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By F. A., King

THE problem of the proper size and capacity of the open-hearth furnace has been a predominant issue ever since its inception some sixty years ago. The original furnaces, built in 1868 at Landore, England, were only to 3 to 4 tons capacity, and from' this there has been a steadily increasing and almost uniform rate of expansion until furnaces producing 300 tons are in successful operation today. At the end of the first half of this 60-year period, or about the year 1900, 50-ton furnaces we're common. Up to this time the problems of expansion had been largely those relating to suficient capital and the engineering development of larger units. But as 75, 100-ton and larger furnaces were proposed apprehension grew and other questions assumed leading consideration.

Jan 1, 1928

By D. F. Kaufman, E. D. Levine, L. R. Aronin

ThE primary slip plane in hcp metal crystals can usually be inferred from the c/a ratio. Basal slip is the primary system at room temperature for zinc, cadmium, magnesium, cobalt, and rhenium, all of which have a c/a ratio greater than 1.60. Zirconium and titanium, on the other hand, each with a c/a ratio of 1.59, deform primarily by (1010) [ll20] prismatic slip. The increasing tendency toward prismatic slip in these materials is generally thought to be associated with the increase in atomic density on (10i0) as c/a is reduced. Beryllium, with a c/a ratio of 1.57, would, according to the above scheme, be expected to exhibit prismatic slip. However, in beryllium of commercial purity, the primary deformation mode at room temperature is basal slip.' The ratio of critical shear stress for prismatic to that for basal slip at room temperature is approximately 5:l. The critical shear stress for prismatic slip decreases quite rapidly with increasing temperature, however, and at 500°C the ratio is approximately unity. The apparently anomalous behavior of beryllium has led to speculation that prismatic slip in this material may be restricted by an anisotropic effect of impurities,' and that, if beryllium could be purified to a sufficient extent, prismatic slip might predominate at room temperature. In such a case, the conditions under which basal cleavage can occur would be suppressed, and enhanced low-temperature ductility might result. With the advent of the floating-zone method for purification of beryllium,3 it has become possible to determine experimentally the effects of purification on basal and prismatic slip. Tensile tests were performed at room temperature on single crystals oriented favorably either for basal or prismatic slip. The crystals had been purified to various extents by zone-refining, employing procedures that have been described elsewhere.4 Relative purities of the crystals were estimated by measuring the ratio of electrical resistance at 4.2"K to that at 298°K. Typical values ranged from 0.40 for commercial-purity material to 7.7 X 10"4 for crystals prepared from vacuum-distilled beryllium and subjected to six zone-refining passes. The purity dependence of the critical shear stresses for basal and prismatic slip is shown in Fig. 1. In the purity range studied, the critical shear stress for basal slip is decreased from 1.4 to 0.14 kg per sq mm. The critical shear stress for prismatic slip is decreased from 6.7 to 5.3 kg per sq mm. The decreases in critical shear stress for each deformation mode, therefore, are approximately equivalent. No purification anisotropy is observed. Because of the absolute magnitudes of the critical stresses, the ratio of the critical shear stress for prismatic slip to that for basal slip actually increases from 5:l to 38:l at the highest purity level studied. It is evident, therefore, that basal slip is the primary deformation mode in high-purity beryllium. This fact must be accounted for in any rationalization of the deformation behavior of hcp metals. This work was performed at Nuclear Metals, Inc., under the sponsorship of the U.S. Atomic Energy Commission.

