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By Don C. Blackmar

THE production of non-ferrous secondary metals has become a large and important industry in the United States, and deals with practically every type of manufacturing concern. Its business is unique in that it generally buys from its customers as well as sells to them, whether they are individuals, cities, corporations, or the United States government. Its operations are of vital importance to the success and prosperity of many of the nation's most important manufacturers; yet there are few industries about which less is generally known by those outside it, whether concerning the magnitude of its operations or the details of its actual technique. The industry itself is to blame for this meager publicity, because its technical men have made few attempts to openly exchange ideas, in spite of the excellent examples set by the iron and steel or the copper and brass industries. Whether this is due to the ancient shroud of secrecy generally supposed to cover smelting operations, or because its technical men actually felt that the industry was too puny to be interesting, is hard to say. This paper will consider its subject in a general way, attempting to show something of the size and importance of the industry, as well as its fitness to do its work well. Attention will be called to the sound economic reasons for the handling of non-ferrous wastes by specialists, and to the often unseen losses of metals and labor which occur when manufacturers reclaim their own metallic wastes. MAGNITUDE OF THE MODERN INDUSTRY No particular thought is given to the kitchen accident whereby a ruined saucepan is sorrowfully tossed into the ash can, yet it is a fairly safe guess that within a month this saucepan, together with hundreds of its fellows, will again be in service, perhaps in an automobile crankcase, or in an electric vacuum sweeper. It is by this conversion of the useless into the useful, whether from home or large manufacturer, that the secondary tonnage is built up.

Jan 1, 1928

By Don C. Blackmar

The production of non-ferrous secondary metals has become a large and important industry in the United States, and deals with practically cvery type of manufacturing concern. Its business is unique in that it generally buys frorn its customers as well as sells to them, whether they are individuals, cities, corporations, or the United States government. Its operations are of vital importance to the success and prosperity of nlany of the nation's most important manufacturers; yet there are few industries about which less is generally known by those outside it, whether concerning the rliagnitude of its operations or the details of its actual technique. The industry itself is to blame for this meager publicity, because its technical men have made few attempts to openly exchange ideas, in spite of the excellent examples set by the iron and steel or the copper and brass industries. Whether this is due to the ancient shroud of secrecy generally supposed to cover smelting operations, or because its technical men actually felt that the industry was too puny to be interesting, is hard to say. This paper will consider its subject in a general way, attenlpting to show something of the size and importance of the industry, as well as its fitness to do its work well. Attention will be called to the sound economic reasons for the handling of non-ferrous wastes by specialists, and to the often unseen losses of metals and labor which occur when manufacturc~rs rcclairn thrir own metallic wastes. Magnitude of the Modern Industry No particular thought is given to the kitchen accident whereby a ruined saucepan is sorrowfully tossed into the ash can, yet it is a fairly safe guess that within a month this saucepan, together with hundreds of its follows, will again be in service, perhaps in an autonlobile crankcase, or in an electric vacuum sweeper. It is by this conversion of the useless into the useful, whether from home or large manufacturer, that the secondary tonnage is built up.

By T. S. Washburn

Deoxidation is one of the most complex metallurgical operations in the basic open-hearth process. The necessity for deoxidation arises from the fact that the refining operations that precede it require the oxidation of the steel bath. when the refining is completed and the desired composition of the bath has been obtained with respect to the elements subject to control by 'oxidation. there is usually an excess of oxygen present in the bath from the standpoint of the amount desired in the finished steel. The objectives of deoxidation are to control the amount and type of oxides and, although not directly ilnp1it.d by the term or always considered as a Part of the process, to control the amounts of gases such as hydrogen or nitrogen that will be present in the finished steel. There are other aspects to be consideretl in connection with deoxidizing procedures. In addition to the primary objectives of oxide and gas control. the composition of the steel is affected by the elements introduced during the deoxidizing process. Factors in furnace operations are likewise involved, such as slag composition, temperature control. arid heat time. .ill of these should be considered in establishing the most satisfactory deoxidizing procedure for each grade of steel. The purpose of this paper is to outline the objectives of deoxidation as related to steel characteristics, and to summarize the factors in furnace practice and the economic aspects to be considered in connection with deoxidation procedures. Objectives of Deoxidation The primary objectives of deoxidation are the formation and elimination of oxides. The amount of oxygen present in the bath prior to deoxidation is an important factor, since it is the basis of any deoxidation procedure. The oxygen content of the bath is primarily a function of the carbon content, although it is affected also by the temperature, the oxidation of the slag, and transient conditions within the furnace. The relation of oxygen to carbon in the bath is shown in Table I. Table I shows that under actual operating conditions, the amount of oxygen present in the bath is higher than the theoretical amount. This relation would be expected, since the bath is in a state of metastablc equilibrium during the period that the carbon is being eliminated. The most important feature demonstrated by this table, however, is the rapid increase

