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By Charles R. Keyes

In the dry regions of the globe many silver-deposits display certain remarkable features, which at the same time are so totally unlike anything met with among ore-bodies elsewhere that they hare long presented exceptional dificulties, not only to a satisfactory explanation of their origin, but to economical milling. A most striking peculiarity of these ores is the haloid character of many of their bonanzas. To this fact more than to any other may be ascribed most of the unusual uncertainties of mining-operations in desert countries—the marvelous local richness of the ores under certain conditions and the often abrupt transition to utter poverty; the inadequacy of ordinary prospecting customs and the constant devising of new exploratory methods; the unaccountable losses in smelting and the continual change in treatment-practice. For these anomalies certain climatic conditions seem to be chiefly responsible.

Jan 1, 1912

By J. E. Lawver, R. R. Beebe, J. L. Wright

This paper describes a separation coefficient Ks useful as a "measure of goodness" to be used in factorial and response surface methodology. The use and limitations of the separation coefficient is discussed, and a computer program for calculating the coefficient is presented (in Fortran). The application of the coefficient is illustrated in terms of electro-dynamic separation of Mesabi semitaconites. Present Mesabi wash ores and gravity concentrates with an iron to silica ratio of only 5 or 6 to 1 are no longer readily salable, for the steel industry now demands concentrates with an iron to silica ratio of at least 10 to 1 and a structure comparable to pellets. THE ELECTRODYNAMIC-FLOTATION PROCESS Wash ores and gravity concentrates consist largely of hematite, goethite, and quartz. Several methods of beneficiation are being tested at the University of Minnesota Mines Experiment Station with a view to improving the salability of these materials. A process that looks particularly promising from an economic view is the combination electrodynamic-flotation process shown in Fig. 1. This process is designed to upgrade gravity concentrates to a 5% silica content and to provide fines — from the flotation circuit —to permit agglomeration. Although electrodynamic concentration of specularite is an established and well-understood process, the electrodynamic concentration of Mesabi goethite-hematite gravity concentrates presents interesting and enigmatic problems. The gravity concentrates are by no means assemblages of clean, free mineral particles. Instead, the concentrates to be retreated consist of a great variety of middlings. More or less complete liberation would require grinding to minus 325 mesh, at which size only flotation could be expected to function, and even then grades and especially recoveries would not be satisfactory. A close examination of the gravity concentrates shows that grinding to 100% minus 48 mesh will produce a product which is approximately 70 weight % plus 325 mesh (see Fig. 1). The remaining 30 weight % can be deslimed and floated by conventional methods, but the resulting iron concentrate is

Jan 1, 1964

By F. E. Steigert, A. H. Geisler

THE permanent magnet alloy comol, which contains 17 pct Mo, 12 pct Co, balance Fe, exhibits a precipitation reaction analogous to that at the iron end of the binary Fe-Mo system. The equilibrium precipitate, (P,), has a structure isomorphous with Fe,Mo, which is rhombohedra1 with parameters a = 8.97A and a = 3038.6&apos; according to the work of Arnfelt and Westgren.&apos; In the ternary alloy the parameters are a = 8.87A and a = 31°0.5&apos;. Oscillating crystal patterns of a single matrix crystal, M, in which P, was precipitated by slow cooling from 1300°C, showed that the orientation relationship of the two lattices is as follows: (110)P3 // (110)* (111)p3 // (110)m There are crystallites of P, in 12 different orientations in a single crystal of the parent solid solution. Microscopic examination shows that the crystallites are generally plate-like with their lateral dimensions parallel to (110) matrix planes. When precipitation in a supersaturated alloy quenched from 1300°C progressed isothermally at temperatures between 600" to 800°C, the evolution of the P, structure could be traced. Diffuse diffraction effects in Laue patterns provided early evidence of the precipitation process. Analyses of these by a previously described technique2 showed that they corresponded to rod-like elements parallel to <110> matrix directions in reciprocal space. With further aging to promote growth of the precipitate, the rod-like elements contracted to points in reciprocal space for normal Bragg reflection from the precipitate as shown by the left diagram in Fig. 1. Thus the diffuse scattering was attributed to the small thickness of the plate-like particles which was inadequate for sharp diffraction. When the precipitate particles were first thick enough to give normal diffraction their structure was different from that of the equilibrium precipitate, P,. The first structure, P1, presumably is a coherent transition struc-

