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IN the footnote on the first page of Prof. Stoek's paper, as printed in vol. xxviii. of the Transactions, I alluded to him, under an erroneous impression, for which he was in no way responsible, as " the present Director of the Scranton Schools." This incorrect statement placed him in a false position, as possibly having authorized the use of a title to which he had no claim. In fact, Prof. Stoek has never had any official connec-

Jan 1, 1900

By D. Murgue

The circulation of air in underground workings is subject to a gradual and continuous reduction of its pressure, from intake to outlet, caused by the friction between it and the more or less rough and uneven surfaces of the passages. For comparison with the flow

Jan 1, 1894

By W. Mostowitsch, H. O. Hofman

The mineral gypsum, CaSO4 + 2 H2O, has been used for many years as a sulphurizing and basic flux in several smelting-operations. Thus, in smelting oxide nickel-ore in the blastfurnace, it is commonly added to the charge to furnish the sulphur necessary for collecting the metal in a matte, and a base for slagging the siliceous gangue. In the concentration of lead-copper matte in the reverberatory furnace it has been used for years at Preiberg, Saxony,1 for a similar purpose, and for producing at the same time a copper-matte with less than 0.15 per cent. of Fe. The latest use gypsum has been put to is in the blast-roasting process of Carmichael-Bradford.2 The term " blast-roasting," given by A. S. Dwight3 to the Dwight-Lloyd method of roasting and agglomerating: is a happy generic term which covers the ground better than the " lime-roasting " of Ingalls5 or the " pot-roasting " of Austin: in that it leaves the operation independent of the character of the flux and the form of apparatus, and retains the characteristic feature of this class of processes—namely, that of using forced draft. In the Carmichael-Bradford process the dehydrated material, mixed with galena-concentrate, acts as a diluent and a flux. The process differs in this from the Huntington-Heberlein7 and the Savelsberg8 processes, in both of which limestone is used.

Jan 1, 1909

By H. R. Hanley

IN AS MUCH as the interesting changes in the economics of the zinc industry are covered nowhere else in this issue, and they are related to technological progress in the metallurgy of zinc, some reference to prices and production will first be made. The latter part of 1939 is outstanding in the large war demand for metals including zinc, whereas in the first eight months the demand for zinc was subnormal. The cause of the rapid in- crease in demand was the European war and hence the future is problematical. When the year began zinc was in the doldrums, with low prices, and continued thus until August when an advance in price started, reaching 6.5. per pound early in October. (Prime Western, St. Louis.) Rapid changes in the price of any metal are viewed adversely by the metal industry. The persistent low price for zinc of 4 to 49512 for about two years curtailed production and in one instance closed one large plant for a brief period.

Jan 1, 1940

By W. H., Bassett

IN January, 1926, the writer began a study of the commercial value of beryllium in its relation to copper. The purpose of the investigation was not to make a mere laboratory study of the characteristics of beryllium-copper alloys, but to determine under mill conditions the behavior of copper when alloyed with beryllium and when other metals were added to such alloys; in other words, it was considered important to know whether the alloy bars could be hot-rolled or cold-worked, and what limits in composition would have to be established for these two methods of working. Consequently, more stress has been placed on the practical application of the alloys in engineering and commercial use than on a discussion of the metallography of the specimens examined, although this part of the matter has not been entirely neglected. Credit should be first given to G. Oesterheld,1 who, in 1916, published the copper-beryllium equilibrium diagram. Fig. 1 has been copied from the original article with the simple substitution of English words. It will be noted from Fig. 1 that alpha solid solutions are formed, up to about 1.5 per cent. Be (10.5 atom.). The freezing-point curve, after falling from 4.2 per cent. Be (23.5 atom.), enters into a very complicated form over the entire beta region. There is a possible compound, Cu2Be, at about 6.5 per cent. Be (32.3 atom.). The pure gamma range extends from 11.2 to 12.2 per cent. Be. (46.5 to 49 atom.), after which the liquidus rises rapidly to 30 per cent. Be. (75 atom.). The delta solution extends from 25 per cent. to an unknown percentage of beryllium. There is a eutectoid point at 575" C., extending from 1.5 to 11.2 per cent. Be., the maximum time interval of which occurs at 6 per cent. Be. Below this line the beta solution is described as breaking up into alpha and gamma. Microscopically, the eutectiferous alloy thus formed closely resembles pearlite, and requires a high magnification for its resolution.