Jan 1, 1945

By J. N. Sicking, F. H. Brinkman

A new method for obtaining equilibrium vaporization ratios (K-values) for reservoir fluids has been developed and tested. By application of the method, complex experimental measurements of liquid and vapor phase compositions are eliminated. This simplified technique reduces the cost of experimental equilibrium-ratio data for reservoir studies of condensates and volatile crude-oil systems. The method is designed for systems of constant composition and, therefore, is best suited for depletion studies where compositional changes at high pressures are minor. The basic data required, in addition to the composition of the initial reservoir fluid, are the relative vapor-liquid volumes and densities at reservoir temperature and variom reservoir pressures. Tests demonstrated that the method predicts equilibrium ratios accurately for condensates. A single test on a crude oil was not conclusive; further testing will be necessary before the accuracy of the method can be determined for crude-oil systems. In addition to determining equilibrium ratios, the calculation method provides information on the physical properties of the "plus" component in the vapor and liquid phases. The "plus" component is that mixture of components heavier than the least volatile fraction analyzed. This information is useful in studies of both natural depletion and cycling operations for condensate reservoirs where the heptanes-plus component in the gas phase is produced from the reservoir. INTRODUCTION As more volatile oil and condensate reservoirs are found, the use of phase behavior techniques to predict their performance is increasing in importance. These techniques have long been used for condensate fields and have more recently been applied to crude-oil fields containing oils of medium-to-high volatility. In these phase behavior methods, equilibrium ratios (K-values) are used to predict compositional changes in the reservoir fluids—thereby accounting for the recoverable oil that exists in the gas phase. The reliability of the predictions depends to a large extent on the equilibrium ratios used. These values must be obtained for each component for the entire pressure range being investigated. Unfortunately, because of the complex nature of hydrocarbon mixtures, accurate K-values are hard to obtain. The equilibrium ratios for a particular component will vary not only with the temperature and pressure, but also with over-all composition of the system. The importance of composition is quite critical at elevated pressures, but becomes negligible at pressures below about 300 psia. Therefore, because most phase behavior problems involve the high-pressure region, each fluid system becomes a special case. Experimental programs to determine characteristic K-values are quite difficult and time-consuming. Thus, it is often necessary to resort to approximations of the K-value data. Charts giving K-values for various mixtures and classes of mixtures are available in the literature. However, there are two major difficulties in using them: (1) the K-values of the "plus" component (that mixture of components heavier than the last one analyzed) must be obtained by extrapolation from the K-values of the other components; and (2) the K-values obtained must finally be adjusted by trial and error to agree with observed volumetric data. To eliminate these difficulties, a new method of determining equilibrium ratios was developed. Briefly, after the composition of the system as a whole has been analyzed, the method uses empirical correlations and the gross fluid properties of the system (relative vapor-liquid volumes and densities) to calculate K-values. Because the calculative procedure is long, it is best solved on a digital computer. About one hour of machine time on an IBM 650 computer is required to develop a K-chart for the fluid being examined. DEVELOPMENT OF THE METHOD OF OBTAINING K-VALUES Equilibrium ratios are defined as the ratio of the mole fraction of a component in the vapor phase to its mole fraction in the liquid phase. This statement is expressed in Eq. 1. A typical plot of equilibrium ratios for a particular system is shown in Fig. 1. It should be noted that, at pressures near the saturation pressure, the K-values appear to converge to a common point. This apparent convergence point is called the convergence pressure and is a characteristic of the system involved. Various empirical correlations of K-values have been noted. It has been observed that an isothermal plot of