Jan 1, 1952

By Leon McCulloch

WHEN clean iron and metallic zinc dust, protected from the air, are heated below the melting point of zinc, the iron takes on a coating that has excellent protective value. This coating is a brittle alloy of zinc and iron, and the process is called sherardizing. Although the zinc particles are covered with oxide and cannot touch the iron, an extremely small amount of the zinc vaporizes and the vapor, reaching the iron, alloys with it. Other zinc then vaporizes to replace that which has been removed from the atmosphere. This process continues indefinitely at a decreasing rate, for the coating already formed permits zinc to diffuse through-it to combine with the iron beneath. In this way, the coating grows outward from the surface of the iron, as the bark grows from a tree. The method of growth was clearly seen while sherardizing small cubes of cast iron, at about 450° C., in a small glass-stoppered bottle enclosed in a rotating drum. The dust contained about 3 per cent. iron, which prevented caking, and coatings 1/2 in. thick were grown in a few hours. After a heavy layer had been formed, the cubes were again: treated for a shorter time. The layer last formed was seen to lie next to the iron, instead of at the outer surface, showing that the growth was from the surface of the iron outward. The coatings split at the edges and corners, leaving the iron exposed there. Flakes of graphite from the iron were lifted upward and embedded in the coatings. The composition of sherardized coatings varies from the outer surface inward, as would be expected from the mode of growth. That is, the iron content increases slowly at first, then more rapidly as the iron is approached. At the surface the least amount of iron possible is 6 per cent., as the experiments described below have shown.

Jan 2, 1922

By J. M. W. Mackenzie, C. J. Wood

In attempting to describe the size classification performance of a hydrocyclone, most workers have elected to use either an equilibrium orbit theory or an non-equilibrium orbit theory. The equilibrium orbit theory has been used by the majority of workers including Lilge,&apos; Bradley; and Yoshioka and Hotta. In applying this theory, it is argued that particles in the body of a hydrocyclone attain an equilibrium radial position where the drag force on the particle resulting from the inward radial fluid velocity is balanced by the outward centrifugal force caused by the tangential component of fluid flow. When considered over the full height of the hydrocy-clone, attainment of this radial equilibrium orbit results in the particle following a conical equilibrium envelope. It is then argued that if this envelope lies outside the envelope of "zero vertical velocity," the particle will report to the underflow, while if the equilibrium envelope lies inside the envelope of "zero vertical velocity," the particle will report to the overflow or vortex finder product. The d50-sized particle which reports in equal quantities to the underflow and overflow is assumed to correspond to particles whose equilibrium envelope is coincident with the envelope of "zero vertical velocity." In considering the equilibrium orbit theory, it is apparent that the horizontal position of the particles in the feed inlet pipe should have no effect on their ultimate destination on the hydrocyclone. Each particle should attain an equilibrium position which depends on the density, size, and shape of the particle; the density and viscosity of the fluid; and the flow patterns within the hydrocy-clone. The nonequilibrium orbit or unsteady state theory has been largely developed by Rietema4 and Mizrahi.6 Mizrahi has listed four main objections to the equilibrium orbit theory. These objections center on the short residence time in the hydrocyclone, the fact that the experimental classification curve is much less sharp than is theoretically predicted, and the absence of negative efficiency conditions in hydro cyclones operating on a feed material which is much finer in size than d50. Proponents of the nonequilibrium orbit theory argue that for a particle to discharge with the underflow it must have sufficient outward radial velocity to reach the downward-flowing region close to the hydrocyclone wall in which the flow lines are parallel to the wall and the ratio of vertical to radial velocity is constant. It is then postulated that a d50 particle entering the cyclone at the center of the feed inlet will just reach this downward-flowing region as it reaches the apex. Thus for uniform distribution of particles across the feed inlet, half the d50 particles—that is, those injected in the half of the inlet area nearest the cyclone wall —will report to the underflow while those injected in the other half will not reach the downward-flowing region and will be carried inward to the center of the cyclone and thus report in the overflow. The exact thickness of the down-ward-flowing region of fluid adjacent to the outer wall of the hydrocyclone is uncertain but Mizrahi considers it to be equal to the apex radius minus the air core radius. Particles larger than d50 have a greater outward centrifugal force acting on them than the d50 particles and may reach the wall even if injected at a distance from the wall greater than Di/2 (Di is inlet diameter). Conversely, particles smaller than d50 may not reach the wall even if injected at a distance less than Di/2 from the cyclone wall. Since the equations put forward by the proponents of both theories yield approximately the same values of d50, it is not possible to decide between these theories by measurement of d50. It should be possible however to examine the theories by injecting a small stream of solids into the feed inlet of a hydrocyclone running on clear water. If the efficiency or classification curve is measured for various horizontal injection positions, then the curves should be coincident if the equilibrium orbit theory holds. If, however, the unsteady state theory describes the cyclone operation, then the classification curves should show finer d50 sizes for particles injected close to the cyclone wall. Experimental A 6-in.-diam hydrocyclone with geometry as in Figs. 1 and 2 was used. Quartz particles were injected as a 50% by wt pulp via an 1/8-in. steel probe. For each in-

