropic under polarized light. Back-reflection Laue patterns were obtained from the ß matrix and from a region comprising both a&apos; plates and adjacent ß matrix (a Cu target was used). By superposition of the two X-ray diffraction patterns, it was possible to obtain a tentative orientation relationship between the two phases. This result was confirmed by a pattern taken after the specimen was rotated to make the basal-plane pole of the hexagonal a&apos; phase strike the film. This necessitated cutting the specimen to expose the a&apos; plate in the new position relative to the X-ray beam. Analysis of Experimental Measurements On the basis of the aforementioned X-ray patterns, the orientation between parent and product

Jan 1, 1955

By G. Sachs, G. Espey

Simple methods can be used for the determination of the residual stresses in thin walled tubing if the stresses consist of high tensile stresses at the one surface and high compressive stresses at the other surface. Such a stress distribution is approximated in sunk tubing and in deep-drawn shells. It is possible to cut sections from such articles in such a manner that a major part of the residual stress is relieved by a bending of the Part that is separated from the adjacent metal. The circumferential stress is evaluated from the change in diameter D, occurring on splitting a length of tubing (Fig. Ib) or from deflection resulting from the cutting out of a circumferential tongue (Fig. Ia) .6 The bending moment M released by such a flexure is. M - EI (I-I) = EI R1-R0 I - u2(R0-R1) I -V2 R0XR1 where E = modulus of elasticity, v = Poisson&apos;s ratio, I = moment of inertia of the section, R0 =. mean radius before splitting, R1 = mean radius after splitting. The release of this bending moment corresponds to the release of stresses, which, in a thin section, vary linearly from one surface to the other, and have the following value in a particular fiber a certain distance (x) from the surface: S = c d I - V2 x c x d 2 2 RI - R0____E (d ) R1 - R0 X R0 X R1 ~ i - u2 (2 x) Ro X R1 where C is the section modulus and d is the thickness of the section, the ratio M:C being d: 2 for a rectallgular section.* The maximum stress values at the surfaces are. Smax = +E X d X R1-R0 I — u2- 2 R0 X R1 For most purposes the simpler equations: EXd AD1 = ± I - u2 x dm2 and will be satisfactory, where D,, is the aver. age of the mean diameters of the tubing

Jan 1, 1942

By G. Sachs, G. Espey

Simple methods can be used for the determination of the residual stresses in thin walled tubing if the stresses consist of high tensile stresses at the one surface and high compressive stresses at the other surface. Such a stress distribution is approximated in sunk tubing and in deep-drawn shells. It is possible to cut sections from such articles in such a manner that a major part of the residual stress is relieved by a bending of the Part that is separated from the adjacent metal. The circumferential stress is evaluated from the change in diameter D, occurring on splitting a length of tubing (Fig. Ib) or from deflection resulting from the cutting out of a circumferential tongue (Fig. Ia) .6 The bending moment M released by such a flexure is. M - EI (I-I) = EI R1-R0 I - u2(R0-R1) I -V2 R0XR1 where E = modulus of elasticity, v = Poisson&apos;s ratio, I = moment of inertia of the section, R0 =. mean radius before splitting, R1 = mean radius after splitting. The release of this bending moment corresponds to the release of stresses, which, in a thin section, vary linearly from one surface to the other, and have the following value in a particular fiber a certain distance (x) from the surface: S = c d I - V2 x c x d 2 2 RI - R0____E (d ) R1 - R0 X R0 X R1 ~ i - u2 (2 x) Ro X R1 where C is the section modulus and d is the thickness of the section, the ratio M:C being d: 2 for a rectallgular section.* The maximum stress values at the surfaces are. Smax = +E X d X R1-R0 I — u2- 2 R0 X R1 For most purposes the simpler equations: EXd AD1 = ± I - u2 x dm2 and will be satisfactory, where D,, is the aver. age of the mean diameters of the tubing