By H. B. Charmbury, D. R. Mitchell

Recovery of fine coal from solids reporting to wash water has become increasingly important. These solids range from about 28 mesh to 0 and constitute 3 to 7 pct by weight of the feed tonnage to a coal preparation plant. In the past they were usually wasted to streams, but present clean stream legislation makes it necessary to remove them from the wash water and, if economically possible, recover the associated coal as a saleable product. Where these solids are not wasted to streams or to slime ponds they are recovered by thickeners and filters. Since filter cake is often high in ash or sulfur, or both, it is not readily marketed or used. Common practice is to mix it with other plant products, generally slack or cleaned run-of-mine. Uniform blending is difficult, not only because the impurity is usually high, but also because during certain operating periods it is possible to get a concentration of this filter cake in a railroad or barge.

Jan 2, 1959

By Desmond De Villiers Oxford, Peter H. Williams

Nchanga Consolidated Copper Mines, Ltd., is one of the four mines operated by the Anglo American Corp. in Northern Rhodesia, now the independent nation of Zambia. Today Nchanga is the second largest single producer of copper in the world, accounting for more than 200,000 long tons of copper annually at a monthly milling rate of 430,000 tons of ore. The average mill-head grade is about 5.20% total copper, of which approximately 60% is copper sulfide. The remainder, referred to as "acid soluble," is copper oxide. Nchanga mines three separate orebodies varying in grade and sulfide-to-oxide ratio. Ore is processed in two separate grinding circuits feeding into three separate flotation circuits. A fourth flotation circuit treats leach plant residue for additional recovery of sulfides.

Jan 1, 1965

By R. G. O’Meara, S. M. Runke

THE Bureau of Mines has been charged by Congress to investigate processes for the production of alumina from low-grade bauxite, alunite, and clay. As one part of the program, an investigation of the application of ore-dressing methods to improve the grade of high-silica bauxite is in progress at the Mississippi Valley Experiment Station at Rolla, Mo. This paper summarizes data obtained so far and presents detailed results of tests on four typical samples. MINERALOGY OF BAUXITE The name bauxite originally was used to designate the dihydrous aluminum oxide (A1203.2H20). The designation has been retained, although the existence of a specific mineral of such composition has been disproved. The term is now applied to ores of aluminum consisting of various mixtures of the minerals gibbsite (A1203.3H20), diaspore (A1203.H20), and boehmite (A1203.H20). The predominant hydrous aluminum oxide in most American bauxite, however, is gibbsite. In some instances bauxite may be amorphous mixtures of the hydrous aluminum oxides that approximate the composition of dihydrous aluminum oxide (A1203.2H20). The proposed name for this material is cliachite. Gibbsite and boehmite, the trihydrate and monohydrate, are soluble in a solution of sodium hydroxide at elevated temperature and pressure, whereas diaspore is practically insoluble. The solubility of these two minerals is the basis of the Bayer process of alumina extraction. All bauxites contain certain impurities, the commonest of which, in the order of their importance, are: silica, principally as a constituent of kaolinite, and to a lesser extent as quartz; iron, as hematite, limonite, and siderite; and titanium, as ilmenite, rutile and leucoxene. Minor impurities are zircon, cobalt and nickel. Bauxite is produced commercially in Arkansas, Alabama, Mississippi, Georgia and Tennessee, but the most important deposits in the United States are in Arkansas, in the vicinity of Little Rock. HISTORY OF BAUXITE BENEFICIATION The literature on bauxite beneficiation is limited, but the reports of Gandrud and DeVaney1 and Clemmer, Clemmons, and Stacy2 show the possibilities of flotation as a means of beneficiating bauxite. Their work has also developed reagent