Jan 1, 1927

By Frances H. Clark

IN wartime, the fabrication and use of metals assumes increased importance, for a modern war of sizable proportions cannot be undertaken with- out a vast supply of this material. Light alloys of aluminum and magnesium, which were comparatively unknown in the last war, will play an important role in this one. Due to research on a vast scale in the interim of years, industry is today well equipped to fabricate metals on an enormous scale. Research for the past year has been most productive and a comprehensive survey in the space of this article would be impossible. It is hoped that the stressing of a few items here and there out of a great quantity of able work will indicate in a small way the advances made within recent times. Specific references to the literature will be omitted at the Editor's re- quest but some authors of papers that I have found of special interest are mentioned.

Jan 1, 1940

By J. E. Johnson

(Cleveland Meeting, October, 11,1912.) THE subject of blast-furnace slag is one which has had much consideration, particularly from the scientific standpoint, and several years ago technical literature contained many learned discussions on the oxygen-ratio of the acids and the bases, all on the assumption that acids and bases must be present in a ratio depending on molecular weight and chemical valency. Much work has also been done, sometimes in conjunction with the former, on the total heat and the temperature of initial fusion or softening of various slags. A wider knowledge of the blast-furnace now enables us to say that for practical purposes this work has been of almost no value. It is now generally admitted that on the physical side the important point of a given slag is neither its total heat of fusion nor its softening-point, but its free-running temperature, since this is the critical temperature of the furnace. This temperature bears no definite relation to the softening-temperature, as determined by Seger cones, for instance, because some slags melt relatively like ice, with a very short viscous-range, while others melt relatively like tar, with a very long viscous-range. In one the difference between the softening- and the free-running temperature may be very small, as little as 100° F., while in another this difference may easily be 200° or 300°. The importance of this difference is so great in practice as to destroy completely the value of exhaustive investigations, even such as those of 0. Boudouard, published a few years ago.1 * Presented also at the Joint Meeting of the Institute with Section IIIa, Metallurgy and Mining, of the Eighth International Congress of Applied Chemistry, New York, September, 1912. 1 It may not be amiss at this point to call attention to the excellent suggestion of Woolsey McA. Johnson, made several years ago, for determining the temperature at which different slags have the same practical fusibility. This suggestion

Oct 1, 1912

By S. F. Emmons

[The following notes of observations made during a visit of a few days in the month of October, 1886, which was cut short by a sudden summons East, are offered, in spite of their incomplete and tentative character, in the hope that they may aid the members of the Institute, in their coming visit to this region, to a clearer understanding of the general geological conditions under which the ore-bodies occur.] The Butte mining region lies in a sort of a depression in the mountains which is drained by Silver Bow creek and its various tributaries. On the east it is bounded by high north and south ridges of granite, and on the west by lower ridges, also running north and south, which, as far as examined, were found to consist of rhyolite. High mountains also inclose the depression on the north and south, but at a greater distance than the more immediate bounding ridges on the east and west, the distance between which is hardly more than six miles.

Jan 1, 1888

By K. S. Lane

The problem of stability of slopes in reservoirs is one of real interest in civil engineering. The problem is whether the valley walls will remain stable or whether they are likely to slide as conditions are changed by storage of water in the reservoir. If major slides are indicated, as on the walls of relatively steep canyons, one must estimate whether they will be so located and of sufficient size as to interfere with operation of the reservoir-as by blocking the outlets, or by displacing sufficient water to over-top the dam in a huge wave. Some cases involve problems in soil mechanics for slides in earth or weaker rock; other locations need the assistance of rock mechanics for slides in harder rock. While this is not a new problem, attention has recently been focused on its importance by the hugh landslide into the Vaiont reservoir in 1963, which claimed the lives of over 2000 people and forced abandonment of the dam and powerhouse. VAIONT RESERVOIR SLIDE Fig. 1 shows Vaiont Dam in Italy which is a double curvature arch, 875 ft high, located on a tributary of the Piave River, north and west of Venice. When completed in 1960 it was the highest arch dam in the world. In 1960 a sizable landslide (some 700,000 cu yd) occurred on the left abutment a short distance above the dam. Following this, the reservoir was held down for construction of a by-pass tunnel through the right valley wall to insure connection with the upper end of the reservoir in event of further slides. In October 1963 a giant landslide occurred on the left valley wall, over a width of some 14 miles (see Fig. 2). Over 300 million cu yd slid into the reservoir, displacing the water and forming a hige wave 700 ft above the top of the dam as it hit the opposite, or right, wall of the valley. The wave then passed some 500 ft over top of the dam, followed down the tortuous winding canyon and debouched into the

