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By R. H. Hadfield

Professor ArnolD, of the Sheffield Technical School, who has done so much excellent work in metallurgical research, recently produced, with the aid of aluminum, a sound ingot and bar from the purest known Swedish brand containing 99.8 per cent. of pure iron. Table 1. shows the physical quantities of this metal. TABLE I.— Tests of a Sample of Almost Pure Iron Prepared by Professor Arnold from D. v Ewedish Bar, Containing Before Fusion 0.04 Per Cent. of Carbon. I. II.+ III. Series mark,.. 136 1.371F ...... C, 0.07 0.07 Si, 0.04 0.04 8, 0.02 0.03 ...... Analysis, per cent,. .. P, 0.02 0.015 ...... Mn, 0.06 0.07 Al, 003 ............ Fe, 99.76 99.81 ...... Specific gravity,........... 7.863 ...... Original diameter, inches,. .. 0.564 0.798 0.798 Original area, square inches,. . 0.25 0.50 0.50 Limit of elasticity, tons per square inch,...... 18. 3.8 Breaking-load, tons per square inch,. 21. 23. 14.75 Total elongation, per cent., measured on 2 in.,...... 50. 49.25 61. Total reduction of area, per cent.,. 80. 69.60 61.20 Extension at permanent set, per cent.,...... 0.007 ...... silky and Appearance of fracture,. .. . silky i granular in parts.

Jan 1, 1894

By F. Weinberg

Lead single crystals have been deformed in tension over the temperature range of 4.2°K to the melting point. Changes in flow stress resulting from temperature cycling and strain rate cycling have been measured as a function of temperature for crystals of different orientations and purity. It was found that the flow stress ratio, after correcting for the temperature dependence of the shear modulus, decreased progressively with temperature above approximately 0.5Tm. The activation energy calculated from the high-temperature portion of the curve was found to be markedly higher than that of self-diffusion. For single glide crystals, the corrected flow stress showed an increase above 0.5 Tm before decreasitzg with temperature. This increase is attributed to static recovery occurrittg during temperature cycling. THE temperature dependence of the flow stress, based on temperature cycling and strain rate cycling, has been extensively investigated,' and on the basis of these results dislocation models of the work-hardening process have been proposed. In general, the flow stress is divided into two parts, ts, the short-range interaction term, which is only effective at low temperatures and which decreases with increasing temperature, and TG, the long-range stress term, which is independent of temperature after allowing for the temperature dependence of the shear modulus. The observations demonstrating that tG/µ is independent of temperature were generally carried out at low temperatures to minimize recovery effects. Several investigations have been reported on flow stress measurements at high temperatures2"5 which demonstrate that TG/µ does not remain constant at temperatures above 0.5Tm (where Tm is the melting temperature of the material in OK). Specifically, Hirsch and warrington3 carried out temperature cycling tests at two strain rates on single and polycrystalline aluminum up to 0.8 Tm and on polycrystalline copper. For aluminum they found that the flow stress ratio (the flow stress at temperature T2, divided by the flow stress at the reference temperature T1 in one temperature cycle) dropped progressively with increasing temperature above 0.5Tm. From the slopes of the high-temperature portions of the curves, they determined an activation energy for the deformation process of 1.6 ev (at best) which they considered was in agreement with the activation energy of self-diffusion, 1.35 ev. Calculations of the activation volume demonstrated that the deformation was not controlled by dislocation climb. They proposed a mechanism in which the rate-controlling process at high temperatures was due to the rate of move- ment of vacancies away from jogs, i.e., that of self-diffusion. Results of Lucke and Buhler4 on single crystals of aluminum confirmed this conclusion. They measured the critical resolved shear stress of aluminum over a wide range of temperature and strain rates. They found that the temperature dependence of the critical resolved shear stress was similar to that of the flow stress ratio, as determined by Hirsch and Warrington, and from their data calculated an activation energy for high-temperature deformation of 1.35 ev identical to that of self-diffusion. More recently Gallagher5 has carried out a detailed investigation of the temperature dependence of the flow stress ratio of copper, silver, and gold. In all cases, he found that the flow stress ratio, after adjusting for the shear modulus temperature change, drops at high temperatures. The activation energies he determined were found to be appreciably higher than the activation energy of self-diffusion of the material being considered. The flow stress ratio was found to be dependent on the orientation of the material, and, in addition, an anomalous increase in the flow stress ratio for copper, oriented for single glide, was observed above 0.5Tm. The purpose of the present investigation was to measure the critical resolved shear stress, the flow stress ratio, and the strain rate sensitivity of lead, primarily as a function of temperature. The results should indicate whether, following Lucke and Buhler, the critical resolved shear stress of lead has the same temperature dependence as the flow stress, and, following Hirsch and Warrington, whether the activation energy for high-temperature deformation in lead is the same as that of self-diffusion. Lead deforms as a normal fee material,6'7 is available in high-purity form, can readily be grown as single crystals, and, for this investigation, has the very considerable advantage of having a low melting point, 327°C. The observations of the critical resolved shear stress of lead have been published elsewhere.' EXPERIMENTAL PROCEDURE The experimental procedure was essentially the same as that used in the critical resolved shear stress measurements.' Single crystals of 99.999 pct (59) and 99.9999 pct (69) lead were deformed in tension with a table-model Instron in a silicone oil bath above room temperatures and in a cooled methyl alcohol or liquid-nitrogen bath below room temperatures. The test specimens were rectangular in section, 0.65 by 0.33 cm, and had a 5-cm gage length. The specimens were grown as single crystals with tapered ends, which fitted into matched tapered grips for testing. To obtain the flow stress between two temperatures, specimens were first deformed approximately 1.0 pct at the higher temperature. The test was then stopped, the load relaxed, the oil bath removed without disturbing the specimen, the grips and specimen cooled with a fan and then immersed in liquid nitro-

