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By K. C. Ko, D. A. Pifer

The theory of probability with respect to the failure of structures is discussed. It is shown that the probability of safety, probability of failure, and factor of safety are directly related to each other and that as standard deviation approaches zero, the probability curves approach a unit step function which can be interpreted as the conventional factor of safety. The factor of safety is numerically the ratio of the load to the strength of the material at a particular point or plane in an engineering structure. Mathematically, it can be illustrated as a unit step function undefined at the point where the factor of safety is one (Fig. 1). The uncertainty of variation of soil and rock strengths require factors of safety much higher than those used in other engineering structures. The factors of safety used are generally determined from past experiences with similar structures. However, the factors thus determined do not have any theoretical meaning or do not indicate any relationship to actual safety.' It seems, therefore, logical to develop a system with a sound theoretical basis to obtain a more suitable factor of safety for structures. An application of elementary theory of probability indicates that it is possible to relate this number to theoretical and practical engineering facts.

Jan 1, 1971

By Deepak Vidyarthi

This paper deals with the significance of Explosive Energy in the optimization of blast design parameters, and the benefits emerging out of it. It is based on the original work done by the author in developing and successfully implementing a site-specific software package on ‘Blast Design Optimization’ at Kudremukh Iron Ore Mine in India with a production level of 22.5 million tonnes of crude ore and off-take of Explosives of approximately 5500 tonnes per annum. The software package has yielded tangible results in effecting reduction in Explosive Consumption, substantial savings in the Cost of Explosive, besides Environmental Improvements by way of attenuation of Blast Induced Ground Vibrations as well as Air-Blasts. By carrying out regular ‘Regression Analysis’, and determination of the Rock Constants, it has been possible to further develop software packages as well as prediction curves for prediction of Peak Particle Velocity, Safe Charge of Explosive, Air-Blasts etc. A model has also been developed for the prediction of ‘Fly Rock’ although at KIOCL, fly rock does not pose any problem.

Jan 1, 2006

By Edward H. Jr. Boyle, Paul R. Thomas

Introduction It is estimated that nearly 40% of all the gold ever mined in free world countries has been produced by South African operations. There is concern that this immense productive capacity will soon decline. Such a decline could reduce world gold supply and lessen the ability of market economy countries (MEC) to exert the major influence upon the world gold market. This paper addresses three general issues concerning South African gold production: • How much gold remains to be recovered from the demonstrated resources of the 44 evaluated South African mines; • How long can production at current levels continue; and • What will be its cost. Table 1 provides production data on the world's 10 largest producers for the years 1971, 1981, and 1983. As shown, South African gold production declined significantly from 1971 through 1981. As of 1981, annual South African gold production had dropped by more than 311 t (10 million oz) in 10 years. Despite this, its mines still produced 656 t (21 million oz) that year, about half the world total. From 1981 through 1983, this trend was reversed. Annual South African gold production increased by more than 21.8 t (700,000 oz). The trend reversal was also evident in the US, Canada, and Australia. This illustrates the general, inverse relationship between gold price and gold production. In South Africa especially, as gold prices increased substantially during the 1970s, the average grade of ore mined (pay limit) was lowered as new, lower grade areas and materials were exploited. Gold production declined in volume. But gold revenues increased, and the lives of the operations were extended. The 1981-83 period was one of declining (US dollar-based, average annual) gold prices that resulted in increasing South African production as average ore grades were raised. South Africa currently accounts for 50% of world production (Fig. 1). Figure 2 illustrates South Africa's contribution to total MEC production in 1971 and 1983. Although South Africa's relative share of production has declined, it still represents the single most important source of new gold supply. In 1983, it supplied more than 65% of total MEC production. South Africa currently produces more than twice as much gold as the Soviet Union (ranked second in world production), and 11 times more gold than the US (ranked fourth in world production). Barring major discoveries, South African gold production is expected to peak in 1987 and begin to decline again throughout the 1990s. The rate of decline is ex-