Jan 1, 1971

By André G. Journel

Geological study of the Prony Nilaterite (New Caledonia) began in 1969 and included drilling, geological mapping and laboratory studies. The deposit is the product of weathering of basic rocks. From top to bottom, the following zones can be distinguished: a compact ferruginous cover; ore associated with yellow laterite, containing 1.0-1.5% Ni and low in impurities (SiO2, Mg); an intermediate silicated ore containing 1.3-2.0% Ni and higher percentages of impurities; garnierite ore much richer in nickel (2-4%) but high in SiO, and Mg contents (Mg up to 20%) ; and parent rock, largely peridotites. Distinction between types of ore is essential because the high grade ore (silicated and granierites) is penalized for its high Mg contents that demand additional acid treatment. All studies made distinguish two types of ore, laterite and silicated.

Jan 10, 1973

By Benjamin Gildersleeve

Uniquely colored, thin-bedded quartzite is quarried between Crossville and Crab Orchard in Cumberland County, Tenn. It is produced in all sizes up to the limits of transportation from beds usually ranging in thickness from less than Vi in. to 6 in. The stone is very resistant to wear and weathering and is marketed throughout the country for many different purposes in exterior and interior construction. The annual production exceeds 36,000 tons, valued at nearly $1,000,000. THE building stone of the Crab Orchard District is a fine-grained, thin-bedded sandstone which is so strongly cemented by silica that it may be classed as quartzite. As used in this paper the term building stone includes dimension stone, rubble, ashlar, flagstone, and rough broken stone. The Crab Orchard District is in the central portion of Cumberland County, Tenn. It is named from the town of Crab Orchard near which the stone was quarried first for industrial use. The heart of the district is an area of some 1200 acres from 1 to 3 miles east of Crossville which is 70 miles west of . Knoxville and 125 miles east of Nashville (fig. 1). At the present time, there are about 15 quarries worked by companies and individuals. Geology: The Crab Orchard District is on the Cumberland Plateau, or Cumberland Mountain as it is called frequently. Most of the area is characterized by a comparatively even surface from 1800 to 2000 ft in elevation and is drained by streams flowing into the Tennessee River. Included in the district are two quarries located 7 miles west of Cross-ville and this area is drained by tributaries of the Cumberland River. Most of the quarries are located near the 1800-ft contour which is just below the general upland surface. The surface rock over most of the district is the Rockcastle sandstone which has a thickness of about 260 ft.1 It is the topmost of the six formations of