Jan 1, 1969

By Maurice Grieves

The great majority of shafts constructed today are still excavated by drilling and blasting, a method which changed very little in over 100 years until the introduction of the mechanical lashing unit and cactus grab by the South Africans, which enabled muck to be removed as fast as massive hoisting systems could handle it and resulted in very rapid rates of sinking. Record breaking month's performances were achieved at -Hartebeestfontein No. 4 shaft, October 1960-337.1 m; Western Reefs No. 4 shaft, October 1961-340.7 m; and Buffelsfontein eastern twin shaft, March 1962-381.2m. The method was very labor-intensive, requiring a crew of over 60 workers at the shaft bottom during the drill cycle. Safety precautions were strict, but in the drive to achieve rapid advance, cases of personal injury were still somewhat high because of the large number of people engaged in this potentially hostile environment. The South African method, as it came to be referred to throughout the rest of the world, was adopted in the United Kingdom in the late 1950s in a modified form with greatly reduced manpower and nonsimultaneous sinking and lining, which was insisted on by the British Mines Inspectorate. In that instance, it was successfully used to sink the 7.3-m-diam concrete-lined shafts at Kellingley to 770 m depth, with rates of advance of over 90 m/month achieved, a British record at that time. During the sinking of the 1.15-km-deep twin shafts at Boulby potash mine in the UK in 1970, the method was again used, but for the first time ever in Britain exemptions from the mining code permitted the use of crash beams, crash doors, jack catches, and semi-simultaneous sinking and lining techniques. New British shaft sinking records of over 120 m/month were achieved in both shafts. Similar equipment and techniques were used in the early 1970s to sink several deep shafts in Canada, notably Creighton #7 and the Con zinc mine at Yellowknife in the NW Territories. Today, this equipment is standard for deep shafts in the US and the rest of the world. However, with the tremendous escalation in mining labor costs, the impact of health and safety legislation, and environmental regulations, coupled with a very real shortage of miners willing to work in this exposed situation it was apparent that an alternative to the labor-intensive conventional method of shaft construction had to be found. Recognizing the trend is inevitable, one or two major German shaft sinking contracting firms began to take a fresh look at full face boring techniques applied to tunnels and raise bored shafts. The results were most encouraging. Tunnel drivage techniques using moles had developed considerably from Colonel Beaumont's original channel tunnel machine circa 1880 to the superbly engineered Priestley machine selected to cut the British side in 1975 and the double shielded Robbins Grandori borer on the French side of the English Channel. Full face tunnel machines were being successfully used to drive uphill in inclined shafts in Austria and Switzerland. At Mapprag in Switzerland, the Demag mole drove the first (intentional) vertical transition and curve, and then went on to successfully complete the 730-m-long penstock shaft at an inclination of 35°. In Austria, the Wirth mole drove the Kaprun Glacier ski-lift railcar tunnel at record breaking rates of 457 m/MONTH (best 30 m/d) through green schist at an inclination of 29° for a distance of 3.35 km while the Hydro tunnel at Sarrelli in Switzerland was being driven by the Robbin's mole at an inclination of 35°. Simultaneously, extremely promising results were obtained using large assemblies of cutter discs on raise borer heads, such as the 4.87-m-diam X 460-m-deep shaft raised by Teton for Jim Walter Resources Inc. Bearing in mind that most mine shafts in the future (unless in exceptionally competent rock) will require some form of lining, and the trend will be toward deeper shafts as the more easily accessible mineral deposits become exhausted, it was seen that normal raise boring had definite limitations in vertical accuracy, in the limitation imposed by the drill string on the available torque that could be applied to the cutter head, and in the risk of collapse of the unsupported shaft rock wall in friable or jointed and fissured ground, since it is not possible to apply any form of temporary support until the permanent lining is being installed. A further problem was the economics of installing a subsequent lining, necessitating setting up a headgear and hoisting arrangement approaching in size that required for conventional drill and blast sinking and lining. Because of the economics, German contractors opted for a phased transition from drill and blast to the full face, rodless, out of the solid shaft mole, by starting off with a down-the-hole shaft boring machine -without a drillstring-but using a pilot hole to get rid of the muck.

Jan 1, 1982

By Sandip K. Mitra, John E. Dorn

The Basinki-modified Seeger equation for deformation of metals by means of thermally activated intersection of dislocations was used to ascertain the various factors responsible for the strain hardening of poly crystalline aluminum and a series of a solid solutions of magnesium in aluminum. The analyses were based principally on the rate of change of strain rate with stress and the Cottrell-Stokes ratio. From measurements of these quantities on a series of strain-hardened states, the force displacement diagram for intersection, the density of dislocations in the entanglements, and the contributions of the athermal local stress and long-range stress interactions were deduced. Poly crystalline aluminum was observed to have the same force-displacement diagram for intersection as single aluminum crystals, and the corresponding diagram for the magnesium alloys differed in a manner that suggested that small amounts of magnesium may decrease slightly the stacking fault energy of aluminum. Although poly crystalline aluminum had about the same initial density of dislocations as the single crystals, the density of dislocations increased much more rapidly with strain in the polycrystals. This factor and the higher back stresses generated in the poly crystalline aluminum were the major factors responsible for the higher strength of the poly crystalline aluminum, As the magnesium content of the alloys was increased, the initial density of the dislocations also increased. Most of the alloy strengthening arose from this factor; alloying effects due to short-range order strengthening, Suzuki locking, Cottrell pinning, and so forth, were estimated to be quite small. The gveater rate of strain hardening in the alloys was deduced to be due primarily to the greater increase in the density of the dislocations with strain as the magnesium content was increased. It is the purpose of the present investigation to shed additional light on the average plastic behavior of a grain in a polycrystalline aggregate, by analyses, based on dislocation theory, of appropriate experimental test results. These deductions when compared with those from single-crystal data will then serve to illustrate the major items of difference between the plastic behavior of single crystals and the average behavior of a grain in a

Jan 1, 1963

By Ellis Clark

THE mining town of Pribram is situated in Central Bohemia, on the western slope of the Heiliger Berg, 30 miles southwest from Prague. Birkenberg, the village in which most of the shafts and ore-dressing establishments are situated, is built on a mountain of the same name. It is about a mile from Pribram, is 1700 feet above the sea, and is surrounded by graywacke rocks of Silurian origin, which are intersected by greenstone dikes, and in the southerly, southeasterly, and southwesterly direction are bounded by granite. The graywacke formations consist on one side of graywacke sandstone and quartzite, and on the other of graywacke slates. These last are separated from the first in the immediate vicinity of the mines by a graywacke seam converted into clay. For many years this so-cal led clay seam (lettenkkluft) was considered as a boundary of the ore deposits in both zones of graywacke. The graywacke formation is divided according to its hardness, structure, texture, and color, into fine, coarse, compact, slaty, whitish-gray, reddish-gray, and black graywacke. The, miner divides the formation into four divisions. The first or lowest division, which is in contact with the granite, consists of a fine-grained dirty gray slate; the -second is a very fine to a very coarse schist, white to reddish-gray in color, and rich in quartz, but containing little mica; the third consists of a slate with a contused cleavage, which has a dirty gray, dark gray, and very often black color and is often graphitic in its composition ; the fourth consists of a fine to coarse-grained graywacke schist, of a grayish-white or reddish-gray color, and rich in quartz. The cleavage in all four divisions strikes from northeast to southwest, and the dip is sometimes northwesterly, sometimes southerly, and often vertical. All four zones are cut through by a great number of diorite and greenstone dikes and chimneys. The thickness of these dikes, which are of