Jan 1, 1964

By M. G., Corson

1. In addition to the alloys of copper with iron previously found by Hanson and Ford to show an increase in the concentration of the alpha range with increase in temperature the following binary and ternary systems have been found by the author to exhibit: the same feature: (a) Copper-chromium. (b) Copper-cobalt. (c) Copper-silicon. (d) Copper-nickel-silicon and its pseudo-binary section Cu-Ni2Si (formula of compound definitely established). (e) Copper-cobalt-silicon and its pseudo-binary section Cu-Co2Si (formula of compound established with some probability but not as definitely as for Ni2Si). (f) Copper-chromium-silicon; formation of a compound definitely established (compare Figs. 1 and 2). The formula of this compound may be either Cr2Si or Cr3Si. (g) Copper-iron-silicon; presence of a phase containing both iron and silicon established in an indirect way only. No definite microconstituents observed. 2. RANGES OF SOLID SOLUBILITY (percentage at various tempera¬tures). (a) For copper-chromium: 0.8 at 1000° C.; 0.5 at 900° C.; 0.25 at 800° C.; 0.05 to 0.1 at 500° C. (b) For copper-cobalt: 3.4 at 1000'C.; 2.4 at 900'C.; 1.7 at 800'C.; 0.9 at 600°C.; 0.35 at room temperature. (c) For copper-silicon (Fig. 3) : 6.8 ± 0.1. per cent. at 800° C.; 3 per cent. at 400° C. and probably below 2 per cent. at room temperature if sufficiently long annealed. (d) For copper-cobalt silicide: 3.3 at 1000° C.; 2.4 at 900° C.; 1.6 at 800° C.; 0.7 at 600° C.; 0.3 at 300° C. (e) For copper-nickel silicide (Fig. 4): 8.2 at 1000° C.; 5.5 at 900° C.; 3.6 at 800° C.; 1.6 at 600° C.; 0.7 at 300° C.

Jan 1, 1927

By Clifford C. Hanninen, Allan H. Caverson

Within the past nine years a means for measuring the distance between mine roof and floor was developed at the White Pine mine which yields relevant information utilized in the mining operation. The technique known as "convergence" is an efficient, low cost way for obtaining large quantities of data for predicting roof falls, caving activity and overall mine stability. Since 1964 the activity of convergence measurements has expanded to become a production tool found in all sections of the mine. The program involves four types of activity: 1) monthly measurements in areas known to be active and in sample blocks scattered throughout the mine for a long-term stability study; 2) semi- monthly measurements along vital travel roads, belt drifts and compressor sites; 3) weekly measurements in areas where men are working; 4) daily measurements in pillar-recovery and caving operations.

Jan 5, 1973

By Walter J. Karplus

By means of a finite difference expansion a fluid flow field in cylindrical coordinates with axial symmetry, is simulated by a network of electrical resistors. A series of DC analog computing units, connected to the network bounrlary corresponding to the free surface effectively adjust the network parameterr to satisfy simultaneously Laplace's equation and the borrndary conditions. The system automatica1ly "re1axes" to the correct boundary shape in a fraction of a second. A detailed application of the method to the water coning problem in oil wells is presented. INTRODUCTION The water coning problem in petroleum production is a prime example of a class of problems known as free surface problems. A free surface arises in fluid flow regions when the shape of the boundary of a single phase flow region is affected in some manner by the pressure or potential gradients within the region. When there exists an interface of two fluids of different densities, the shape of this interface will be determined by the relative velocities of the two fluids and will therefore comprise a free surface. Other free surface problems of interest to petroleum engineers include the gas coning, water injection, and gravity drainage probIcms. In each case it is desired to predict the shape of the boundary of the oil zone as a function of the flow rate, the well penetration and the physical parameters and dimensions of the system. Such problems do not lend themselves to the classical analytical treatments of boundary value problems because in this case the boundary of the potential field and the potential distribution within the field are interdependent and must be calculated simultaneously. A further difficulty arises from geometric considerations. Since the fluid flow is of the radial type in most cases, such effective methods as conformal transformation and the hodograph are not applicable. It is the purpose of this paper to present a method whereby free surface problems of this type may be solved rapidly to the desired order of accuracy by means of a combination of a network of electrical resistors and conventional analog computer units. The water coning problem is treated in some detail. Then the procedure for extending the technique to other free surface problems is indicated. FORMULATION Most commercial oil reservoirs consist of an oil-saturated sand, bounded above by an impermeable strata and below by a water-saturated sand. Gravimetric separation results in a horizontal oil-water interface. When an oil well is drilled so that it partially penetrates the oil zone, and production is initiated at a constant rate, the oil-water interface will assume a new shape as a result of the pressure gradients in the oil zone. It should be emphasized that this is a steady phenomenon. After an initial transient period the water phase will be completely static and only the oil will be in motion. The new steady-state shape of the interface, as shown in Fig. 1, depends upon the depth of penetration, d, the thickness of the oil zone, I, the production rate, q, the hydraulic permeability zone of the sand, k, the viscosity of the oil, µ, and the densities of the oil and water, p.,. and pw.. The problem is to determine this relationship. Darcy's law + = - (P f g p z).....(1) it.