Jan 1, 1944

By E. B. Swanson

There is only one way to transport natural gas and that is by pipe lines. In the past few years, these lines have been extended rapidly into areas which previously had been served mainly by solid and liquid fuels. In the subject given me, this extension is referred to as an invasion, which implies a rather forceful entry. Whether or not such an implication may be applied to recent natural-gas developments is unimportant. It is the fact of the extension, not its definition, which is important. For centuries, natural gas has been utilized for various purposes in many parts of the world. It was the foundation of fire worship at Baku. The Chinese used it for the evaporation of brine in salt manufacture. In our country, its history seemingly dates back 110 years to the vicinity of Fredonia, N. Y., where seepage gas was assembled and used for lighting purposes. A few years later, a %inch pipe was laid to a lighthouse on Lake Erie, and the early records of the Lighthouse Service tell of the difficulties surrounding this use. With the discovery of oil in Pennsylvania, there followed further development; the town of Titusville was piped with natural gas and, some few years later, gas was made available for manufacturing plants adjacent to the oil fields. For more than a half century, the industry was concentrated in the

Jan 1, 1932

By C. R. Van Hise

[Concluding Contribution of Prof. Van Hise to the Discussion of his Paper, and Others on the Same General Subject, presented at the Washington Meeting, February, 1900 (see Ram., xxx., 27, 177, 323, 424, 578) ; also of the contributions of Vogt, De Launay, Beck, Lindgren, Kemp, Rickard, Bain, Keyes, Collins and Adams, presented at the Richmond Meeting, February, 1901, and to be printed in the present volume.] In June, 1900, shortly after my paper was published in the Fransactions, I made a briefer statement* before the Western Society of Engineers covering the same ground, which, in certain respects, is somewhat of an improvement. For instance, instead of using the terms descending and ascending &th reference to the waters resulting in the two concentrations, my modified statement is as follows: " The first concentration of many ore-deposits is the work of a relatively deep water-circulation, while the reconcentration is the result of reactions upon an earlier concentration through the agency of a relatively shallow water-circulation. Commonly the deep water-circulation is lacking in free oxygen, and contains reducing agents, and the shallow water contains free oxygen. The deep water is therefore a reducing, and the shallow water an oxidizing agent."† Of the papers upon ore-deposits which, in vol. xxx. of the Fransactions, follow my own, or which were presented at the Richmond meeting, a considerable number are wholly con-

Jan 1, 1902

By Andrew Roy

THE Mahoning Valley coal region lies on the extreme northern outcrop of the Ohio coal-field, and all the mines, with one exception, are opened on the lower coal of the series, No. 1 of the Ohio Geological Survey. The coal ranges from an inch to five, six, and sometimes seven feet thickness, the workable height being between two and a half and six feet. There are two varieties of coal, known in market as "Briar Hill coal " and " Mineral Ridge coal;" both varieties are drawn from the same seam. The Briar Hill coal is generally called block coal, and is the kind so largely used in a raw state in smelting iron. It pos¬sesses a laminated structure, easily splitting into horizontal sheets, but is very difficult to break in the opposite direction. The faces of the layers are often covered with a soft, dead, carbonaceous material, like charcoal, and the whole seam throughout is marked by alternate layers of dead and bright-looking coal. In the act of combustion the coal neither swells nor changes form, the masses retaining their shapes until they fall to ashes in the furnace. The Mineral Ridge variety is much softer, and is also shorter in the grain than the Briar Hill. kind, and it contains a good deal of

Jan 1, 1876

By Andrew Roy

The Mahoning Valley coal region lies on the extreme northern outcrop of the Ohio coal-field, and all the mines, with one exception, are opened on the lower coal of the series, No. 1 of the Ohio Geological Survey. The coal ranges from an inch to five, six, and sometimes seven feet thickness, the workable height being between two and a half and six feet. There are two varieties of coal, known in market as "Briar Hill coal " and " Mineral Ridge coal;" both varieties are drawn from the same seam. The Briar Hill coal is generally called block coal, and is the kind so largely used in a raw state in smelting iron. It possesses a laminated structure, easily splitting into horizontal sheets, but is very difficult to break in the opposite direction. The faces of the layers are often covered with a soft, dead, carbonaceous material, like charcoal, and the whole seam throughout is marked by alternate layers of dead and bright-looking coal. In the act of combustion the coal neither swells nor changes form, the masses retaining their shapes until they fall to ashes in the furnace. The Mineral Ridge variety is much softer, and is also shorter in the grain than the Briar Hill kind, and it contains a good deal of