Jan 1, 1881

By Chandler Morse

RENEWABLE VS. NONRENEWABLE NATURAL RESOURCES Nonrenewable resources, such as minerals, are the inevitable center of attention in discussions of depletion and exhaustion. Nevertheless, it may well be proper to regard some nonrenewable resources as not subject to exhaustion, and renewable resources may sometimes be treated as if they were finite stocks. Thus, the availability of nonrenewable resources is not and probably never will be known completely Chap. 2.5A, and therefore is not subject to firm predictions concerning exhaustibility. Moreover, because exploration and discovery are more or less continuous processes it is often appropriate to regard mineral supplies as flows, and to treat the estimated reserves as working capital, an inventory, continually depleted by use and augmented by discoveries.23 The aggregate economically exploitable stocks of a given mineral are seldom estimated (or estimatable) with precision, as Chap. 2.5A shows, and even when they are, forecasts concerning years of remaining life can be and often are falsified by changes in one or more of the multidimensional conditions of supply and demand; or the productive services formerly derived from an exhausted stock may continue to provided without material impairment by one or more substitutes b Conversely, the renewable resources are all subject to depletion when the rate of use exceeds the natural or induced rate of replenishment, and cases of exhaustion or near exhaustion, as through soil erosion, overcuttmg of forest lands, and overfishing, are rather common c Where exhaustion is a clear possibility the resource may either be exploited on a consciously adopted "sustainable yield" basis or be treated as an exhausting asset." In some cases, conscious treatment

Jan 1, 1976

By Robert H. Richards

This is in part a review paper, indicating the various steps that have been taken in developing hindered-settling apparatus, some of the standard data that have been obtained, and some of the conclusions one is led to as to the effect of it in improving concentrating-methods and machinery, and in part it brings in some unpublished work. Causes oF Loss in ORe-ConcEntration. In making a study of the separation of valuable minerals from the waste gangue, particularly by water concentrators, it is necessary to define, first of all, what are the causes of loss that are likely to interfere with the concentration. Having made this definition, we can then study to see in what may the machines make their losses, and plan remedies for them in an intelligent way. Losses may be stated to occur as included grains, as flat or long grains, as fine free mineral, and as absolute slime. We will take these up one by one, as follows: Included Grains.—Fig. 1 shows by a set of diagrams how included grains may occur : first, where the heavy mineral grains attached to the quartz are of large size; secondly, where they are of small size; and thirdly, where very fine particles of heavy mineral are included in the quartz. We have to decide in regard to included grains whether they are rich enough to go direct to the furnace, or poor enough to throw away, or whether they lie between these two points and require recrush-ing as the only means of severing the values from the waste. This last case is the orlly one requiring special treatment at our hands. We will therefore consider that next.

Jan 1, 1911

By C. S. Samis, J. C. Mitchell

Sodion activity data have been obtained for the Na-A1 system for sodium concentrations in aluminum between NN, = 25 . 10-and 300 x 10'. This concentration intert-a2 encompasses those sodium concentrations nor1)zally encountered in aluminum reduction cell operation. The sodium activity data were measured by a two-phase equilibration of sodium between a lead and an aluminam rich phase. The Na-Pb system was emplojed as a reference for the determination of the actiz7itj 0.f sodium. The activity of sodiin in aluminuwz exhibits large positi2.e deviations frorn ideality and a strong dependence, on concentration below NN, = 100 x 1K6. The inteated data indicate that the activity of aluminium is equal to its mole fraction over the range of miscibility of the Na-A1 sgstem. The data on the Na-A1 binary have been combined with experimental data on the cryolite-A1 system at 1025°C to obtain the activities of Na F and AlF, in liquid cryolite oz2er the cornposition 1-ange encountered in aluminum cell operation. The results are in agreement with activities calculated from the NaF-AlF, phase diagram. ALUMINUM is produced commercially by the electrolytic reduction of aluminum oxide dissolved in molten cryolite. There is considerable controversy over the actual mechanism of the discharge processes, but sodium potentials in the systems appear to play an important role in the reduction mechanism. The metal-salt reaction involving NaF and aluminum to produce A1F3 and sodium is responsible for the presence of sodium in the aluminum metal phase. Additional sodium may be produced from the simultaneous deposition of sodium and aluminum at the cathode as a result of a cathodic overvoltage. runert' has suggested that sodium gas at atmospheric pressure would be the result of reaction between cryolite and aluminum at 1000°C. Subsequent investigations have shown that production of sodium at atmospheric pressure does not occur. These later investigations can be conveniently separated into two categories. The first involves sodium, aluminum, and cryolite, in which the sodium activity was measured. The second includes a lead phase for sodium activity measurement. Jander and errmann,' studied the reaction: at 1090°C in alumina crucibles under an atmosphere of dry, oxygen-free nitrogen. The equilibrium constant for the reaction was expressed in terms of concentration. Their results in Fig. 1 show an increase in sodium content of the aluminum with increasing NaF/A1F3 weight ratio. Pearson and waddington3 performed similar experiments at 1000°C. Their results are included in Fig. 1. Dewing and ollinshead have measured the sodium content of aluminum as a function of the NF/AF, ratio at 1025"C, Fig. 1, and ewin' measured the sodium content of the aluminum in a system involving the solid reactants NaF, cryolite, and liquid aluminum. This reaction is different from those discussed above. Two solid phases, NaF and Na3A1F6, and a liquid aluminum phase were present. The sodium concentration in the aluminum was determined by the temperature. Dewing's measurements covered the temperature range 679" to 896°C. Omo, Matsushima, and 1t02" investigated the equilibrium 6NaF ential thermal analysis. Stokes and Frank6 determined sodium activities by