Jan 1, 1957

By H. C. Weed

THE Inspiration Consolidated Copper Co., located in the Globe-Miami district at Inspiration, Ariz., became a producer of copper in 1915. From 1915 until 1948, 116,278,000 tons of ore were produced from underground workings by the block-caving system of mining. In April 1948, open-pit ore production from portions of the ore body was started and earlier plans for block-caving in these areas were abandoned. The change was due to economic conditions.

Jan 8, 1950

By C. W. Spencer, J. Singer

A PARTIAL phase diagram for the As-Te system is given in Hansen.' The only compound reported is As2Te3, melting at 362°C. Stoichiometric quantities of reagent-grade elements were reacted in evacuated quartz and directionally cooled. The resulting ingot consisted of very thin threadlike crystals from which only very small single-crystal fragments were isolated. A powder diffraction diagram disclosed nonisomorphism with the analogous V-VI compounds insofar as these have been reported; Sb2S3, As2S3, Bi,S,, and Bi2Te3 data in the ASTM index of powder patterns, together with the single-crystal data on Sb2Se3,2 were used for the com- parison with the observed spacings. Single-crystal data confirmed the uniqueness of the As2Te3 structure. Single-crystal Weissenberg diagrams have so far yielded the following data: As2Te3 is monoclinic, space group C-m (OkO data still lacking), a = 14.4A, b = 4.05A, C = 9.92A, ß = 97". The cell volume is about 5802. The set of isomorphous ortho-rhombic cells of Sb2Se3, Sb2S3, and Bi2S, are apparently related to As,Te, in having one lattice constant close to 4.0 and with cell volumes as large as 540A8. Assuming Z = 4 for As2Te3 also, the density is calculated as 6.1 which agrees well with a roughly determined value of 6.0. A complete structure analysis is under way.

Jan 1, 1956

By H. C., Weed

THE Inspiration Consolidated Copper Co., located in the Globe-Miami district at Inspiration, Ariz., became a producer of copper in 1915. From 1915 until 1948, 116,278,000 tons of ore were produced from underground workings by the block-caving system of mining. In April 1948, open-pit ore production from portions of the ore body was started and earlier plans for block-caving in these areas were abandoned. The change was due to economic conditions. Prior to the war years Inspiration's costs of mining by block-caving methods were comparable to, or even below, the costs of some open-pit operations. By the end of the war these conditions were completely changed. Underground costs had risen steadily for labor and supplies. Difficulty was being experienced in finding competent underground men and underground development was almost hopelessly behind schedule. On the other hand, open-pit costs had been sharply reduced through the development of modern earth-moving machinery and plenty of labor was available for surface work.

Jan 1, 1950

COUNCIL OF NATIONAL DEFENSE W: S. GIFFORD, Director, GROSVENOR B. CLARKSON, Secretary. The Council of National Defense The Advisory Commission NEWTON D. BAKER, DANIEL WILLARD, Chairman, Secretary of War, Chairman.. (Transportation). JOSEPHUS DANIELS, BERNARD M. BARUCH, Secretary of the Navy. ' (Raw Materials). DAVID F. HUSTON, HOWARD E. COFFIN, Secretary of Agriculture. (Munitions, Manufacturing). FRANKLIN K. LANE, HOLLIS GODFREY, Secretary of the Interior. (Science and Research, including En¬ WILLIAM C. REDFIELD, gineerlng and Education). Secretary of Commerce, SAMUEL M. GOMPERS, WILLIAM B. WILSON, (Labor). Secretary of Labor. F. H. MARTIN, (Medicine and Sanitation). ' JULIUS ROSENWALD, (Supplies). At the request of Dr. Hollis Godfrey, Chairman of the Advisory Committee On Science and Research, which includes Engineering and Education, a Sub-Committee of Engineering Societies has been appointed with representatives as follows:

Jan 6, 1917

(This list. includes only those who have entered military service within the past month, or whose entry has only recently become known to us; it also includes a few names of those whose titles or assignments have been changed within the month. A complete list will he found in the Year Book mailed with this Bulletin. Another Honor Roll is maintained in the reception room of the Institute.) ALDEN, HERBERT W., Lieutenant-Colonel, Ordnance Dept. ALDER, ALFRED; Engineers' Reserve Corps. ALFORD, NEWELL G., Sergeant, Bureau of War Risk Insurance, Headquarters 84th Division. AMBLER, HARRY A., Lieutenant, 30th Infantry. ANDERSON, GEORGE K., JR., Sec. C, 1st Co.; 3d Officers' Training Camp. AYER, -FRANK A., 1st Lieutenant, 43d Squadron, 3d Prov. Regiment, Aviation Camp.

Jan 3, 1918

By C. L. Sollenberger, R. B. Greenwalt

PERHAPS the most widely used dispersants or gangue depressants in nonmetallic flotation are sodium silicates, which vary in silica-to-soda ratio from 1 to 3.75. Typical manufactured silicates in order of decreasing solubility and increasing amounts of silica are Metso, silica-to-soda ratio of 1.00; D, 2.00; RU, 2.40; K, 2.90; N, 3.22; and S-35, 3.75.* References in flotation literature's to the use of sodium silicates are often weak because they fail to mention the type of silicate used. Metso and silicate N have occasionally been mentioned, but when the type of silicate is not mentioned, it is usually assumed to be N, the cheapest of the soluble silicates and the one recommended by sodium silicate manufacturers as a flotation agent.

Jan 6, 1958

By O. E. KEOUGH

AT the Tooele custom lead-zinc ore concentrator,' two sections, each having a daily capacity of 500 to 600 tons, are operated on slightly different types of ores with but little difference in flow sheet and reagents. The ores comprising the two general classes are the coarsely crystalline type, with low pyrite and sphalerite low in iron content, from the Park City district, and the more finely disseminated higher pyrite ores from Bingham, which are more difficult to treat by flotation. Laboratory testing determines with which general class a new ore will work better. The ores are crushed to minus 1 1/4-in. size at either the Utah Ore Sampling Company's plant at Murray, Utah, the Tooele smelter sampling plant, or the crushing plant at the concentrator. The ores for each section are mixed to maintain as nearly as possible uniform lead and zinc contents.

Jan 1, 1930

By J. L. Perry

FOR many years, you and your fellow members of the American Institute of Mining and Metallurgical Engineers have devotedly and ably applied yourselves to the art of making iron and steel. having foremost in your minds the conservation of raw materials, suitable and efficient facilities, economical processes, and improved quality of product. For the past three strenuous years you have contributed wholeheartedly to meeting the problems of increased production. You have conducted scientific and technical investigations and research, recommended experiments. and gathered all the available and valuable information possible to gain the desired objectives. You have had many obstacles and difficulties to overcome. In the early days of your organization, there was some lack of co-operation from the industry itself-perhaps, for example, some failure to recognize the mutual advantages of free exchange of experiences and information. But regardless of any hindrances, you have made many and valuable contribution which have tended to make iron and steel manufacture leas of an art and more of a science.