Jan 1, 1967

By P. B. Baxendell, R. Thomas

Work on the calculation of vertical two-phase flow gradients by Cia. Shell de Venezuela has been based mainly on the "energy-loss" method proposed by Poett-mann and Carpenter in 1952. The "energy-loss-factor" correlation proposed by Poettmann and Carpenter was based on relatively low-rate flow data. This correlation proved inapplicable to high-rate flow conditions. In an attempt to establish a satisfactory correlation for high rates, a series of experiments was carried out at rates up to 5,000 BID in Cia. Shell de Venezuela's La Paz field in Venezuela, using tubing strings fitted with electronic surface-recording pressure elements. As a result of these experiments a correlation between energy-loss factor and mass flow rate was established which is believed to be applicable to a wide range of conduit sizes and crude types at high flow rates (e.g., above 900 BID for 27/8-in. OD tubing). It is anticipated that the resulting gradient calculations will have an accuracy of the order of % 5 per cent. At lower flow rates the energy-loss factor cannot be considered as constant for any mass rate of flow, but varies with the free gas in place and the mixture velocity. No satisfactory correlating parameter was obtained. As a practical compromise for low flow rates, a modification of the curve proposed by Poettmann and Carpenter was used. In practice this was found to give gradient accuracies of approxirnately ± 10 per cent clown to flow rates as low as 300 B/D in 27/8-in. tubing. INTRODUCTION Production operations in Cia. Shell de Venezuela's light- and medium-crude fields are principally concerned with high-rate flowing or gas-lift wells. Under these conditions the analysis of well performance, the selection of production strings and the design of gas-lift installations are vitally dependent on an accurate knowledge of the pressure gradients involved in vertical two-phase flow. Initially, attempts were made to establish the gradients empirically as done by Gilbert,' but the results were not reliable due to scarcity of data over a full range of rates and gas-oil ratios. Several methods of calculation based on energy-balance considerations were attempted, but the computations were cumbersome and the results cliscouraging. In 1952 a paper was published by Poettmann and Carpenter' which proposed a new approach. Their method was also based on an energy-balance equation. but it was original in that no attempt was made to evaluate the various components making up the total energy losses. Instead, they proposed a form of analysis which assumed that all the significant energy losses for mutiphase flow could be correlated in a form similar to that of the Fanning equation for frictional 1osses in single-phase flow. They then derived an empirical relationship linking measurable field data with a factor which, when applied to the standard form of the Fanning equation, would enable the energy losses to be determined. The basic method was applied in Venezuela to the problem of annular flow gradients in the La Paz and Mara fields" This involved establishing a new energy-loss-factor correlation to cover high flow rates and, also, some adaptation of the method to permit mechanized calculation using punch-card machines. The final result was 1 set of gradient curves for La Paz and Mara conditions which proved to be surprisingly accurate. With the encouraging results of the annular flow calculations, several attempts were made to obtain a corresponding set of curves for tubing flow. Here, unfortunately, little progress could be made. The original correlation of Poettmann and Carpenter was based on rather 1imited data derived from low-rate observations in 23/8- and 27/8-in. OD tubing. It did not cover the higher range of production rates, and extrapolation proved unsuccessful. A new correlation covering high flow rates was required, but this proved to be extremely difficult to establish since tubing flow pressure measurements at high rates did not exist—due to the difficulty of running pressure bombs against high-velocity flow. The necessity for reliable tubing flow data increased with the development of the new concessions in Lake Maracaibo, where high-rate tubing flow from depths of 10,500 ft became routine. Thus. it was decided to set up a full-scale test to establish a reliable energy-loss factor for tubing flow conditions. A La. Paz field light-oil producer with a potential of approximately 12,000 B/D on annular flow was chosen. To obtain full pressure gradients, a special tubing string was installed which was equipped with electronic surface-recording pressure measuring devices,

By Blamey Stevens

(San Francisco Meeting, October, 1911.) My previous paper is entitled, The Laws of Igneous Emanation Pressure. The present paper lays no claim to the exactitude and completeness of a law, since it is of a provisional nature and may be disregarded when experiments have established a basis for more exact reasoning. The general physical states in which aqueous emanations may occur are first considered. The possible physical conditions under which the mineral elements may occur in emanations are then discussed, and a classification of deposits, dependent on emanation, is proposed. A system of scientific experimental investigation is outlined, and it is shown that the physical and chemical properties of emanation may be exactly determined thereby. The investigation is urged as feasible and simple, and not necessarily requiring large and costly apparatus. It is the only step necessary to make possible the formulation of a complete set of laws of igneous emanation. Process of Emanation. In a rising column, magma ranges in temperature from 900° to 1,200°C. Exhalation must begin at some fairly great depth. What this depth may be we can only surmise, since no experimental evidence is available. Exhalation, however, continues as the magma flows upward, until at another level the occluded gases have all escaped. This depth is probably upward of 5,000 ft. (See Fig. 1.) All exhalations must come from between these two levels. As the whole emanation is the sum of the exhalations and residues, the residues must come from below the uppermost level. They will be most abundant when coming, from those parts of the intrusion which have solidified below the lower level.