By B. G. Klugh

The present paper represents a preliminary investigation of the ultimate structure of iron-bearing materials which have been subjected to heat treatment for the purpose of agglomerating the fines, or for chemical changes, or for both. Primarily, the object of this inquiry was to determine the relation of the microstructure of each of these materials to its specific susceptibility to the action in the blast-furnace. It is hoped that this small contribution will serve as a nucleus to a line of research that will throw some light upon the debated questions involved in blast-roasting. Thus far the investigation has been conducted along lines of analogy of known principles, rather than through the application of any well-defined system of microscopic petrography. This is obviously due to the fact that we are dealing with ma-terials which are the artificial products of a new art, rather than with the natural materials from which the essence of the pure science has been evolved. In the limited time allowed for this research, it has been conducted upon those materials the chemical content of which allows of their use commercially in the blast-furnace. The following microphotographs are arranged in the order of the degree of complete fusion to which the mass in question has been subjected, in effectively binding the particles together. A very notable fact here clearly demonstrated is that the degree of fusion to which the material has been subjected is inversely proportional to the reducibility of the product. The characteristic of the material under consideration to which reducibility is almost universally attributed call be progressively traced in the following arrangement, through the identity of the obvious microscopic constituent. Furthermore, the degree of fusion to which a bod? has been subjected is recorded in the presence of resultant products of fusion in that body. Such readjustment is generally apparent

Jan 1, 1914

By F. L. Grammer

The analyses given in Table I. were made several years ago at my request at a plant using Lake ores. They are of two furnaces, one making basic, the other Bessemer pig— they gave 6 casts each in 24 hr., also two flushes of cinder between each cast. They are offered simply for the sake of reference as, so far as I know, it is unusual to find so frequent full analyses made and none are on record. The variations in manganese-content in the first and second flushes on the basic furnace are interesting, if no more than a freak—the first flush being invariably higher in manganese. The iron-content of the two slags from an average of 12 flushes shows: Basic. Bessemer. Per Cent. Per Cent. Total iron...................................... 2.85 1.70 Combined iron................................ 0.72 0.52 Free iron....................................... 2.13 1.18 The greater iron-loss in the basic slag, while known, has never heretofore been so clearly set forth. This may modify the arrangement for handling slag; heretofore usually determined by proximity of the dumping-heap. If a nearby heap is used on contiguous territory, in the past, tilting molten-slag pots were used. If the Pittsburg flood-records for 30 years are a fair criterion the government regulations were inadequate, and molten slag was dumped in such a manner as to throttle the Monongahela at the time of the spring thaws. At Pittsburg the slag, where it is carried to a distance, is frequently granulated in pits and then removed in cars to which it is conveyed by clam-shell buckets. This practice is also quite customary where the slag is intended for the manufacture of slag cement. The production of 500 tons of cast-iron daily means about 300 tons of- slag and at 2.113 per cent. equals 6.4 tons

Jan 1, 1914

By M. L. Requa

EVERY forward step in civilization brings with it an increase in population and increasing demand for raw materials. Modern civilization, because of its industrial development, depends more and more for its well-being on ample supplies of raw materials; the higher the type of that civilization, the greater its dependence. No fact is more obvious than that the raw materials should be put to use with greatest prudence and efficiency. National life is not a matter of a decade or a century. Conservation is no longer a matter for political discussion; it is a vital element in the future welfare of all nations. Unfortunately, to the minds of many, conservation means the locking up of natural resources, their arbitrary withdrawal, bringing about, in short, a condition of industrial stagnation. This has occurred in past centuries through misdirected governmental effort. Two eminent engineers have variously defined conservation as follows:

Jan 1, 1925

By J. D. Price, W. M. Bertholf

One of the chief difficulties with which the operator of a coal washing plant has been forced to contend is the handling of the very fine coal. First he has the problem of separating the fine coal from washery water. This is usually accomplished by the use of settling cones or Dorr thickeners: in either event the separated fine coal contains a high amount (40 to 80 pct) of water and, somewhat loosely, dependent upon the size of the coal particles present, may be known as sludge or slurry. His second problem is the satisfactory further dewatering of such separated sludge and/or slurry. At the coal washing plant of the Colorado Fuel and Iron Corp., washed coal from the Deister Plat-O tables is sluiced to a stationary inclined de-watering screen provided with 3/16 by 1-in. slots, and the coarse coal passing over this screen is conveyed by a Baum-type elevator and a flight-type distributing conveyor to a battery of Carpenter centrifugal driers. The fine coal and water passing through the openings of the primary dewatering screens, plus the fine coal passing through the screens of the centrifugal driers (and no small portion of which is the result of the disintegrating action of these driers) is pumped to two 30-ft Link Belt settling cones. The sludge recovered as underflow from these cones was formerly dewatered on stationary screens having 1/16 by 1-in. slots and discharged on top of the coarse washed coal in the Baum drainage conveyor; but after a relatively few hours of op eration the circulating load of fine coal on this conveyor built up to a point where it became necessary to reduce the quantity of feed to the washing tables. The original arrangement of our coal washing and dewatering equipment is shown in Fig 1. In order to regain the loss in active throughput which had been caused by this circulating load, an installation of six vibrating filters was made during the year of 1936. This resulted in an increase in normal tonnage of washed coal from 1430 to 1750 tons per 8-hr shift, a gain of slightly over 22 pct. This increase in throughput has made a very substantial decrease in the " conversion cost" per ton of washed coal. Since the vibrators were installed, we have gained about 2,000,000 tons in production, compared to what would have been produced in the same number of shifts at the former rate. Putting it in slightly different form, we have saved in the past 12 yr the cost of 1400 operating shifts in the washery. Fig 2 shows the location of the vibrating filters as applied to the original flowsheet. It will be noted that the sludge from the bottom of the settling cones is passed through a distributing box and thence to the filters. The de-watered coal from the filters is de-livered to the conveyor receiving the dried coal from the Carpenter driers.

Jan 1, 1950

By J. L. Rodda

The desirability of a uniformly sized abrasive for metallographic polishing has probably been recognized in a general way for a long time. Certainly all metallographers have recognized the damage that can be done to a polished surface by a piece of grit, especially if one of the softer metals, such as zinc or aluminum, is being polished. It is to be doubted, however, whether many metallographers have had any adequate idea of the particle size of the abrasives they were using or of the range of sizes encountered in any given grade of abrasive. At any rate, the descriptions of abrasives for metallographic work found in the literature are generally very meager. It was with the idea of securing an abrasive with a limited range of particle size that a study of this problem was commenced. Commercial abrasives, even when recommended for metallographic work, are made up of particles of varying sizes. One such abrasive contains some particles so fine that they remain in suspension for days and other particles so coarse that they settle at the rate of 3 in. per minute. It is evident that the coarsest particles are over 100 times the diameter of the smallest ones, or over 1,000,000 times the volume. The hopelessness of avoiding scratches under these conditions is evident. Vanderwiltl has described a laboratory method for grading abrasives in which the elutriator is used. Le Chatelier's method, described by Goereq2 also makes use of an elutriator. However, the elutriator is too slow for this purpose and requires too delicate a control for the range of sizes desired. The method of stirring up the abrasive in water, allowing it to settle for a given time, then drawing a measured depth off the top of the suspension, has been finally adopted as the simplest procedure. The largest particle in a given portion is then determined by Stokes' law:3

Jan 1, 1932

By Clamer, G. H.