Jan 11, 1984

By A. Koski

A pond rehabilitation and environmental education project were proposed by Cleveland-Cliffs Michigan Operations (CCMO) and approved by the Michigan Department of Environmental Quality (MDEQ) and the United States Environmental Protection Agency (USEPA) as partial fulfillment of conditions for a stream mitigation permit. The goals of the project were the rehabilitation of a pond on a tributary of a local trout stream, enhancement of public access and appreciation, and the initiation of a site-based environmental educational curriculum. Cleveland-Cliffs undertook a suite of actions to rehabilitate a pond created by a previous mining operation in 1912 and make accessible to local schools the aquatic and riparian ecosystems. Cleveland-Cliffs partnered with the local governmental unit and two local school districts. The rehabilitated pond and riparian zone provide an accessible natural area that local residents can use for such activities as hiking, biking, walking, fishing and nature study. Vegetative enhancement includes the planting of native shrubs, wildflowers and showy herbaceous plants in the pond, on the riparian fringe and the surrounding area. An interpretive trail was developed around the pond with signs created by a local master watercolor artist. Local schools built and installed picnic tables, benches and a kiosk. Cleveland-Cliffs created pond lesson plans tied to the Michigan Curriculum Framework, developed inexpensive teaching kits and hosted a workshop for teachers from nine local schools. Classes regularly utilize the pond during the school year conducting environmental studies. Nesting boxes, wildflower gardens, bat houses, frog deformity surveys and water quality studies are a few of the activities that classes have conducted at the pond.

Jan 1, 2007

By M. Moys

The use of temperature measurements for unusual applications in the analysis and control of column flotation and milling is discussed. This is followed by a review of some of the authors current research in the application of the discrete element method to the modelling of particulate processes, specifically milling, fluidized beds and chute flow.

Jan 1, 2005

By A. Ersoy, M. D. Waller

The principal factors which require consideration in predicting drilling rates are the bit-type, the bit operating parameters and the characteristics of the penetrated rock. A single index is not a sufficient basis for predicting performance. A variety of rock types were drilled in the laboratory with polycrystalline diamond compact (PDC) and impregnated diamond core bits using a fully instrumented drilling rig at different rotational speeds and with a range of weights on the bit. Quantitative determinations of a wide range of textural, mechanical and intact rock properties were also made. Multi-variable linear regression analysis was then used to develop predictive models of rates of penetration from the operating and rock property data. The models have been verified by statistical tests. The analysis indicated that the models for the pin and hybrid PDC bits have potential for practical application. However, although the model for the impregnated diamond bit appears to be reasonable from a purely statistical point of view, it may not be satisfactory for drilling uses as it is based on two measures of rock hardness alone. The application of multiple regression analysis to PDC drilling performance is novel and the technique shows promise for the prediction of rock drillability with PDC bits. The ability of the technique to provide a mathematical characterisation of the performance of new drill bits in specific rocks may prove to be of value to drill manufacturers and users

Aug 1, 1995

By Harlowe Hardinge

[Crushing Tests by Pressure and Impact (T.P. 1895, by F. C. BOND,, Min. Tech. Jan. 1946). Discussion by H. HARDINGE and the author 1 Pumping Sands, Slurries and Slimes and Installation and Performance of Sand Pumps (T.P. 2013, by W. B. STEPHENSON, Min. Tech., May 1946 and T.P. 1978, by C. G. SOUTHMAYD, Min. Tech., March 1946). Discussion by OSCAR LEE, G. J. HOLT, L. D. ANDERSON, and the author 2 Rapid Polarographic Method for Determination of Copper, Zinc and Lead in Flotation Tailings (T.P. 2010, by G. A. CROWE and W. T. BISHOP, Min. Tech., March 1946). Discussion by E. H. ROSE and the authors 4 Ball Wear and Functioning of the Ball Load in a Fine-grinding Ball Mill (T.P. 1984, by W. I. GARMS and J. L. STEVENS, Min. Tech., March 1946). Discussion by J. F. MYERS, E. W. DAVIS, F. M. JARDINE, H. HARDINGE, F. C. BOND and the authors 5 Correlation between Mineral Behavior in Cataphoresis and Flotation (T.P. 2005, by A. M. GAUDIN and S. C. SuN, Min. Tech., May 1946). Discussion by 0. C. RALSTON, G. L. SIMARD and D. J. SALLEY 7 Accident Experience in Milling (T.P. 1981, by J. F. MYERS and S. E. SHARP, Min. Tech., May 1946). Discussion by C. E. MCKNIGHT, C. H. BENEDICT, T. S. WILSON and S. POWER WARREN9 Mill Design for Labor Economy (T.P. 1997, by NORMAN WEISS, Min. Tech., May 1946). Discussion by R. S. HANDY and the author13] Crushing Tests by Pressure and Impact (0.C. Ralston presiding) HARLOWE HARDINGE.*-Has the impact method described in the paper been used to compare the resistance to reduction in size of various materials with actual operation results of mills in the field? Is this impact method a better index of the true resistance to grinding under actual field conditions than other methods the author has reported in the TRANSACTIONS? F. C. BOND (author's reply).-The impact crushing device was designed to measure relative resistance to crushing, or what may be called the crushability, and is not used for comparing the resistance to grinding, or grindability. The correlation between crushability and grindability of different materials is not at all close, since fractures, zones of weakness, and structural features of rock have a much greater effect upon the crushability than upon the grindability. We still depend upon our standard grindability tests for measuring resistance to grinding, and use the impact crushing tests only in relation to crusher installations. The impact crushing device has several advantages over the measurement of crushing strength in pounds per square inch as an index of crushing resistance.