Jan 1, 1942

By L. A. Rapoport

This paper is intended as an aid in the perfornzance and interpretation of experimental studies of multi-phase flow in porous tnedia. The mathenmatical formulation of incompressible, two-phase flow phenomena in a three-dimensional porous medium is presented. The resulting equations which account for the effects of gravitational and capillary forces are used to derive general scaling laws permitting accurate representation of water-oil displacement processes by means of experimental flow models. The significance of the scaling laws is examined in the light of the physical concepts of micro-behavior of fluids in porous media. Formulations of scaling con(litions obtained by application of dimensional analysis are reviewed. The principles of application and the limitations of flow model studies are discussed. INTRODUCTION Most of the problems facing a reservoir engineer involve three-dimensional, two-phase flow systems. influenced by the effects of gravitational and capillary forces. Present computational procedures generally do not permit the evaluation of such systems without introducing greatly simplifying assumptions. The actual reservoir configuration is usually replaced by one or a combination of several "equivalent" linear systems, and the effects of capillarity and gravity are considered to be negligible. While these assumptions may in many instances be justified, there are a number of important practical problems for which the results obtained on the basis of such simplifications remain open to question. An alternate approach to the problems that are not amenable to analytical treatment consists of seeking their solution by experimental laboratory investigations. The main difficulty of such investigations lies in the fact that multiphase flow phenomena subjected to gravity and capillary forces proceed differently at different rates and in systems of different dimensions. Therefore, unless great discrimination is exercised in selecting the conditions and interpreting the results of laboratory tests, such tests may be entirely misleading in regard to field applications. The purpose of this paper is to present a theoretical background for the performance of laboratory tests that are more nearly representative of field behavior. It will be shown that simulation of field behavior can be achieved by conducting laboratory tests under conditions selected in accordance with definite scaling laws. The formulation of conditions required for the scaling of two-phase flow experiments in porous media has been presented in the literature on several occasions.12,3,4 One of these formulations advanced by Leverett1, cannot be considered applicable to most practical cases inasmuch as it does not cover generally the regime of laminar flow. An adequate treatment, based on the consideration of dimensional analysis, was presented by Engelberts and Klinkenberg.2 Their treatment, however, is concerned primarily with the scaling of linear flow systems, and hence somewhat limited in scope. Accordingly, the formulation of more general scaling laws, applicable to three-dimensional systems, appeared to be warranted. It appeared, furthermore. desirable to establish this formulation on the basis of a mathematical treatment, rather than by application of general principles of dimensional analysis, to permit more explicit

Jan 1, 1956

By E. N. Mazza, H. S. Kalish

The effect of sintering types 302, 3028, and 430 stainless steel powder compacts in hydrogen and dissociated ammonia was investigated. It was found that sintering in dissociated ammonia resulted in as much as 0.5 wt pct increase in the nitrogen content of stainless steel even though the dissociation of the gas was complete. Sintering in hydrogen, on the other hand, reduced the nitrogen content of the stainless steel to less than 0.01 wt pct. In the case of the 302-type stainless steel, the low nitrogen content resulted in a material that was largely ferritic, whereas the high nitrogen content rendered the material fully austenitic. Sintering in dissociated ammonia resulted in lower density, generally lower tensile strength, less ductility, and higher hardness than sintering under equivalent conditions in hydrogen. The reduction of oxides on both stainless steel and iron particles was found to be effected by hydrogen partial pressure in the sintering atmosphere. Compacting pressure was found also to effect oxide reduction during sintering. DISSOCIATED ammonia often is used as a substitute&apos;.&apos; for hydrogen in sintering and in annealing, since economic advantages sometimes can be obtained by such a substitution. In addition, anhydrous ammonia contains very little impurity. Thus, dissociated ammonia gas is very dry whereas tank hydrogen often must be freed of oxygen and water vapor prior to use in many applications. The sintering of stainless steel powder compacts as well as bright annealing is well recognized as requiring a hydrogen atmosphere and for the foregoing reasons dissociated ammonia is frequently substituted. It has generally been overlooked, however, that the nitrogen in dissociated ammonia might have an important effect on the sintering process and on the properties of stainless steel compacts. Considered an inert gas in many applications, nitrogen, on the other hand, is very reactive with cer- tain metals. Dissociated ammonia could not be used for hydriding zirconium or titanium. Nitrogen reacts with columbium, tantalum, chromium, uranium, thorium, and many other active metals. Iron and iron-base alloys are, for the most part, inert in nitrogen but there are many borderline cases. It has been reported that stainless steel stabilized with columbium or titanium should not be sintered in dissociated ammonia.3 olybdenum has been reported as reacting with dissociated ammonia to a minor extent.&apos; Although most of the reactions with iron-base alloys are attributed to the action of un-dissociated ammonia and the action of nascent nitrogen, Uhlig4 showed how readily pure molecular nitrogen reacts with and diffuses into 18-8 stainless steel at 1150°C. He also pointed out how readily nitrogen diffuses out of 18-8 stainless steel when heated in pure dry hydrogen, and these thorough investigations on the subject show that commercial stainless steels are nitrogen-bearing, since they are melted in air. The effects of nitrogen in stainless steel, particularly the 18-8 Cr-Ni type, previously have received considerable attention." In 1926, it was pointed out

Jan 1, 1956