G. H. CLAMER, * PHILADELPHIA, PA.-Unfortunately, prior to the war no serious attention was given to the conservation of tin, notwithstanding that this country is practically dependent upon outside sources for its entire tin supply. Tin is of vital importance in many industries, but it is surprising how many and how excellent are its substitutes when we become acquainted with them. Tin has always been a relatively high-priced metal, and it is part of the human attitude to associate high prices with high standards; it is not until the price of a commodity becomes well-nigh prohibitive that we hunt for substitutes, because the idea of substitution seems always to involve an assumption that the substitute must necessarily be inferior. The history of the development of bearing bronzes is a striking example of this policy. In the early clays, copper-tin alloys were almost universally used, the idea then being prevalent, which is still held by many, that a bearing to resist wear must be hard, and the harder the better. The favorite bronze bearing contained 90 per cent. copper and 10 per cent. tin; frequently, in service which was considered severe, even higher proportions of tin were used.. Such hard alloys have great resistance to compression, but as a rule they had a very wide factor of safety in this

Jan 12, 1918

By R. H. Tien

Temperature distribution as well as position of the solidified front is solved by means of "heat balance integral", for the case of freezing a slab with time-dependent surface temperature. Numerical solutions for the cases of linear variation and exponential decay for surface temperature are given. Application also includes solidification of casting. An increased interest in the heat-transfer problem involving a change of phase has been developed in recent years. Practical problems include solidification of a casting, freezing and thawing of soil, ice formation, and others. Despite the importance of the topic, a literature search reveals relatively few solutions which may be extended to practical problems. Due to mathematical complexity, which comes from the nonlinearity of governing differential equations, exact analytical solutions which have been published are limited to a few cases with simple boundary conditions. Although numerical solutions of these problems have become available after highspeed digital computers were introduced, lack of simple and general methods of programming for computation makes this approach impractical. The case of the semi-infinite slab with constant surface temperature was solved in the 19th century. In honor of Neumann, who first found an analytical solution, this kind of problem is generally referred to as the Neumann solution. As has been shown in Fig. 1, the problem to be analyzed is the freezing of a semi-infinite region (x > 0) which is initially liquid at the melting temperature with the surface (x = 0) maintained at time-dependent temperature. This analysis can be applied to the study of many casting processes where most of the heat removal is essentially unidirectional. "Heat balance integral" which has been used by Goodman1 is employed in this analysis. The concept of "heat balance integral" is to define a quantity, d(t), called the thermal layer. Beyond this thermal layer, for all practical purposes, there is no heat transfer, and the region is at the equilibrium temperature. "Heat balance integral" is obtained by integrating the conduction equation with respect to the space variable over this thermal layer d(t). Choosing some plausible temperature distribution, usually a polynomial or a finite trigonometric series in the space variable, this integral equation becomes an ordinary differential equation, with time as the independent variable, which can be solved by classical methods. The thermal layer and "heat balance integral" are equivalent, respectively, to the boundary-layer thickness and the momentum integral in hydrodynamics. A modern account of Prandtl's concept of the boundary layer and von Karman's momentum integral may be found in Ref. 2. Although the problem considered here has been limited initially to uniform melting temperature, the present method is equally applicable to the case with arbitrary temperature distribution in the liquid. STATEMENT OF THE PROBLEM The physical situation and coordinate system used in the problem to be analyzed are shown in Fig. 1. Notations used are listed in the table of nomenclature. Let us assume a semi-infinite region extending over positive x, initially at the uniform melting temperature. At the surface x = 0, a time-dependent temperature, which has a numerical value