Jan 1, 1951

Swedish mining companies are noted for their excellence in underground mining practice, and this classification certainly has to be applied to their design of crushing plants also. All these mines are highly mechanized with either rail or truck haulage, and typical examples of underground crushing plants designed for each of these haulage practices are presented here. Almost all the primary breakers are of the overhead eccentric, single- toggle jaw crusher type with units as large as 55 by 71 in. (1400 by 1800 mm) being used. In contrast to North America, where jaw crushers are almost always preceded by apron or vibrating feeders, many of the. Swedish crushers are choke fed with the dump pocket being located directly above the crusher. This practice results both from excellent knowledge of the ore characteristics and the ability of the overhead eccentric crusher to also act as a feeder. An excellent example of a crushing plant of this design is shown by the sketch of the LKAB Alliansen Crusher No. 64 at Malmberget, Sweden. Forty-six st (42 mt) trucks dump magnetite ore into a 91.6 cu yd (70 m3) dump pocket mounted over a 55 by 71 in (1400 by 1800 mm) Morgards- hammar overhead eccentric crusher using a 180 hp (132 kw) motor and belt drive. Crushed ore at 10 in. (250 mm) size drops onto an air- operated tipping chute which diverts the ore to either of two 1962 cu yd (1500 m3) pockets equipped with 3 ft 11 in. by 7 ft 11 in. (1200 by 2000 mm) Schenk vibrating feeders. Dust is drawn into a wet scrubber and exhaust air is combined with mine exhaust air. Because the crusher must be assembled underground, a 45/5 ton crane is installed over the crushing installation. A crusher above ground such as at Sacaton can easily utilize a smaller crane. Capacity of this &apos;most interesting crushing installation is 1653 st (1500 mtph) .

Jan 1, 1978

By Benjamin Gildersleeve

Uniquely colored, thin-bedded quartzite is quarried between Crossville and Crab Orchard in Cumberland County, Tenn. It is produced in all sizes up to the limits of transportation from beds usually ranging in thickness from less than Vi in. to 6 in. The stone is very resistant to wear and weathering and is marketed throughout the country for many different purposes in exterior and interior construction. The annual production exceeds 36,000 tons, valued at nearly $1,000,000. THE building stone of the Crab Orchard District is a fine-grained, thin-bedded sandstone which is so strongly cemented by silica that it may be classed as quartzite. As used in this paper the term building stone includes dimension stone, rubble, ashlar, flagstone, and rough broken stone. The Crab Orchard District is in the central portion of Cumberland County, Tenn. It is named from the town of Crab Orchard near which the stone was quarried first for industrial use. The heart of the district is an area of some 1200 acres from 1 to 3 miles east of Crossville which is 70 miles west of . Knoxville and 125 miles east of Nashville (fig. 1). At the present time, there are about 15 quarries worked by companies and individuals. Geology: The Crab Orchard District is on the Cumberland Plateau, or Cumberland Mountain as it is called frequently. Most of the area is characterized by a comparatively even surface from 1800 to 2000 ft in elevation and is drained by streams flowing into the Tennessee River. Included in the district are two quarries located 7 miles west of Cross-ville and this area is drained by tributaries of the Cumberland River. Most of the quarries are located near the 1800-ft contour which is just below the general upland surface. The surface rock over most of the district is the Rockcastle sandstone which has a thickness of about 260 ft.1 It is the topmost of the six formations of

Jan 1, 1951

By J. J. Strohl, H. J. Schwellenbach

This paper relates the results obtained by decreasing the size of feed to a rod mill screen circuit. As would be expected, added production was gained and a finer grind with no tonnage loss was made possible. THE MacIntyre mill of the National Lead Co. has four parallel sections in which magnetic and gravity separations are made. Ore from a 5000-ton bin is fed by Hardinge constant weight feeders to a 6x12-ft open-end Marcy rod mill in each section. Rod mill discharge is bucket elevated to two 4x10-ft Tyrock screens whose oversize is returned to the rod mill. Screen undersize is pumped to Crockett separators for magnetite removal, and the Crockett tailings are sized and tabled to make an ilmenite concentrate. Minus 200-mesh material, overflowed by the Crockett and Dorrco sizers is thickened, de-slimed, and concentrated by flotation.&apos; By 1948, the development of a successful slime flotation process and numerous improvements in the gravity circuit of the mill had increased the capacity of the available concentrating equipment. At the same time, improvements in the operating techniques of the dry crushing plant and improved feeding of the crusher by the mining department had appreciably increased the production rate per operating hour in that plant. Therefore, it was decided to take advantage of the added crusher capacity to produce a finer rod mill feed and in that way increase grinding capacity. At approximately the same time, finer screens were installed in the rod mill circuits to give finer grind and thus improve liberation of the magnetite and ilmenite from the gangue and from one another. Prior to the first part of 1948, a 3/4-in. limiting screen was used for sizing rod mill feed. The first reduction in crushing plant screen size was to 1/2 in. With this screen, the circulating load in the tertiary crushing circuit was too high and plant capacity dropped below a practical hourly rate. A 9/16-in.-sq opening screen, installed next, proved satisfac-