Apr 1, 1912

By C. J. Rosa, W. C. Hagel

An attempt is made to determine the diffusion coefficients of oxygen ions in hypostoichiometric zirconium oxide. A phenomenological theory is developed for three-phase, unidirectional volume diffusion of a gaseous species from a planar source. Knowledge about oxygen diffusion in a and ß zirconium and experimentally measured rates of movements of interfaces permit the evaluation of oxygen ion diffusivi-ties in ZrO2-x. The results conform to the relationship: sq cm per sec, for the temperature range of 875" to 1050° C. DIFFUSION coefficients of oxygen ions in stoichio-metric oxides have been studied by many investigators. The obtained results not only supplement the knowledge about the lattice-defect structures of oxides and conduction mechanisms but also provide information of technological importance. Rate processes such as oxide sintering, high-temperature creep deformation, and oxidation of metals and their alloys are directly dependent on diffusion phenomena. Unfortunately, diffusion coefficients obtained from studies on stoichio-metric oxides cannot be treated without restraints when applied to oxidation kinetics, if precise evaluations of oxidation rates are desired. Oxides formed on metals are usually nonstoichiometric and exhibit nonuniform distribution of either cation or anion vacancies across their thicknesses. Debuigne and Lehr1 extended Danckwerts'2 mathematical analyses and furnished a semitheoretical treatment for evaluating oxygen diffusion coefficients in zirconium oxide in terms of weight gain measurements during oxidation of zirconium in the temperature range 400° to 850°C. Their calculations are based on theoretical partitioning3 of the total amount of oxygen between a zirconium and its oxide phase. An inherent discrepancy appears to continue throughout their calculations. The amount of oxygen confined to the oxide phase should be corrected by multiplying the calculated oxide thickness by the inverse of Pilling-Bedworth ratio, if expansion of zirconium dioxide is taken into account. The purpose of the present investigation is to provide a new semitheoretical treatment for evaluating diffusion coefficients of moving species in hypostoichiometric oxide. The analyses are relevant to unidirectional volume diffusion. Although the presented method is quite general, its applicability will be discussed in terms of kinetic measurements from oxidation of zirconium at temperatures above the a/ß transition, for reasons stated in the later part of this paper. EXPERIMENTAL Pure, 99.93 wt pct, zirconium samples of approximately 2 by 1 by 0.35 cm were exposed to oxygen for various times at four temperature levels: 875°, 950°, 1000°, and 1050°C. High-purity, better than 99.9 vol pct oxygen was passed through a cold trap and columns containing anhydrous CaSO4 to remove residual water vapor. Before exposing to oxygen at a pressure of 500 Torr, specimens were subjected to wet abrasion on 200- through 600-grit Sic papers and polished with 1—p diamond dust. Prior to oxidizing, all zirconium samples were vacuum-annealed at 10-6 mm Hg for about 15 min at the test temperature. The temperature variation across the uniform heat zone was ±2°C from the preset value. Final polishing, for phase thicknesses measurements, was performed by using 8- and 1-p diamond dust and followed by vibrator polishing with 0.05-µ ? Al2O3 solution. Measurements of phase thicknesses were made by projection on a metallographic viewing screen. Conventional powder X-ray analyses for the oxide were employed. RESULTS Fig. 1 is an example of the cross section of oxidized zirconium. Designations of phases given below this figure are the same as those used in the three-phase diffusion system represented by Fig. 5 in the following section. Zirconium oxidized for longer exposure times showed two types of oxides: white oxide at the surface and an underlaying layer of gray oxide. X-ray powder patterns of these oxides at room tern-