Jan 1, 1944

By BLAllEY STEVENS

(Canal Zone Meeting, November, 1910.) I. INTRODUCTION. TEH object of this paper is to show how igneous intrusion is governed by definite mechanical laws. A distinction is made between dikes and fissures, and the various characteristics of intrusions are explained on an exact scientific basis. The modification of rock-stresses by intrusion is then considered and extensive isostress regions are recognized. Finally, a complete classification of intrusions is constructed covering all pos-sible cases. The generalizations of observed data, taken from Geikie's Textbook of Geology, conform to the laws of intrusion herein stated, and the deductions based upon these laws. No authority, however, is quoted for the type which I have named a corrugated intrusion. Its existence is a necessary deduction from the laws of intrusion, and even the entire absence of examples in technical publications cannot disprove its reality. In all probability, corrugated fissures would have remained undiscovered, but for the working of mineral veins. As intrusions of tabular form are seldom worked for commercial purposes, it has been left for theory to anticipate the discovery of corrugated dikes. In the light of these laws of intrusion and the corresponding laws of fissures,1 there seems to be a remarkable uniformity of stress-distribution in rocks at moderate depths. This renders .possible the mathematical calculation which should help us to approximate exact science in this and kindred branches of applied geology.

Jan 1, 1911

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 A. D. LeClaire

This paper claims to provide a description of diffusion processes in solids which is said to be a reformulation of Fick's Laws and therefore, presumably, is supposed to be as general as those laws. In fact, it appears to provide no more than an atomic model of a rather restricted type leading even to results in conflict with experiment. The restriction lies in the assumption, carried throughout the paper, that even in a chemical gradient the jump frequency i of an atom of species i is a function only of the composition on the plane from which it jumps, i.e., ?i = ?i(cl, c2 ...). This means that atom jumps in opposite directions from a site would occur with equal probability. There would then be no tendency for atoms to migrate preferentially in one direction along the gradient, so the model is incapable of accommodating the well established phenomenon of atom drift in a chemical gradient.10-" A more general model that does not suffer this difficulty was discussed in a paper13 I wrote in 1958, and the results therein already contain as a special case those given by Dr. DeHoff. The simplest sufficiently general assumption is to suppose that ?i is a function ?i(a1 a2,...; wl, w2, ..-) of the concentration aj and ? ?j at the site from which and to which, respectively, a jump is made. Any such function can always be expressed as a function of the sum and difference of its arguments. Thus d is the jump distance and g a geometrical constant. Obviously this is zero, i.e., no drift, if ??ri/??j = 0. X is written in this form, revealing two components of the total drift, because it can be shown that only the second component, depending on ??'i/???(?j -aj), actually contributes to the net diffusion flux Ji. This component can be shown,13 by a straightforward ther-modynamic transcription, to be responsible for the so called "thermodynamic factor" in the Darken approximation for a chemical diffusion coefficient is the activity coefficient of i. Because the jump rate ?i in DeHoff's approximation has no dependence on the concentration gradient it does not seem possible to derive the Darken equation from his Eq. [6] without the further rather arbitrary assumption that ?i = const ri. It is to be noted too that the author's derivation of Eq. [12] is only valid when ?i is in fact a function only of the cj at the plane from which the atom jumps—for only then is ci?i a unique function of position and therefore of A. Author's Reply R. T. DeHoff I am indebted to Dr. LeClaire for his penetrating discussion of my paper, "A Reformulation of Fick's First Law". I concede that it does appear initially that the relationship presented in my paper could be derived from the detail atomic model of random walk and atom drift presented in Dr. LeClaire's approach. However, there are some important differences in concept and viewpoint which deserve further amplification. Dr. LeClaire's description is penetrating, detailed, and fundamental. His approach describes an extremely complex phenomenon, the displacement of atoms in a multicomponent gradient, at a sophisticated level. For precisely these reasons, his analysis has not proved to be useful for experimental studies that have practical objectives. For example, in order to obtain the information required to complete the analysis of the jump frequency distribution in a ternary system, the following series of experiments would, I believe, be required: 1) chemical (gradient) experiments, covering the composition range;