Jan 1, 1970

By S. Gstalder, J. Raynal

Consideration was given to simple tests which could be performed on rocks to give a measure of rock drillability. Various methods of breaking rocks were considered and the hardness test developed by Schreiner was selected for this study. The test involves application of an increasing load on the rock face through a flat-faced cylindrical punch until rupture occurs. Test results show that hardness is a good measure of the breaking strength of rocks. Useful relationships are shown to exist between hardness and other physical quantities such as specific disintegration, Young's modulus and sonic velocity. Specific disintegration (volume of rock broken per unit of work input) provides a possible means of comparing the effectiveness of other methods of rock breakage. The relationship between hardness and sonic velocity may be very significant for it may be possible to deduce rock drillability from sonic log data. provided that a mineralogical factor is taken into account. TO test further the results of the work, laboratory drilling tests were performed which closely simulated down-hole pressure conditions. Correlations of drilling results with rock hardness measurements were quite good. It was concluded that rock hardness, as measured in the laboratory or as deduced from sonic logs, could be used in relations for predicting rock drilling performance. INTRODUCTION Drillability of rocks cannot be defined in an absolute manner by a single quantity or measured by a single test. Resistance of rock to drilling depends to a large extent upon the means used for rock destruction. This complicates drillability classification of rocks for there may be as many classifications as there are methods of rock breakage without known functional relations between them. The objective of this work was to develop. in terms of rock destruction behavior, means of selecting the best drilling method for a given rock or the conditions for optimum output from a given drilling method. ANALYSIS OF ROCK DESTRUCTION TESTS Gauthier and Baron' have reviewed the many test methods which have been developed for determining the resistance of rocks to breakage. These include drilling tests, punch tests, scratch tests, resistance to shock, wear tests, etc. A standard drilling test might be to determine the time required to drill a standard depth (1/16 in.) in a rock using a bi-cone microbit (1 1/4-in. diameter) when a standard load (417 Ib) is applied at a standard speed of bit rotation (110 rpm). From the standpoint of similarity, the results of microbit drilling tests would seem to be most representative of the several methods suggested above. However, evaluation of drilling performance by this method is only qualitative and cannot be applied directly to actual drilling conditions. Punch tests basically measure rock hardness. Punches of various shapes and sizes, including small cones for Vickers' and Knoop's tests, the wedge for Epstein's test and the right circular cylinder for Schreiner's test, have been used. Results of these tests lead to a quantitative hardness classification which would seem to be related to the resistance of rock to bit-tooth penetration. Scratch tests are related to the resistance of rocks to abrasion such as would be encountered in drilling with diamonds. Either the width of the scratch obtained at a fixed load or the load required to give a scratch of a fixed width may be used to evaluate surface hardness of the rock. This should be related to the resistance of the rock to wear. The above tests, and probably many others. give relative measurements of the breakage or destruction characteristics of rocks. There is no direct relation between results of these tests and the drillability of rocks. Also, the tests each measure different quantities which have different dimensions and they do not permit direct comparison of numerical values. As one step in rectifying the above difficulties. it is proposed that the results of all test methods be expressed in terms of volume of rock destroyed per unit of work required; this is referred to as "specific disintegration". Test results may then be reported in a form which shows both a classification of rocks in regard to each method and a comparison of methods with regard to each rock. The disadvantage in using specific disintegration is the difficulty of measuring this quantity with accuracy. The volume of rock damage is difficult to measure. as is the true value of work input. Rock heterogeneity adds to the

Jan 1, 1967

By Jack A. Simon, M. E. Hopkins

Coal is defined as a combustible rock that originated in the accumulation and physical and chemical alteration of vegetation. Coal can be ignited and burned like the wood that was man's earliest fuel, but coal gives more heat than the same amount of wood and has many industrial uses. Unlike wood, coal is not generally found on the surface of the ground but is mined from the solid rock of the earth. Before taking up the occurrence, formation, and the unique character of coal in the rock sequence, let us briefly consider the general character of all rocks in the crust of the earth. Relatively little is known about the very earliest history of the earth, although a number of logical theories have been developed. Manned exploration of the moon and the rocks returned to earth continue to provide some answers to questions concerning the earth's origin and history. The period of earth history with which we concern ourselves here begins after great areas of water had evolved on earth and substantial land areas of once molten (igneous) rock existed. Weathering and other processes that attacked the surface of the rocks reduced them to small particles. Water provided by rainfall transported this material, ultimately, to large bodies of water where it was deposited. Thus was initiated the geologic sequence of sedimentary rocks that lie above the once molten igneous rocks. The crust and upper mantle of the earth are made up of several large plates along which differential movement (primarily horizontal) takes place. Such movements, although small, are occurring today. These horizontal movements are accompanied by vertical movements causing important changes in the relative position of the continents and oceans. Low-lying coastal swamps with favorable climates are ideal locations for coal accumulation and burial by river-borne sediments, and large areas

Jan 1, 1981

By J. Szekely, V. Stanek

Heat and gas flow interactions in nonisothermal packed beds were examined in the paper. A study was made of the response of the system to a step or pulse change in the inlet gas temperature, with a fixed value of the overall pressure drop across the bed. Under these conditions the heat flow and fluid flow transients are coupled because the convective heat transfer rate is alfected by the mass flow rate of the gas which, in turn, for a fixed pressure drop will depend on the temperature profile in the system. The Problem was stated in terms of differential equations, which were integrated numerically. The parameters used in the computation were so chosen to reflect the operation of the stack region of blast furnaces and sinterbeds. The computed results showed that the pressure drop-flou1 relationships and the rate of progress of the temperature fronts (waves) were strongly interrelated and were also markedly affected by variations in particle size and in void fraction. MANY metallurgical processes involve the contact of solid particles with a gas stream in a packed bed arrangement under nonisothermal conditions. Examples are shaft furnaces, regenerators, pebble heaters, and the sinter process. Although the heat and mass transfer aspects of packed bed processing have been extensively studied, the associated flow phenomena and in particular the effects of nonisothermality on the flow, have received little attention to date. :In fact, most of the previous workers considered the flow rate of the carrier gas time invariant and independent of the heat or mass transfer processSzekely and carr2 have shown that the pressure drop-flow relationships in nonisothermal packed beds may be strongly affected by the temperature profile within the system. These authors have devised a method for relating the pressure drop to flow for a given temperature profile. thus providing an extension of the Ergun equation to steady nonisothermal systems. Finally, in a recent paper willmot3 examined the response of regenerators to externally imposed changes in the gas flow rate. Both these investigations were somewhat specialized since, in general, neither the temperature distribution nor the gas flow rate may be regarded as truly independent variables, thus the heat transfer and the fluid flow problems have to be solved simultaneously. The work reported here is divided into two parts: in Part 1 the general formulation is given and a detailed discussion is presented of fixed bed systems. Part is devoted to systems in which a gas and particulate solids are contacted in a counter flow arrangement. FORMULATION Consider a nonisothermal fixed packed bed, extending from through which a gas is flowing. The problem is to develop a relationship between pressure drop and gas flow (with the gas flow being the dependent variable) and to evaluate the rate at which a change in the gas temperature, imposed at the inlet, travels through the system. Let us consider an infinitesimal section of the bed and establish differential heat, mass, and mechanical energy balances over this region. In addition, relationships are needed describing the temperature dependence of gas density (equation of state) and the temperature dependence of viscosity. These may be written as: where c, and are constants. It is noted that in this formulation we neglected any temperature gradients within the solid particles, thus assuming these to be either sufficiently small or of sufficiently high thermal conductivity to meet this condition. The justification and consequences of this assumption will be mentioned in the discussion.