Jan 1, 1951

By H. J. Schwellenbach, J. J. Strohl

This paper relates the results obtained by decreasing the size of feed to a rod mill screen circuit. As would be expected, added production was gained and a finer grind with no tonnage loss was made possible. THE MacIntyre mill of the National Lead Co. has four parallel sections in which magnetic and gravity separations are made. Ore from a 5000-ton bin is fed by Hardinge constant weight feeders to a 6x12-ft open-end Marcy rod mill in each section. Rod mill discharge is bucket elevated to two 4x10-ft Tyrock screens whose oversize is returned to the rod mill. Screen undersize is pumped to Crockett separators for magnetite removal, and the Crockett tailings are sized and tabled to make an ilmenite concentrate. Minus 200-mesh material, overflowed by the Crockett and Dorrco sizers is thickened, de-slimed, and concentrated by flotation.&apos; By 1948, the development of a successful slime flotation process and numerous improvements in the gravity circuit of the mill had increased the capacity of the available concentrating equipment. At the same time, improvements in the operating techniques of the dry crushing plant and improved feeding of the crusher by the mining department had appreciably increased the production rate per operating hour in that plant. Therefore, it was decided to take advantage of the added crusher capacity to produce a finer rod mill feed and in that way increase grinding capacity. At approximately the same time, finer screens were installed in the rod mill circuits to give finer grind and thus improve liberation of the magnetite and ilmenite from the gangue and from one another. Prior to the first part of 1948, a 3/4-in. limiting screen was used for sizing rod mill feed. The first reduction in crushing plant screen size was to 1/2 in. With this screen, the circulating load in the tertiary crushing circuit was too high and plant capacity dropped below a practical hourly rate. A 9/16-in.-sq opening screen, installed next, proved satisfac-

Jan 1, 1951

BURKE BAKER, Philadelphia, Pa. (written discussion*).-The small briquetting plant of the American Briquet Co., at 25th Street and Washington Ave., Philadelphia, was built primarily as a demonstration plant. Its output per hour is 4 tons of 2-oz. briquets, which have been retailed in the, vicinity during the year the plant has been in operation. They have proved very acceptable for use in ranges, heaters and grates in-home, and in steam heating plants in apartment houses and hotels. They have not been sold for power purposes, although satisfactory tests have been made in. this field. Anthracite silt is used and is shipped direct from breaker or washery, the only preparation it receives being the removal f excess moisture by means of a Ruggles-Coles rotary dryer. Care is taken, however, to purchase silt containing less than 18 per cent. ash. The method is covered by U. S. Patent No. 941454, issued to Chas. E. Hite, and is known as the "emulsion process." The binder, which is the, basis of the patent, is composed. of 0.5 per cent. cornstarch or wheat flour; 1 per cent. asphaltum or hydrolene, and 6.5 per cent. water, on the weight of coal dust. It is prepared in a tank equipped with paddle agitators and heated by steam jets. The starch and water are first made into a paste by being brought to the boiling point with live steam; the melted asphaltum is then introduced and thoroughly beaten into the paste by the agitators. This rapid stirring breaks. the hot asphaltum into minute particles which are distributed through the paste, producing a smooth chemical emulsion. This emulsion, when dried, is not soluble in water. The binder is mixed with the dry coal dust in a horizontal paddle mixer, 8 per cent. binder to the weight of coal being used. The resultant plastic mass is then discharged into the press, which is of the simple roll type. Since the binder is a liquid and is not sticky or gummy until