Jan 1, 1969

By W. Philippoff, Donald E. Cadwell, S. R. B. Cooke

THE importance of contact angles in flotation has long been recognized, but little has been done to get quantitative relationships between the surface coverage of the mineral by the reagent, the length of the hydrocarbon chain, and the contact angle. It is well known that for a complete monolayer on the surface of a mineral the contact angle 8 is determined only by the reagent1 and principally by the chain length of the hydrocarbon radical. Although for flotation the monolayer usually is regarded as being complete, early experiments of Wark and Cox&apos; showed that at very small concentrations of potassium ethyl xanthate the contact angle on galena changed in a continuous way from 0&apos; to the equilibrium value of 60". Further, Gaudin and Vincenta showed a similar continuity using heptylic acid and sphalerite. This shows that with probably incomplete monolayers, 0 varies with the degree of surface coverage. At the time these experiments were made it was impossible to measure the actual amount of surface coverage, especially since the decrease of the collector concentration in the liquor could be influenced by chemical side reactions. Through the use of the radioactive tracer method for the measurement of the amount of collector adsorbed on the surface of the mineral, Gaudin and Bloecher&apos; were able to determine accurately the actual surface coverage of dodecylamine acetate on quartz, but they did not measure any contact angles. It is believed that the relationship between the surface coverage and the contact angle is extremely important in flotation, especially as Gaudin and Bloecher showed that a 95 pct recovery is possible with a coverage of only 5 pct. Theoretical Considerations The work of adhesion W is the energy bound (in ergs per sq cm) when an interface is formed. It is determined by the difference of the free surface energies (surface tensions) of the respective phases 7j and yZ before contact and the interfacial free surface energy y, after contact. The definition of the contact angle permits the elimination of the unknown surface energy of the solid and hence the calculation of W from the surface tension of the liquid y and the contact angle 8: W = y (1 + COS0) [1] Consider a surface consisting of two components, identified as 2 and 3, 1 being the liquid. The amount of 2 in the composite surface is x, where 0 < x < 1. The respective contact angles with 1 and air are 8, and 8.. The total work of adhesion of such a surface is the sum of the values of the components multiplied by their respective areas. A formal relation can be written: Wm = x-W2+ (l-x)-W, [2] in which W, is the work of adhesion of the composite surface. Eq 1 can be introduced into Wt and Wa, but in the case of W, some discussion is needed. If the two components are segregated, each component forming an integral part of the composite surface there is no physical meaning for a contact angle 8m calculated from W,, by using eq 1. If, on the other hand, the area of each patch of the components is small in comparison with, say, the diameter of the bubble used in measuring, it could be expected that 0m would have a physical significance, because of the action of the surface tension of the liquid-gas interface tending to smooth out sharp corners. How small these patches would have to be is difficult to predict, but by using composite surfaces with microscopically

Jan 1, 1953

By S. R. B. Cooke, W. Philippoff, Donald E. Cadwell

THE importance of contact angles in flotation has long been recognized, but little has been done to get quantitative relationships between the surface coverage of the mineral by the reagent, the length of the hydrocarbon chain, and the contact angle. It is well known that for a complete monolayer on the surface of a mineral the contact angle 8 is determined only by the reagent1 and principally by the chain length of the hydrocarbon radical. Although for flotation the monolayer usually is regarded as being complete, early experiments of Wark and Cox&apos; showed that at very small concentrations of potassium ethyl xanthate the contact angle on galena changed in a continuous way from 0&apos; to the equilibrium value of 60". Further, Gaudin and Vincenta showed a similar continuity using heptylic acid and sphalerite. This shows that with probably incomplete monolayers, 0 varies with the degree of surface coverage. At the time these experiments were made it was impossible to measure the actual amount of surface coverage, especially since the decrease of the collector concentration in the liquor could be influenced by chemical side reactions. Through the use of the radioactive tracer method for the measurement of the amount of collector adsorbed on the surface of the mineral, Gaudin and Bloecher&apos; were able to determine accurately the actual surface coverage of dodecylamine acetate on quartz, but they did not measure any contact angles. It is believed that the relationship between the surface coverage and the contact angle is extremely important in flotation, especially as Gaudin and Bloecher showed that a 95 pct recovery is possible with a coverage of only 5 pct. Theoretical Considerations The work of adhesion W is the energy bound (in ergs per sq cm) when an interface is formed. It is determined by the difference of the free surface energies (surface tensions) of the respective phases 7j and yZ before contact and the interfacial free surface energy y, after contact. The definition of the contact angle permits the elimination of the unknown surface energy of the solid and hence the calculation of W from the surface tension of the liquid y and the contact angle 8: W = y (1 + COS0) [1] Consider a surface consisting of two components, identified as 2 and 3, 1 being the liquid. The amount of 2 in the composite surface is x, where 0 < x < 1. The respective contact angles with 1 and air are 8, and 8.. The total work of adhesion of such a surface is the sum of the values of the components multiplied by their respective areas. A formal relation can be written: Wm = x-W2+ (l-x)-W, [2] in which W, is the work of adhesion of the composite surface. Eq 1 can be introduced into Wt and Wa, but in the case of W, some discussion is needed. If the two components are segregated, each component forming an integral part of the composite surface there is no physical meaning for a contact angle 8m calculated from W,, by using eq 1. If, on the other hand, the area of each patch of the components is small in comparison with, say, the diameter of the bubble used in measuring, it could be expected that 0m would have a physical significance, because of the action of the surface tension of the liquid-gas interface tending to smooth out sharp corners. How small these patches would have to be is difficult to predict, but by using composite surfaces with microscopically