Jan 1, 1970

By Klaus Schwerdtfeger

In order to test the performance of ZrO, (CaO) and Tho,(Yz03) electrolytes in the electrochemical determination of oxygen activities in liquid metals at steel-rrzakitng temperatures , electromotive force measurements have been made with the following cells: The oxygen-- activities are calculated from the electmrnotive forces for the investigated systems. The standard free energy of- formation of MnO and the activity of manganese in Fe-Mn melts are derived. Indications are that the Zr 0z(Ca0) electrolyte exhibits little electronic conductivity at oxygen pressures as low as 10'a atnz at 1600°C; however, the partial electronic conductivity may become noticeable at lower oxygen activities. The Tho,(Yz03) electrolyte is found to be an ionic conductor at the oxygen pressure as low as that for the Mn + MnO equilibrium, but exhibits partial electronic conductivity at oxygen pressures higher than 10"1 atm (1500°C). fi. better control of oxidation and deoxidation reactions in steelmaking may be facilitated if the oxygen activity in the steel is known during various stages of the process. In the present work oxygen activities have been measured in liquid iron, manganese, and iron alloys with galvanic cells using ZrOz(CaO) and s solid electrolytes with the object of establishing the range of oxygen pressure in which these materials can be used as electrolytes at steelmaking temperatures. Calcia-stabilized zirconia and Tho2-Y203 solid solutions are oxygen ion conductors. Such electrolytes were first used by Kiukkola and Wagner1 and Peters and ~ann' in galvanic cells for the determination of thermodynamicquantities of oxide systems in the temperature range 700" to 1200°C. At these moderate temperatures calcia-stabilized zirconia has been found to exhibit predominantly ionic conductivity at oxygen pressures as low as those for the Cr + Crz03 equilibrium,394 but at lower oxygen pressures elec- tronic contribution to conductivity becomes significants4 The Th02-Y203 solid solutions are ionic conductors at oxygen pressures lower than those applicable to zirconia base electrolytes.5'6 At high oxygen pressures Thoz base electrolytes exhibit significant p-type semiconduction. At the time the present experiments were carried out several papers1'-* were published on the electrochemical determination of oxygen activities in liquid iron using the ZrOz(CaO) electrolyte. The results of different authors do not agree well. For instance, according to Fischer and ~ckermann" stabilized zirconia can be used to measure oxygen contents in liquid iron larger than 0.02 wt pct, but according to Baker and west1' ZrOz(CaO) cannot be used for the determination of oxygen content in liquid iron because of high electronic contribution to the conductivity. Fig. 1 is a schematic diagram of the apparatus used. About 500 g of liquid metal is contained in a crucible into which a stabilized zirconia or Th02(Y203) tube is immersed. A platinum contact wire is pressed (with a spring mechanism) against the inside bottom wall of the electrolyte tube. The tube is flushed continuously with a stream of air, CO-CO, (or Hz-C02) (at 0.96 atm and at a rate of about 300 cu cm per min), via an alumina tube inserted inside the electrolyte tube. This alumina tube also contains the Pt-Pt/10 pct Rh thermocouple. A capillary alumina tube shielding the other contact wire is immersed in the melt. The molybdenum contact wires were used mostly; in some cases platinum wire was employed. Molybdenum has the advantage that it dissolves more slowly in the melt than platinum. The whole cell was contained in the alumina reaction tube of a resistance furnace with molybdenum winding. The reaction tube was closed gas tight at both ends and flushed continuously with argon. Because of the poor thermal shock resistance of the electrolyte tubes the cell had to be assembled in the cold furnace. The electrolyte tube and alumina sheath