Jan 1, 1970

By A. O. Dady

PRODUCERS of both bituminous and anthracite coal have for many years been worrying about the gradually decreasing consumption of their product in the United States. Twenty years ago production had climbed to a peak of 569,000,000 tons of bituminous and around 90,000,000 tons of anthracite. In 1939 it was about 393,000,000 tons of bituminous and 51,000,000 tons of anthracite. This does not mean that the country is using less polver than it did twenty years ago, or that we are living in colder buildings. As a matter of fact, about three times as much electric power is now being consumed as in 1920. In general two factors are responsible for the drop in coal consumption: (1) greater efficiency in the use of coal, and (2) increased competition from hydro power, internal-combustion engines, and substitution of oil and gas for coal in conventional furnaces. As to the first factor, it took 3 Ib. of coal to generate a kilowatt-hour of electricity in central stations in 1920 and it takes 1.4 Ib. now; it took about 175 Ib. of coal in railroad locomotives to haul 1000 long tons a mile in 1920 where it talces about 120 lb. now: and marked economies have also been made in the use of coal in steel plants: in by-product coke ovens, and in other large uses. As to the second factor, three times as much electricity is produced from water power now as was produced in 1920; three times as much oil is being consumed in various ways; and likewise, the consumption of natural gas has tripled- whereas coal consumption in the same period has dropped by 40 per cent

Jan 1, 1941

By R. B. Fuller, E. T. Casler

MANY changes were made in the methods and equipment used in the mining of pebble phosphate rock in the generation immediately preceding the present World War and it would be extremely interesting to note the improvements that will be made during the next generation. Literally, much water has gone over the dam since the days when we used local cordwood for generating steam and drying pebble phosphate rock. belt-driven centrifugal pumps operated by steam engines. and floating dipper or centrifugal dredges; when we removed overburden by small steam shovels and transported it by dinkey locomotives and six-yard cars; when washing machinery was installed on wooden structures the washers being replaced every four to six years. Those were the days when men were plentiful, and 47 different mining companies were selling their products, based on .decidedly meager information; and. like so many mining operations, little thought was given to conservation. As the importance of phosphate rock has become more prominent in the thoughts of our economists, a more intelligent approach has been made to mining problems. Vast improvements have been made in the technique and processing of the phosphate matrix and stripping of overburden, which, in turn, have brought developments in machines and equipment and a more

Jan 1, 1944

By R. E. Miner, J. K. Jackson, T. L. Wilson

A study has been made of the transformation kintetics and morphology in gas-quenched Fe-5 pct Ni alloys. Massive ferrite or nlurtensite was found to form at temperatures in agreement with earlier results. Surface Preparation appeared to have the greatest effect in determining the type of transformation Product formed. Grain size change, subgrain morphology, and dislocation densities of massive ferrite were essen-tinlly invariant functions of cooling rate. The mar-tens~tic structures were typical of transformation in austenite grains of the order of the sample thickness. BY introducing the idea of a massive transformation in dilute iron-base alloys, Gilbert and Owen in 1962 served to stimulate a closer inspection of phase transformations in ferrous systems.' A wealth of literature has followed concerned with the morphology,2-5 transformation mode,2'3'6-8 and thermodynamics of transformations.2,5,9 interesting controversies have resulted from the experimental observations; closer attention has been paid to the definition of massive transformations and still to be resolved is the Ms temperature of pure iron. The purpose of this note is to report some observations made in a detailed kinetic and metallographic examination of the transformations that occur in gas quenched Fe-5 pct Ni. The results are pertinent to the Ms extrapolations that have been made for pure iron and the observed substructure of massively transformed alloys. PROCEDURE The material used in this investigation was cast as a 5 lb vacuum induction melted, carbon deoxidized heat. The ingot was hot worked to a strip 0.10 in. thick, decarburized, and cold rolled to final thickness. Specimens were punched to sample shape and decarburized in wet hydrogen at 600°C. The chemistry of test specimens is indicated in Table I. Samples 1 by $ in., by thickness were resistance heated and rapidly cooled in an apparatus as illustrated in Fig. 1. Similar helium quenching apparatuses have been described previously;2,6'10 the distinguishing feature of this apparatus is the nozzle geometry. Twin nozzles with three convergent-divergent, sonic ports were mounted perpendicular to the specimen for quenching purposes. The specimen temperature was monitored with an intrinsic 3 mil chromel-alumel thermocouple spot welded to the specimen and con- nected to an oscilloscope. A single switch stopped the current flow through the specimen, opened a gas flow solenoid valve, and initiated an oscilloscope sweep. Cooling rates were read directly from a photograph of the oscilloscope trace and the quenching rates quoted later were made at a point immediately prior to transformation on the trace. All quenching studies were conducted either under a vacuum of 10"-5 torr or a helium atmosphere. The sample geometry was chosen large enough to permit optical and electron microscopy to be performed on samples. The samples were electropolished for both types of examination in a perchloric-acetic solution. Electron microscopy was conducted on a HU 11A microscope operated at 100 kv. Dislocation densities were determined at the same general operating reflection (110) on foils thick enough to produce Kikuchi patterns. RESULTS AND DISCUSSION Transformation Temperature Observations and OD-tical Microscopy. The quenching results of this study are illustrated in Fig. -2(a). Samples which were treated in the as-decarburized condition transformed in a manner similar to that reported previously—a decrease in transformation temperature occurred as the quenching rate increased until a plateau region was reached. Within the scatter of the results obtained here, there was no break in the transformation temperature-quenching rate plot. This suggests no change in transformation mode. Further metallographic examination confirmed this observation. A martensitic transformation was obtained for similarly treated samples except that the surface was first electropolished. The Ms temperature was approximately 85°C below the plateau determined for the unpolished samples and cooling rates as slow as 2000°C per sec were adequate for producing marten-site. The transformation temperatures are in gen- / STRIP SAMPLE / COPPER I SAX/-/}' / CONNECTOR-----A f, SON|C poRTS AC LEADS 3j ]j"I rofe[ \ Mf/yinK/iKj''^ THERMOCOUPLE X-(^—iie"s*c? ' LEADS 1 INCH Fig. 1-—Schematic scction of gas quenching apparatus