Jan 1, 1953

By C. F. Weinaug, P. M. Blair

Many difference equations used to approximate reservoir flow problems treat the phase pressures implicitly but not the mobility-density coefficients. Such difference equations are neither wholly explicit nor implicit, but might be described as mixed. Mixed equations are relatively easy to apply. But the associated time truncation error is relatively large, and when used to solve problems characterized by high flow rates, these equations may be unstable for practical size time steps. This paper outlines the development of a completely implicit difference analogue for reservoir simulation, along with a Newtonian iterative method for solving the resulting nonlinear set of algebraic equations that arise at each time step. While this implicit equation requires two to three times more work than does the mixed equation, it is shown to markedly decrease the time truncation error and to yield a stable solution for much larger time steps than does the mixed equation. INTRODUCTION Calculation of multiphase, multidimensional flow in porous media is generally accomplished by numerical methods that involve approximating systems of partial differential equations by systems of partial difference equations. The early development of difference equation techniques was directed toward the solution of linear differential systems. However, the equations of multiphase fluid flow through porous media are highly nonlinear in that mobility and density often are strong functions of pressure and saturation. Thus, solution of the flow problems by difference equations involves solving sets of algebraic equations whose coefficients change from step to step of the calculations. Current practice is to evaluate most coefficients at the beginning of a time step and then to apply difference methods well suited for solving linear problems. At least two major difficulties arise from the use of this practice. First, evaluation of coefficients at the old time level and evaluation of pressures at the new time level results in larger time truncation errors near displacement fronts than if all quantities in the distance derivative were evaluated at the same time level. Second, evaluation of mobility coefficients at old time levels results in an unstable difference equation in regions of high flow rate. The first of these difficulties often results in optimistic recovery behind the displacement front, and the second requires the use of small time steps or special techniques in solving coning problems1 or problems of gas percolation.2 Evaluation of all quantities in the distance differences at the new time level results in a completely implicit difference system. Such a difference system has a lower time truncation error than equations in which mobilities are evaluated at the old level and pressures evaluated at the new level. The algebraic equations resulting from the fully implicit difference equation are, in this case, nonlinear and require some iterative method for their solution. This paper develops fully implicit difference equations for two-phase flow in porous media, describes their solution by Newtonian iteration, and gives examples of problems more easily solved by the new method than by previous methods. EVOLUTION OF DIFFERENCE EQUATIONS FOR NONLINEAR PROCESSES The completely implicit difference equation used in these calculations results from evolution beginning with explicit difference equations, proceeding through what we will call "mixed" equations, and arriving now at a completely implicit equation. Let us illustrate the evolution by considering different analogs of the nonlinear equation

Jan 1, 1970

By G. Birkbeck, T. C. Wells

Pearlite morphology in three commercially produced, low-carbon steels has been studied using optical and electron microscopy. A reduction in the cooling rate from 600° to 6°C per hr increased the interlamellar spacing but had little effect on pearlite content. The form of the lamellae was also assessed in terms of a new parameter, the ratio of lamellae length to interhmellar spacing. The variation of this parameter with cooling rate depended on steel composition. For each steel, it would appear that an optimum cooling rate exists at which lamellar pearlite can be produced to the greatest extent, though not necessarily the same extent in different steels. PeARLITE morphology depends principally on steel composition, prior austenite grain size, and either cooling rate or isothermal transformation temperature. Alloying with manganese,&apos;" fine grain size,374 and slow cooling rates reduce the likelihood that a well-developed lamellar structure will be produced. Instead, imperfect structures usually consisting of partly globular carbides are formed in a ferrite matrix. Such structures have been described as granular.1,2,5 degenerate,6 or semi4-pearlite. Manganese additions also progressively lower the eutectoid temperature and the carbon concentration at the eutectoid so so that, for a given carbon content. the pearlite fraction is increased as manganese is added. While the effects of manganese are understood in a general way, quantitative studies of pearlite morphology have been carried out mainly on steels of eutectoid composition;9 little quantitative data is available for low-carbon steels. Certain anomalies exist in the behavior of steels containing -1.5 pct Mn, however. The pearlite morphology in niobium-treated steel differs from that which is generally accepted as typical of low-carbon/manganese steels in that a reasonably well developed lamellar structure is sometimes observed. In the present work, the effects of changes in cooling rate from 600° to 6°C per hr on the pearlite morphology in three commercially produced, low-carbon steels have been studied by both optical and electron microscopy. I) MATERIALS The steels were of the following types: 1) 0.1 pct C, 0.4 pct Mn steel (En 2, a composition similar to specification SAE 1010); 2) niobium-treated, 0.2 pct C, 1 1/2 pct Mn steel (BS 968:1962); 3) silicon-killed 0.2 pct C, 1 1/2 pct Mn steel (En 144, a composition similar to SAE 1320). The chemical analysis for each steel is given in Table I. To facilitate the comparison of pearlite morphology in the three steels, steels 1 and 3 (which were obtained as 1/2-in. plate and 1-in.-diam bar, respectively) were hot-rolled in the laboratory to $ in. thickness, finishing at around 850°C. The BS 968:1962 was received as 1/8-in. plate finished at 885°C and was not further worked. Specimens from each steel were heat-treated in vacuo at 950°C for 1 hr and cooled at rates of 600°, 60°, and 6°C per hr. 11) EXPERIMENTAL Pearlite contents were determined by point counting (500 points) on longitudinal sections mechanically polished and etched in 2 pct nital. Pearlite morphology is usually considered in terms of interlamellar spacing. For pearlite colonies randomly distributed in space and having a true, constant interlamellar spacing So Pellissier et al.9 determined the distribution curve for the apparent spacings of the lamellae on a random section plane. The areal fraction fs of the pearlite colonies occupied by apparent spacings up to a limiting value S is given by:

Jan 1, 1969

By R. M. Brick

EDUCATIONAL benefits for veterans of World War II have largely removed one of the two former barriers to a college education for everyone, namely financial means and intellectual capacity. This latter limita¬tion has not kept privately endowed institutions from increasing 50 to 100 percent in size of student body, even after applying moderately rigid entrance standards. Growth of some land-grant universities, which cannot well exercise such restrictive judgements, has been even greater. After a weary board of admissions, subject to student, alumni, faculty, and even political pressures, has admitted double the former number of freshmen, the university&apos;s worries really begin: to find laboratory, classroom, and instructional facilities. If this were a one- or two-year problem, the answer would be simple: double up, hold night classes, particularly of laboratories, rent space, and have instructors work 24 class or contact hours a week instead of twelve (it takes usually two to three hours of outside work by the instructor for one hour in class). However, most engineering school faculty men are worn out now from four to five years of "accelerated" (frequently downward!) programs and they couldn&apos;t continue teaching in a way satisfactory to their own consciences on

Jan 1, 1947

By W. I. Duvall

A brief review of the resonant frequency and ultrasonic pulse methods for obtaining elastic constants of rock samples shows that the equations for an iso-tropic elastic solid commonly used to calculate Young&apos;s modulus, modulus of rigidity and Poisson&apos;s ratio can result in appreciable error if the rock is even slightly anisotropic. Consideration of the equations that relate bar velocities and free medium velocities to elastic constants for orthotropic, transversely isotropic and isotropic solids shows that a combination of the two methods can be used to determine average elastic constants for a single sample of rock. The determination of elastic constants in different directions requires a large number of tests on oriented samples. The use of both the resonant frequency and ultrasonic pulse methods is recommended so that the determination of both Young&apos;s modulus and modulus of rigidity is independent of the determination of Poisson&apos;s ratio. The dynamic elastic constants of rock can be determined in the laboratory from measurements on small samples which may be in the form of right circular cylinders (diamond drill core). Either the resonant frequency6 or ultrasonic pulse method1 can be used to determine the longitudinal and shear velocities in the same specimen. The resonant frequency method provides a measure of the longitudinal bar velocity, V,, and the torsional bar velocity Vt; whereas the ultrasonic pulse method provides a measure of the free medium longitudinal velocity, Vp, and the free medium shear velocity, V, . The elastic constants (Young&apos;s modulus E, modulus of rigidity G, and Poisson&apos;s ratio v) are calculated from the density of the specimen, p, and one of the pairs of velocities by means of equations from isotropic elastic theory. For the resonant frequency method the equations are: It should be noted that Eq. 5 is derived from Eq. 4 and 6 and the relation between the elastic constants for an isotropic solid as given by the first part of Eq. 3. The in situ determination of dynamic elastic constants is accomplished by generating a complex seismic pulse in the rock and measuring the arrival times for the longitudinal and shear phases of the pulse at two distant points.5 From these travel times and the distance of the travel path both Vp and Vs are determined. The density of the rock is determined from samples in the laboratory, and Eq. 4 to 6 are used to calculate the elastic constants. These three methods involve the assumption of isotropy and perfect elasticity, and require the use of the relation v = (E/2G) - 1, which holds only if the elastic constants are the same in at least two directions. The calculation of v by means of Eq. 3 introduces considerable error, as a 1% error in V, and V, results in a 20% error in v. If frequencies for samples with a length-to-diameter ratio greater than four and a length greater than 8 in. are measured carefully, the experimental error can be kept to 1%. However, it is not unreasonable to expect that the variation in Vb and Vt with direction may exceed 1%. Thus, for even a small percentage of anisotropy the use of Eq. 3 can result in considerable error in v. The calculation of v by Eq. 5 also involves some uncertainty as a 1% error in Vs and Vp can result in a 6% error in v. By means of the pulse method both