Jan 1, 1968

By K. Mukai, M. Ishihara

This report is a brief discussion of the impurity levels both in primary aluminum and super-purily alnminim in connection with raw materials and proc-essing methods. Particularly, truce amounls of im-purities were analyzed by introducing nittss-speclro-gruphy and nenlron-aclivalian analysis techniques. Vanadium and gallium content in primary aluminum metal corresponded to theor amounls in anode coke. but the nickel content in primary aluminum was hide-pendent oj its amount in the anode cake. Sulfur in the anode colic might result in an increase of the iron content in the molten metal in the reduction cell. The content of sodium and calcium increased with increasing bath ratio. In the holding furnacc sodium content decreased rapidly, and nonmetallic inclusions merit separated front the mollen metal. Three-layer elctrolysis was effectire in eliminating many impuri-ties with the exception of copper, aluminum oxide. aluminum nitride, and some rare-earth elements. THE amount of impurities and nonmetallic inclusions in aluminum metal depends on impurities in the raw materials and various production processes. This paper presents an investigation of the behavior of impurities and nonmetallic inclusions in aluminum during the electrolysis process, the period in the holding furnace, and the process of three-layer electrolysis. Chemical analysis and emission spectrometric analysis have generally been used as methods to determine small amounts of impurities in both primary aluminum and super-purity aluminum; however. mass spectrography and neutron-activation analysis have been recently introduced into this field, and trace amounts of impurities can accurately be determined by these latter methods. EXPERIMENTAL WORK Common impurities were determined by means of absorptiometric. polarographic, flame-photometric. and emission-spectrometric methods. However, in the determination of trace amounts of impurities and non-metallic inclusions, the following methods were applied. In the analyses of trace impurities by mass-spec- trographic analysis, samples were exposed in the vacuum spark of double-focus ing Mattauch-Herzog type mass spectrograph (Japan Electron Optics Laboratory, Ltd.). Ilford Q2 photographic plates were used as ion detectors. Fe was used as the internal standard, and the atomic concentration of each element was calculated by the following expression and converted into the weight concentration: where E, and Ei are the exposures (coulomb) when isotopes of the internal standard and impurity elements (on which the estimate is based) show the same density, X is the percent (atomic) concentration of the standard, IF and Ii are the percent abundances of the isotopes of the standard the impurity elements (on which the estimate is based), and Ms and hfi are the mass of the isotopes of the standard and impurity elements (on which the estimate is based). The coefficient of variation in this method is about 40 pct in the range of 0.1 to 1 ppm. In neutron-activation analysis, irradiations were done in the nuclear reactors TRIGA-I1 (neutron flux: 4.7 x 10 11 n per sq cm per sec; Rikkyo University) or JRR-2 (neutron flux: 2 x 1013 n per sq cm per sec: Japan Atomic Energy Research Institute). After the chemical separation, a NaI (3 by 3 in.) scintillator connected to a 256-channel y-ray spectrometer (R.C.L.) was used for counting and recording various activated impurities. The coefficient of variation in this method is about 20 pct. In the analyses of nonmetallic inclusions, aluminum-oxide determination was carried out according to Fischer's method, 3 as follows. A slice of sample was cut off and the surface was cleaned. It was dissolved in bromine-methanol. The solution was filtered and the residue was washed. The residue was fused with potassium bisulfate flux. Then it was dissolved in weak acid, and oxine solution was added. The aluminum oxinate was extracted with benzene. Finally, aluminum was determined absorptio-metrically. Aluminum nitride determination was carried out as follows. A slice of sample was cut off and the surface was cleaned. It was put in the distillation apparatus and decomposed with sodium hydroxide solution. The solution was distilled. Then ammonia was absorbed and

Jan 1, 1967

By S. R. Titley

The recent emphasis placed upon the use of molybdenum as a geochemical indicator has stimulated considerable inquiry into the behavior of molybdenum in the zone of oxidation. This paper represents a summary of recent and continuing experimental work and calculations in an investigation of a portion of the system Mo-Fe-S-H20 and treats the stability of various iron and molybdenum compounds with respect to oxidation potential and pH. Using experimentally determined free energy values for ferrimolybdite, diagrams of the stability fields of this mineral have been calculated with respect to ilsemannite (?), molybdenite, pyrite and limonite. This theoretical approach is the one utilized by Garrels3'4 in studies of the relationships of various minerals in the zone of oxidation. Use of this approach is particularly suited to the study of geochemistry in the zone of supergene processes because of the low temperatures, low pressures and other relatively easily determined and duplicated factors that exist in the near surface environment. Such a study of molybdenum, however, is complicated by several factors. One of these is the fact that the strong amphoteric behavior of molybdenum makes possible a wide variety of substances and complexes whose exact chemical natures are unknown. The second factor is the dearth of thermodynamic data for many of the simplest of the possible compounds and ions important to the study. For the purpose of this study, the problem of complexes has been approached through considering only the simpler possibilities realizing that the complexes and systems so treated may be gross oversimplifications. All the complexes considered, however, have been suggested in the chemical 2,7,9,12 or geologi-cal literature. EXPERIMENTAL WORK Studies of the behavior of molybdenum ions and ferrimolybdite have been carried out in aqueous sys- tems, and reactions have been followed by simultaneous measurement and recording of pH and oxidation potential. A major problem involved in this study was the long periods of time necessary for equilibrium to be established in some of the systems considered; in a few instances, these periods exceeded four weeks, that is, four weeks during which measured conditions changed continuously. Another problem, in some instances, was the indeterminate nature of the reactions that have taken place. Because of the tendency of molybdenum to complex, reactions which take place under some of the more extreme imposed conditions of oxidation and acidity or alkalinity are unknown. However, useful data for the present work were obtained from studies of the molybdate ion and ferrimolybdite between pH 2 and 8 and under only moderately oxidizing to nonoxidizing conditions. Instruments used in the experiments were a Hewlitt-Packard Model 412A VTVM, a modified Beckman Zeromatic pH Meter and two Varian model 11 recorders. pH was measured between glass and calomel electrodes and Eh was measured between calomel and platinum electrodes. Conditions of pH were varied with 1N H2SO4 and 1N NH4OH and 1N NaOH. Eh was varied with gaseous nitrogen, oxygen or aqueous H202. Ambient temperature was essentially uniform at 24ºC and was increased in the reaction vessel by the positioning of a magnetic stirrer whose temperature was sufficient to bring the temperature to 2S°C in the reaction. The temperatures of reaction did not vary more than 1/2ºfrom 25°C. Two reactions were investigated, the ferrimolybdite-limonite-water reaction and the reduction of molybdate ion. Studies of both reactions yielded useful data that were used in preparation of the Eh-pH diagrams. The traces of the reactions are shown on Fig. 1. Ferrimolybdite-Limonite- Water: Studies of this reaction involved analysis of the solution of ferrimolybdite and simultaneous formation of ferric hydroxide. The data are summarized on Fig. 1. In this reaction, equilibrium was attained at various pH's when coexistence of the two solid phases (ferrimolybdite and ferric hydroxide) was attained. At the proper pH, controlled by the amount of ferrimolybdite and thus the dissolved content of molybdate species, both phases were observed and reaction times to complete the transition were on the order of weeks. The reac-

Jan 1, 1963

By Henry Lloyd Smyth, J. Ralph Finlay

The most important area of the so-called Keewatin rocks of northern Minnesota is that which runs westerly from Lake Saganaga, near the national boundary, and finally disappears beneath the drift (or has not been farther traced), in the neighborhood of Vermilion Lake. With this belt we have a general acquaintance, extending back some four years. During the past year we have had the opportunity of studying in considerable detail a small part of it, embracing an area of about 12 square miles on the south and east shores of Vermilion Lake. In this paper we desire to record our observations and conclusions, which seem to us important. II.—Literature. Outside the Minnesota Geological Survey, the list of the investigators who have studied the geology of the Vermilion Lake area is not long. Whittlesey, in 1876,* mentioned the occurrence, in the area about Vermilion Lake, of rocks resembling the Canadian Laurentian. Chester,? in 1884, described the iron-ore at Vermilion Lake as occurring in connection with jasper and quartzite, intimately bedded with the country-rock, chiefly sericite schist, and standing in a nearly vertical attitude. The Vermilion iron-bearing rocks, and those of the Mesabi range, he says, are of the same age.