Jan 1, 1970

By M. King Hubbert

In 1856 Henry Darcy described in an appendix to his book, Les Fontaines Publiques de la Ville de Dijon, a series of experiments on the downward flow of water through filter sands, whereby it was established that the rate of flow is given by the equation: q= - K(h2- h2)/I1 in which q is the volume of water crossing unit area in unit time, I is the thickness of the sand, h1 and h2 the heights above a reference level of the water in manometers terminated above and below the sand, respectively, and K a factor of proportionality. This relationship, appropriately, soon became known as Darcy's law. Subsequently many separate attempts have been made to give Darcy's empirical expression a more general physical fornzulation, with the result that .so many mutually inconsistent expressions of what is purported to he Darcy's law have appeared in published literature that sight has often been lost of Darcy's own work and of its significance. In the present paper, therefore, it shall be our purpose to reinform ourselves upon what Darcy himself did, and then to determine the meaning of his results when expressed explicitly in terms of the pertinent physical variables involved. This will be done first by the empirical method used by Darcy himself, and then by direct derivation from the Navier-Stokes equation of motion of viscous fluids. We find in this manner that: q = (N4(p/p)[g - (l/p) gradPI = WE, is a physical expression for Darcy's law, which is valid for liquids generally, and for gases at pressures higher than about 20 atmospheres. Here N is a shape factor and d a characteristic length of the pore structure of the solid, p and IL are the density and viscosity of the fluid, a = (Nd2)(pip) is the volume conductivity of the system, and E = [g - (l/p) grad p] is the impelling force per unit mass acting upon the fluid. It is found also that Darcy's law is valid only for flow velocities such that the inertial forces are negligible as compared with those arising from viscosity. In general, three-dimensional space there exist two superposed physical fields: a field of force of charucteristic vector E, and a field of flow of vector q. The force field is more general than the flow field since it has values in all space capable of being occupied by the fluid. So long as the fluid density is constant or is a function of the pressure only, curl E = 0, E = - grad F where F = gz + dp/p The field of flow, independently of the force field, must satisfy the conservation of mom, leading to the equation of continuity div pq = — f ap/at , where f is the porosity, und t is the time. For steady rnotion ap/at = 0. and div pq = 0 .

Jan 1, 1957