Jan 1, 1965

By F. O. Garrabrant

Power is furnished to the Climax Molybdenum Co. by the Public Service Co. of Colorado over two 100,000-volt lines to a bank of three 3333-kva. transformers 100/13.8 kv. These transformers are so designed that with the addition of forced cooling their capacity may be increased 33? per cent at 12,000-ft. altitude. Under present conditions, these transformers are operated at 140 Per cent of their rating with forced air cooling. On the secondary side of this bank there is a 15-kv., 1200-amp. Westinghouse oil circuit breaker provided with automatic reclosing relays allowing three successive short circuits before lockout. From this breaker 13.8-kv. power is transmitted to a central switching station (Fig. I) where all circuits radiate to the different operations of the property. Each circuit is protected by a 23-kv., 600-amp. oil circuit breaker with by-pass and isolating disconnecting switches. Mine Power at 13.8 kv. enters the mine through a ventilation raise over a three-conductor, size 1-0 varnished cambric insulated, leaded, steel-wire armored cable, insulated from 17 kv. This power is received and distributed through one switching station and four underground substations, shown in Fig. 2. No. 370 substation (Fig. 3) contains three a 13,800/440-volt, single- phase Pyranol transformers protected on the high-voltage side by a 600-amp. manually operated oil circuit breaker. This station serves 20 slusher-hoist motors, a 45-kw., three-phase, 220-volt electric furnace, a Massco hot miller for tempering and milling Timken detachable bits and a hoist with 175-hp motor on the No, 3 development shaft. Also at this shaft are three pumps. One two-stage pump, 1200 gal, per min., 500-ft. head, 3600 r.p.m., driven by a 150-hp. motor, is at the bottom of the shaft, Two deep-well pumps, 500 gal. per min., 500-ft. head, are at the collar of the shaft. under normal operation the one pumping 1200 gal. per min, is controlled by a float switch to take care of the water. If this pump fails, or if its capacity is insufficient, the first 500-gal. pump is automatically started1 and if still more capacity is needed the second 500-gal. pump automatically starts. Time delay relays are provided on the deep-well pumps, so that if power fails the column will have time to drain before the Pumps restart. On failure of any Of these, an alarm is sounded in the train dispatcher&apos;s office, so that mechanics can be sent to ascertain the cause of failure and make repairs. The cable from No. 37&apos; substation is run to the switching station, in which are four 15-kv., 600-amp. direct-current sole-noid-operated oil circuit breakers. The current for Operating and tripping is furnished by a 125-volt storage battery. All breakers are operated from the switchboard in the compressor room. One circuit from this switching station goes to the

Jan 1, 1946

By John Sasadi, Karl Heinz Zepter, Leonard Sugin, Roger L. Hulette

Mt. Newman Mining Co. is now completing an expansion program, begun even before initial construction was complete, which will result in the ability to ship up to 35 million tpy of iron ore by early 1973. Located in the Pilbara region of Western Australia, the mine at Mt. Whaleback is about 700 road miles north of Perth and 265 railroad miles south of the port facilities at Port Hedland. Development of the tertiary crushing and screening facilities best illustrates the orderly, but rapid, sequence through which the capacity of the port loading terminal has been expanded. When the present program is completed, crushing and shiploading capability will reach - - 35 million tpy. Operations commenced in 1969 with 3 crusher lines in service; and despite the 5-million annual ton rating, 6.46 million tons of ore were shipped during the first full year of operation. With continuing increase in ore sales, expansion to an annual capacity of 12 million tons was authorized, and installation of two more crusher lines was begun. As a part of this program, provision for installation of a sixth crusher at some future date was included in the planning; but before construction was completed, new ore sales contracts demanded further expansion to an annual rate of 20 million tons, and the sixth crusher line was authorized. The distributing and collecting conveyors had been designed for extension in length and increase in capacity, therefore, conveyor service was provided for the additional crushers with additional belting and hardware only.

Jan 6, 1972