Jan 1, 1965

By J. R. Johanson

With the continuing development of automatic operations, it is important that reliable discharge rates through hoppers and bins be obtained for bulk solids. In most applications a feeder is used to control the feed rate. The selection of this feeder size is usually based on the rated ability of the feeder to move material without regard to the capability of the material to flow through the opening in the hopper onto the feeder. The dis charge rate through a given hopper opening may vary from zero to a theoretical maximum depending on the flow properties of the material. This paper presents an equation for the maximum discharge rate for a bulk material as a function of the hopper shape, the opening size and the flow properties of the material. Discharge-rate tests on various materials indicate good agreement with calculated values for opening sizes from a fraction of an inch to several feet. As part of a program to develop improved design criteria for bulk storage and handling facilities, a specific study of the methods involved in calculating the rate of discharge of bulk solids from hoppers and bins has been made. This study is closely related to earlier work done on the prevention of flow problems through the choice of proper design geometry of hoppers and bins1. The present paper is an extension of this earlier work, and therefore many of the concepts previously derived and explained will be used without explanation. Two types of flow will be considered: plane-strain flow in a wedge-shaped hopper and axial-symmetry flow in a conical hopper. The literature contains many studies on discharge rate for regular-shaped dry particles2*3 such as glass beads, lead shot and coarse dry sand. However, the work is empirical in nature, and it is difficult to extrapolate the given information to apply to moist, sticky materials typical of many industries. Some studies4 have shown a decrease in discharge rate with an increased moisture content of the material. However, no attempt was made to correlate the discharge rate with moisture. The method of calculating discharge rate presented in this paper was derived analytically from the basic knowledge of the flow of frictional, cohesive, granular solids, The equation includes the effect of material cohesion (stickiness), hopper configuration, opening size and bulk density of the material. THEORETICAL WORK The basic assumptions made in deriving the discharge rate equation are as follows: 1) The material is a frictional, cohesive, granular solid. 2) The flow is considered continuous and without significant density change. 3) The material at the hopper opening forms a continuously failing arch that is in dynamic equilibrium. 4) The strength of the material in the arch, which must be overcome for the arch to fail, is caused by the pressure in the flowing mass near the hopper opening. 5) This pressure at the hopper opening can be calculated5. If we consider the dynamic equilibrium of an arch of uniform thickness such as that shown in Fig. 1,

Jan 1, 1965

By James Kemp

PostScript to a paper presented at the New York meeting, February, 1915, and printed in Bulletin No. 98, February, 1915, pp. 129 to 154. The writer looked over the quarry with care in the search for fossils, having in mind shells or corals of fairly large size. In the brilliant summer sunshine, none were observed on the glaring white ledges. The impression was gained that none were present and the statement to this effect was made in the edition of this paper published in the Bulletin' of the Institute for February, 1915, p. 136. On closer examination in the laboratory it has been discovered that the limestone itself is made up of minute organisms, which are clearly revealed by microscopic examination of thin sections. The principal component of the rock is a small foraminifer, 0.1 to 0.3 in. (2.5 to 7 mm.), of the genus Orbitoides, presumably an Oligocenic form. Figs. 1 and 2. illustrate it. The accompanying description has been kindly summarized by Marjorie O'Connell, M. A., Curator in Paleontology in Columbia University, who first detected the evidences of organisms in the rock. Orbitoides kempi O'CONNELL N. SP.1 The foraminiferan which makes up the Seboruco limestone is an Orbitoides of a Species new to North America. The only Orbitoides heretofore described from this country is 0. mantelli from the lower Oligocenic of the Gulf States. This form from Cuba, then, so different in all of its characteristics from the 0. mantelli, is of great interest as perhaps forming a basis of correlation over wide areas. The most closely related Species is 0. dispansa Sowerby, which occurs in the Nummulite limestone of the Eocenic of the Bavarian . Alps, in the Priabona beds of the lower Oligocenic of Massano, and elsewhere in Italy, as described by Gümbel.2 The age of the limestone in Cuba would thus Seem to be of upper Eocenic or lower Oligocenic age, probably the latter. The fossil has the form of a sphere Surrounded by a wavy rim of horizontal extent, the whole resembling two flat-brimmed, round-crowned hats placed base to base. The total extent of the Shell ranges up to 7+ mm., while the thickness of the central sphere is 2.5 mm. in one of the largest individuals. Like all of the other Species of Orbitoides, this form begins with a Single layer of chambers which multiply in one plane and assume a circular outline; but it is in the subsequent growth that the distinguishing specific characters appear, for the chambers at the central portion of the shell increase more rapidly than do those near the periphery and in consequence a Swelling is produced which finally gives the Spherical form which is so characteristic. The rim, on the other hand, shows little chamber-increase and remains thin. This is clearly Shown in the sections figured, where the central row of larger chambers forms the equatorial zone. Radiating from this row, in section, there appear, a number of solid cones alternating with broad reticulated ones. The solid cones mark the more dense structure forming the walls surrounding the reticulated or chambered cones. These appear upon the Surface as distinct pits, whereas the solid part appears as raised walls.

Jan 7, 1915