Jan 1, 1946

By M. Q. W. Jones

This paper summarizes important features of a compilation of thermal properties of stratified rocks from Witwatersrand gold mining areas. The database consists of more than 1000 thermal conductivity measurements, more than 700 density measurements, and nearly 100 heat capacity measurements. Most important rock types and stratigraphic units are well represented. Heat capacity does not differ significantly from one rock type to another, and density is relatively uniform although particular rock types are characterized by distinct average values. Different rock types also have distinct thermal conductivities, but this parameter varies by a factor of four to five. Primary factors controlling the thermal properties are mineral composition, degree of metamorphism, and porosity. In addition, the temperature dependence of thermal conductivity and heat capacity of quartzite may significantly decrease the thermal diffusivity of this rock at deep mining levels.

Jan 1, 2003

By F. Peer

This Technical Note was presented as a poster at the Western Cape Mineral Processing Symposium held in August 2001 The cleaning of fine coal (-1000 µm) in today?s coal preparation plants is an economically important factor. Coals with high ash contents are, in general, commercially undesirable. Current well-known techniques for treating fine coal include froth flotation and spirals. The primary critical factor with regards to spirals is the efficiency of the process whereas that of flotation, is the cost of there agents used. Research into enhanced gravity separation techniques has resulted in several commercially available enhanced gravity separators. This project was based on a preliminary investigation into the feasibility of one such separator, to effectively treat fine (-500 µm) coal. Experimental variables included particle size and speed of rotation of the said instrument. The performance of the separator was compared to the results obtained from liquid density separations done for the two coal fractions evaluated. From the results obtained in this preliminary study it appears that the piece of equipment investigated does not measure up to expectations. Recommendations for further investigation include the evaluation of the instrument on other South African coals to obtain conclusive results.

Jan 1, 2002

By S. C. Richardson

The electrowinning (EW) circuit involves using DC current in the electro-deposition of metal ions dissolved in an electrolyte solution. This paper reviews a method to generate an electrical model of an EW circuit and the resulting DC current flow and voltage distribution within the circuit. Topics include: calculations of electrolyte conductivity and the equivalent electrical resistance of the electrolyte within the electrolyte pipelines connected to the EW circuit; the breakdown and classification of the EW cell voltage into thermodynamic and ohmic potentials; methods to calculate current flow and voltage distribution throughout the EW circuit; and the development of an interactive visual computer model to simulate an actual EW circuit. Stray current can pose an electrical shock hazard to employees in electrolytic tankhouses. Increased awareness and understanding of the voltage distribution and potential stray current in an EW circuit can help mitigate the risk of tankhouse workers becoming exposed to electrical shock hazards. INTRODUCTION Copper electrowinning tankhouses include rectifiers that deliver large amount of DC current to a series of electrolytic cells consisting of electrolyte solution and electrode pairs. The design also includes metallic conductors in the circuit which include the rectifier’s positive and negative busbar, inter-cell busbar, and the anode and cathode frames. The electrolyte acts as an electrical conductor that transfers current via ions between the anodic and cathodic electrodes within the cell. Electrolyte, as a conductor, is also capable of conducting DC current outside the main EW circuit through the connected electrolyte feed and return pipe systems. DC current that follows a path other than the intended path through the series of electrolytic cells is referred to as “stray current”. Developing an electrical model enhances understanding of voltage distribution and current flow in an EW circuit. This paper discusses the derivation of the various representative components of the model as well as the output from the model. An interactive visual computer simulation incorporates the model output in order to aid in the understanding of voltage distribution and current flow throughout the EW circuit.