Jan 3, 1918

By G. R. Fritterer

Investigators in the field of temperature measurement have long sought a thermoelectric couple fulfilling the following requirements: 1. It should be useful up to and including high industrial temperatures; i. e., 1000 to 1800 C. 2. Its thermoelectric variation with temperature should be linear and be maintained after heating to high temperatures for long periods of time. 3. It should be reproducible; i. e., different couples of the same elements should have similar calibration curves. 4. Its thermoelectric power should be large so as to allow the industrial use of rugged recording instruments. 5. Chemical reactions with, and physical changes within the elements of the couple should not alter its calibration. No thermocouple proposed to date exhibits simultaneously all of these characteristics, whereas the couple about to be described fulfills all requirements to a satisfactory degree. New Thermoelectric Materials A thorough survey of the literature on thermoelectricity revealed that present-day thermocouples could not meet the specifications mentioned above because their thermoelements are metallic. Metals have a marked tendency to deteriorate chemically and their melting points limit their use to low temperatures. Refractory substances, however, are usually resistant to chemical attack and are quite stable at high temperatures. Hence a survey of refractory substances having thermoelectric possibilities was made. One class of thermocouples considered was that in which carbon and a carbide of some metal or nonmetal were the thermoelements. Previous investigators neglected to study this field but certain recommendations were made by them for the use of couples in which carbon served as one element. These proposals are listed in Table 1. The couples suggested are unsatisfactory because of their low thermoelectric powers, the low melting points of their metallic elements, etc. The

Jan 1, 1933

Weston Portable Electrodynamometer The Weston Electrical Instrument Co. of Newark, N. J., believes that problems hitherto considered impossible of solution in the designing of portable electrodynamometers have been solved in its new models. The voltmeter, Model 341, is an instrument&apos; of precision adapted to use on alterating- or direct-current circuits, guaranteed to an accuracy of 0.25 per cent. full-scale value either on direct or alternating-current circuits of any frequency to 133 cycles per second and commercial frequencies even as high as 500 cycles per second with very slight error. The polyphase electrodynamometer, Model 329, is accurate to 0.5 per cent. under the same conditions.; Double ranges are furnished in all instruments of this model. All current ranges can be used for 100 per cent. overload indefinitely without introducing error in Models 310 and 329.

Jan 12, 1915

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.&apos; THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy&apos;s Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. &apos;Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If&apos; .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By R. L. Parsons, Herman Dykstra

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.&apos; THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy&apos;s Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. &apos;Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If&apos; .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By C. O. Burgess, W. D. Forgeng

The results of an investigation of the ternary system iron-chromium-silicon were reported in 1936 by the present authors.l Partly for the sake of theoretical interest, and partly because of the possible commercial importance of these alloys, the present investigation was undertaken to determine the effect of some of the commoner elements likely to occur, deliberately or otherwise, in such alloys if made on a commercial scale. The elements thus added were carbon, nickel or manganese. The alloys studied were, therefore, parts of quaternary systems. This investigation was concerned primarily with the effect of these additional elements on the alpha-iron phase and the boundary between this phase region and the alpha plus sigma two-phase region. The sigma phase is a ternary solid solution based upon the compound FeCr. The work was performed mainly by X-ray methods, but a number of microscopic examinations were also made and are reported. While isolated alloys in the composition ranges studied may have been discussed in metallurgical publications, no systematic investigation of any assistance to us was found. Of the earlier work, the investigations on the iron-chromium-carbon system and on the chromium carbides by Westgren and his coworkers2&apos;3 enabled us to identify the carbide phase. Several articles appeared after the present experimental work had been completed. Lucas and Wintrup4 determined the solubility of carbon in molten iron-chromium-silicon alloys. Tofaute and his coworkers5&apos;6 have made detailed studies of the iron-chromium-carbon system, which will be referred to later. Materials and Methods Materials.—The iron, chromium and silicon used were essentially the same as those used in the investigation of the ternary system.l The