Jan 1, 1896

By J. M. Woodall

GuAs crystals which have been grown in quartz boats by the horizontal Bridgman method in the pvesence of Ga20 vapov have beetz found to have carrier and donor distributions which do not correspound to those expected from simple dopant seg-vegation during directional freezing; Instead, the carrier distribution is determined by the heat-trentnzent history of the crystal, while the donor distribution, zohiclz is principally due to silicon, is fixed by the pozuth rate, the geo)tlet.ry of the crystal growth vessel, and tlze initial Ga20 pressure. WHEN semiconducting materials are made into doped crystals by the normal freezing method,&apos; they usually exhibit doping variations along the growth axis. If a) there is no dopant diffusion in the solid, b) the dopant is distributed uniformly in the melt, and c) the distribution coefficient, k, does not vary with composition, then the doping variation along the growth axis is represented by the equation: where C is the doping level in the solid at a point where a fraction g of the original liquid has frozen, and Co is the mean concentration. When the dopant is either a singly ionized shallow donor or shallow acceptor, C also represents the carrier concentration. Even though this equation accurately describes the dcping profiles of a large number of normal freeze systems, there are several special systems for which Eq. [I] does not apply. One such system is the horizontal Bridgman method for preparing oxygen-grown GaAs crystals using quartz vessels. Several workers2"* have shown that GaAs crystals grown by the horizontal Bridglnan method using quartz vessels are generally contaminated with silicon in concentrations in excess of 5 < 10lG atoms per cu cm. This contamination is ascribed to a reaction: occurring at the walls of the crystal-growth vessel which liberates silicon into the melt and Ga2O vapor. It has been shown4 that this reaction, and, hence, the silicon contamination, can be suppressed by the addition of oxygen to the crystal-growth apparatus. It is the purpose of this paper to describe a special apparatus capable of yielding single crystals of GaAs grown in the presence of oxygen and to describe both the kinetics of silicon suppression in this system and the relationship between the carrier concentration profile and the silicon concentration profile. EXPERIMENTAL-CRYSTAL GROWTH A schematic diagram of the apparatus used in the oxygen addition experiments is shown in Fig. 1. The most important features of this apparatus are: a) the use of a sand blasted quartz boat, h) a quartz rod of length 1, with a hole of cross section A, that is placed near the boat to limit the free space volume V, over the melt during the growth, and c) the temperature gradient at and near the solid-liquid interface. Sand blasting the boat is necessary to prevent wetting of the melt. The quartz rod retards the diffusion of the GazO vapor away from the melt to the colder portions of the ampoule. A crystal is prepared by first loading a 5.5-in. boat, which has been cleaned in aqua regia, with 40 g of 99.9999 pct Ga along with 1 to 8 mg of Ga203 powder. GazO3 is a convenient source of oxygen since it reacts with gallium at the melt temperature to form Ga20 vapor, the species which apparently controls the suppression of silicon contamination. The loaded boat, the quartz rod, and the 99.9999 pct As are placed in the ampoule as shown in Fig. 1. Generally, GaAs seeds were not used since most of the unseeded growths resulted in monocrys-tals. The ampoule is evacuated to 10-5 Torr and sealed off. The GaAs melt is synthesized by placing the ampoule into a two-zone horizontal Bridgman furnace. The two zones are separated by several sandwiched layers of -in. Fibre-Fax board drilled with holes slightly larger than the OD of the ampoule. This causes a very large temperature gradient between the two zones, which is necessary for single-crystal growth. The two-zone furnace is mounted on a stand fitted with a roller bearing which allows uniform motion of the furnace in a horizontal direction. A uniform velocity of the stand is achieved by the use of a windlass device which winds up a wire attached to the stand. Movement of the solid-liquid interface is accomplished by fixing the position of the ampoule and moving the stand. Growth rates investigated in this experiment were between 0.4 and 1.2 in. per hr. The composition of the melt is fixed by maintaining an arsenic reservoir at 618°C. The stand is moved away

Jan 1, 1968

By J. Chipman, N. J. Grant, H. L. Bishop

Lime and dicalcium-silicate crucibles were equilibrated with molten iron and liquid slags containing iron oxide and small amounts of sulfur. The oxygen content of metal, iron oxide activities, and desulfurization values of the slags were determined in the temperature range 1530 to 1700°C. The influence of magnesia in the slag and the temperature dependence of the solubility of lime in liquid iron oxide and the ferric oxide content were established. The temperature contour of the liquidus surface of iron-silicate slags saturated with lime and dicalcium silicate was also established at 1600°C. THE importance of the role that slag composition plays in the refining of steel has been known for many years. Numerous studies have been made using actual plant data in order to establish the relationship between the composition of the slag and metal during the refining of a heat of liquid steel. These results rarely represent equilibrium conditions since completion of the various chemical reactions involved in steelmaking is seldom realized. In order to establish quantitatively the equilibrium conditions existing between the slag and metal, several laboratory studies have been conducted in the past 20 years to determine the reactions important in slag control. These investigations have included studies of simple liquid basic and acid slags as well as more complex slag systems which approach those commonly found during the refining of a heat of steel. Since most of the previous studies of simple basic iron-oxide slags equilibriated with molten iron were made in magnesia crucibles, it was not possible to establish the distribution of sulfur and oxygen between molten iron and slags consisting only of the three essential components, lime, silica, and iron oxide. This investigation was undertaken to establish the equilibrium conditions for simple lime-iron oxide and lime-silica-iron oxide slags. Accordingly, it was expedient to prepare crucibles both of lime and dicalcium silicate to establish the equilibrium conditions between molten iron and iron-oxide slags saturated with the refractory materials and free from other components. The only other studies of the equilibrium between molten iron and lime-saturated slags are those of Fischer and vom Ende, 1, 2 in which the solubility of oxygen was determined in an air atmosphere. The

Jan 1, 1959

FRIENDS of the late Charles F. Rand presented in 1930 a sum of money from which the income is available to support various phases of the work of the Institute in which Mr. Rand was so deeply interested. At present the fund amounts to $10,400. The specific terms of the deed of gift are as follows: "The fund collected to establish a memorial to the late Charles F. Rand shall be placed in the custody of the Board of Directors of the American Institute of Mining and Metallurgical Engineers, to be set up as a trust to be known as the `Charles F. Rand Foundation,&apos; the income of which shall each year be applied to a distinct purpose to be decided upon in that year by vote of the Board of Directors. This purpose shall be such as to promote the general welfare of the Institute and to constitute a permanent memorial of the usefulness of Mr. Rand, who for many years gave unstintingly of his time and talents in its service. "It shall be within the discretion of the Board of Directors to establish a medal to be known as the Charles F. Rand Memorial Medal to be awarded at such a time and under such rules as may be determined by the Board of Directors, for Distinguished Achievement in Mining Administration." The establishment of this medal was announced at the annual meeting in February, 1932, the term "mining" being defined in its broad sense to include metallurgy and petroleum. Robert Linton is chairman of the Charles F. Rand Foundation Award Committee.