Jan 1, 1938

By C. O. Burgess, W. D. Forgeng

The results of an investigation of the ternary system iron-chromium-silicon were reported in 1936 by the present authors.l Partly for the sake of theoretical interest, and partly because of the possible commercial importance of these alloys, the present investigation was undertaken to determine the effect of some of the commoner elements likely to occur, deliberately or otherwise, in such alloys if made on a commercial scale. The elements thus added were carbon, nickel or manganese. The alloys studied were, therefore, parts of quaternary systems. This investigation was concerned primarily with the effect of these additional elements on the alpha-iron phase and the boundary between this phase region and the alpha plus sigma two-phase region. The sigma phase is a ternary solid solution based upon the compound FeCr. The work was performed mainly by X-ray methods, but a number of microscopic examinations were also made and are reported. While isolated alloys in the composition ranges studied may have been discussed in metallurgical publications, no systematic investigation of any assistance to us was found. Of the earlier work, the investigations on the iron-chromium-carbon system and on the chromium carbides by Westgren and his coworkers2&apos;3 enabled us to identify the carbide phase. Several articles appeared after the present experimental work had been completed. Lucas and Wintrup4 determined the solubility of carbon in molten iron-chromium-silicon alloys. Tofaute and his coworkers5&apos;6 have made detailed studies of the iron-chromium-carbon system, which will be referred to later. Materials and Methods Materials.—The iron, chromium and silicon used were essentially the same as those used in the investigation of the ternary system.l The

Jan 1, 1938

By N. Christensen, B. Augland, T. H. Johansen

Samples of an Fe-Nb alloy were brought to equilibriurtr with hydrogen-methane mixtures in the temperature range from 950° to 1050°C, and subsequently analyzed on their carbon contents. The solubility pvoduct L = [%Nb] [%C] may be represented by the equation Approximate solubilities indirectly assessed through hardness measurements have been included from a previous report. These data are shown to be in a fair agreement with the present solubility measurements. IN an investigation based on hardness measurements by de Kazinczy, Ms, and pachleitnerl the molal heat of solution of NbC was estimated to 11.5 kcal per mole. This value was considered rather small, and an investigation using a similar technique was carried out. The results indicated a heat of solution about 35 kcal per mole.2 At this stage it was decided to determine the solubility under conditions of true equilibrium . During the course of this work a similar investigation was published by Smith. 3 His heat of solution, 41.6 kcal per mole, is not very different from the value resulting from the present work (42.5 kcal per mole). Our solubility product, on the other hand, is at considerable variance with that reported by Smith. Possible reasons for these differences are discussed below. Mori, Tokizane, and saheki 7 have studied the behavior of niobium in commercial steels, with special attention to the formation of niobium carbide, nitride, and sulfide. Assuming a carbide composition Nbco.87 based on X-ray diffraction and chemical analysis of residues extracted from Fe-Nb-C-S alloys, the molal heat of solution of niobium carbide was estimated to 35.2 kcal per mole. MATERIALS AND EQUIPMENT The chemical analysis of the materials is given in Table I. Electrolytic iron* was used in the preparation of

Jan 1, 1968

OPEN-HEARTH refractories are not merely an accessory to the furnace. They themselves ore the furnace, to all intents and purposes. The steel work of the main structure is merely a frame which helps to support the refractories; and the regenerators, a necessary part of the furnace system, consist almost entirely of refractories with very little supporting structure. Not only do refractories constitute the essential part of the furnace, but they also carry the liquid steel all the way to the point where it begins to solidify. On leaving the furnace the liquid passes through a refractory runner into a refractory-lined ladle, then through a refractory nozzle closed by a refractory stopper on the end of a refractory- protected rod. The liquid is sometimes sent through an additional refractory-lined tun-dish, a supplementary ladle, or a refractory runner for bottom pouring, until it finally enters the iron mold in which it solidifies. Even in the mold, refractory materials are sometimes used to provide a non-conducting "hot top." These materials, from ladle to hot top inclusive, are often referred to as the "pouring-pit refractories." CAUSES OF FAILURE Compared with the equipment used in most industrial processes the open-hearth furnace has a relatively short life. The most important quality of an open-hearth refractory, therefore, is its rate of failure. The discussion here of the individual refractory materials will therefore keep uppermost the question "Why, how, and where does it fail?" The principal causes of failure of open-hearth refractories are, in their order of importance: 1. Reaction with iron oxides. 2. Reaction with slag. 3. Flow and failure under load. 4. Melting. 5. Spallimg. 6. Mechanical breakage. Reaction with Iron Oxides and Slag. This is by far the most important cause of failure. Liquid iron oxide comes very near to being the

Jan 1, 1944