Jan 1, 1943

By S. L. Lopata, E. B. Kula

A variation of yield and tensile strength with direction has been noted in heat-treated 4340 steel which had been warn-worked by rolling in the austenitic condition prior to quenching. Measurements by X-rays showed a preferred orientation of martensite crystals. Various ideal preferred orientations of martensite were calculated by assuming a preferred orientation for austenite and transforming this to martensite by the Kurdjumov -Sachs and Nishiyama relationships. Comparison with the measured preferred orientation showed that the ideal rolling texture for austenite in 4340 steel could be expressed as a (112) [111] texture with a component of (110) [112]. No evidence was found for any fiber axis in the rolling direction, or fop- a (123) [412] texture. The observed martensite pole figures can be adequately accounted for by these ideal austenite textures and by the Kurdjumou-Sachs or Nishiyama transformation relationships between austenite and martensite. ALTHOUGH preferred orientations are found in cold-rolled steel sheet and in many nonferrous metals, they are not generally encountered in wrought, heat-treated high-strength steels, since such steels are generally not cold worked sufficiently to develop a strong texture, and any texture that is present is removed during heat treatment by the phase transformations taking place. This report gives details on a preferred orientation found in warm-rolled and hardened 4340 steel. In a recent study, a special combination heat-treating and working technique was used in which 4340 steel was deformed in the austenitic condition, and before re crystallization of the austenite could occur, quenched to form martensite.&apos; Since the austenite was unrecrystallized, it was cold worked and hence could have contained a preferred orientation which could be transmitted to the martensite on quenching, and this in turn could be manifested as a directionality of mechanical properties. Such a directionality of properties was found as a result of working, and this prompted an X-ray study of the preferred orientation. Literature Survey— Rolling Texture in Face-Cen-tered-Cubic Austenite—M a preferred orientation is found in a rolled and hardened steel, it is first appropriate to consider what texture existed in the austenite as a result of the rolling but prior to the transformation to martensite. The changes taking place as a result of the austenite-martensite transformation are then considered. In view of the instability of austenite in 4340 steel at low temperatures, no direct determination of the austenite texture was made. However, an estimate of the texture for austenite in 4340 steel may be made by considering the textures found for other face-centered-cubic metals. Barrett&apos; has reviewed the rolling textures for many materials. The most common orientation in face-centered-cubic metals has the (110) planes parallel to the rolling plane and the [112] directions parallel to the rolling direction, or (110) [112]. Other orientations found are (112) [111], as well as (100) [001], (110) [001], and others. Beck and his co-workers, using quantitative pole figures, report that (123) [121],3 later corrected to (123) [412],4 better describes the ideal orientation. smallman5 reported that the ideal preferred orientation for high-purity face-centered-cubic metals is (123) [121], but that there is a transition to (110) [112] as solid solution elements are added. The latter texture tends to occur more readily at lower temperatures. This transition between the two textures was explained by differences in the slip characteristics with concentration or temperature. More recently, Jones and Fell6 concluded that the (123) [412] texture for face-centered-cubic metals could equally well be represented by a mixture of (110) [112] and (112) [111] textures, and hence it had no physical reality. From the above results it can be seen that there is no agreement on the "ideal" texture for fcc metals and, hence, no firm basis for assuming a texture for austenite in 4340 steel. Therefore, the orientations (110) [112], (123) [412], and (112) [111] have been considered in the following.* *The (123) [4121 is identical to the (123) [121] rotated 90 deg. Orientation Relationship between Austenite and Martensite—When martensite forms from austenite, certain crystallographic planes of the martensite are parallel to planes in the austenite. This orientation relationship was first determined by Kurdjumov and

Jan 1, 1960

By D. L. Katz, M. J. Rzasa

The derivations of three methods of computing the static pressure gradients in natural gas wells have been presented to show the assumptions made. Charts were developed from which the pressure gradients may be read when the well-head pressure, the well fluid gravity, depth, and the average well temperature are given. A chart for estimating the well fluid gravity from the condensate content and separator gas gravity is included. The effect of the increased average well temperature after flow on the calculation of the static pressure gradient is discussed. Introduction Reservoir pressures have been calculated from well-head pressures for gas wells for many years. As the pressure measurements become more accurate, the need for a reliable calculation of the static pressure gradient often arises. This paper will develop the several methods for computing the pressure gradient in gas wells and make a comparison between them. The method of calculating static pressure gradients in common use is Eq. I (ref. I) or its counterpart which includes a factor for the deviation of the gas from the ideal gas law. P2 - P1 = P1(e0.0000347GX _ I) Eq. [I] in which P1 = pressure at well head, lb. per sq. in. abs. PP = pressure at bottom of well, Ib. per sq. in. abs. G = gas gravity X = depth of well, ft. An alternate method is to compute the average density of the gas in the well and multiply by the well depth in a manner similar to that used for liquid gradients. Derivation of Formulas A static pressure gradient is a special case of the general fluid-flow equation. Consider a pound of fluid flowing in a vertical column from point I to point 2, Fig. I. By an energy balance for fluid flowing from I to 2: U1 + P1V1 + u12/2g + X1 + q = U2 + P2V2+ u22/2g+X2 +W [2] in which U = internal energy, ft-lb. per lb. P = pressure, lb. per sq. ft. V = volume, cu. ft. per lb. u = average linear velocity, ft. per sec. X = height above datum, fl. q = heat absorbed by fluid, ft-Ib. pcr lb. W = work done by system, ft-lb. per lb. An energy balance on the fluid itself gives: U = ?TdS - ?PdV + etc. [3] in which T = temperature, deg- R- S = entropy, ft-lb. per deg. R. per lb.

Jan 1, 1945