Jan 1, 2019

The recovery by flotation of some complex uranium minerals such as brannerite and davidite is described. Anionic reagents used for flotation of iron and titanium oxides' are suitable. If care is taken, to emulsify the reagents the slime fractions may be satisfactorilytreated.INTRODUCTIONUranium ores are usually treated by direct leaching with acid or alkali according to the nature of the gangue materials. Concentration of the uranium minerals prior to leaching is not commonly practised because of the earthy nature of most uranium minerals and the difficult mineral dressing problem they pose. Some of the harder complex oxides such as davidite and brannerite are amenable to flotation. This is fortunate since they usually require an expensive, strong acid treat~ent to dissolve the uranium. Flotation tests were commenced in 1949 by officers of the South Australian Department of Mines stationed at Adelaide, first in the School of Mines, then in the University of Adelaide and finally in Departmental mineral dressing laboratories at Thebarton. Separation of daviditefrom Radium Hill and Mount Victoria ores, brannerite from Crocker's Well ore, and secondary uranium minerals from Myponga ore was attempted.The development of the flotation reagents to separate the oxides from silica and the silicates is first described, then some of the results obtained are presented as tables.DEVELOPMENT OF FLOTATION REAGENTSThe davidite at Radium Hill is associated with iron and titanium oxides, qu;a,rtz and biotite as replacement deposits in shears. The davidite, rutile,' ilmenite and hematite usually occur in segregations from nut size to masses of several pounds. They are associated as a complexity of...

Jan 1, 1955

By Ihsan Berk Tulu

In the Analysis of Retreat Mining Pillar Stability (ARMPS) program, the magnitude of the abutment loading adjacent to a gob area is calculated using an ?abutment angle? concept. The extent of the abutment loading is determined solely as a function of depth from an empirically derived equation. In the recommended calibration method for LaModel, it was believed that the empirical equations for calculating the magnitude and extent of the abutment load, as used in ARMPS, were the best available methods for determining these critical overburden loading values. Therefore, similar calculations were implemented in the LaModel calibration method. However, the latest in situ stress measurements of abutment loading performed in the United States and Australia have shown that there can be significant deviations in the measured abutment magnitude and extent as compared to the predicted values from the empirical formulas used in ARMPS and LaModel. It seems reasonable that the overburden geology, depth, extraction panel width, and mining height should have a significant effect on the extent and magnitude of the abutment load. However, the current empirical formulas do not incorporate many of these significant parameters into determining the abutment load on the pillars. In this paper, stress measurements from US and Australian mines were back-analyzed by using analytical and numerical methods to investigate the measured abutment extent and loading. Ultimately, it was determined that the original empirical abutment extent formula in conjunction with the original ALPS square-decay stress distribution function was supported by the case histories in this paper. Also, for depths less than 900 ft, the average 21° abutment angle was supported by the case histories; however, at depths greater than 900 ft, the abutment angle was found to be significantly less than 21° and should be calculated with a new proposed equation.

Jan 1, 2012

The geological features of the destructive plate margins of the southwest Pacific favour the formation of porphyry type deposits. The major controlling factor favouring the formation of gold-rich deposits of this type is a dense crust. This results in shallow intrusion of large magma bodies beneath andesite stratovolcanoes. Where the intrusives have near vertical sides, the comparatively low temperature of transfer of volatiles from the solidifying melt favours the partitioning of gold into bubbles of volatiles. They reduce the viscosity and density of the melt, resulting in the upward movement of a mineralised melt. With the drop of pressure with upward movement the bubbles separate into a two phase mixture, triggering freezing of the mineralised melt and the formation of a gold mineralised stockwork.

Jan 1, 1995

The opening session of the Institute was held at the rooms of the American Society of Civil Engineers, No. 4 East 23d Street, VicePresident R. W. Raymond in the chair. After a short introductory address by the chairman, the following names were presented by the Council for election as members and associates of the Institute. They were unanimously elected : MEMBERS. Abbott, James W.,.....Lake City, Col. Abbott, J. J., Jr.,...... Lake City, Col. Bartlett, J. C.,.....Cambridge, Mass. Billings, G. H.,.....Boston, Mass. Blake, Frank C.,.....Lafayette College, Easton, Pa. Dewey, Fred. P.,.....Lafayette College, Easton, Pa. Douglass, Samuel T.,. .. . Ann Arbor, Mich. Emmons, 9. F.,.....New York City. Engle, George U.,.....Philadelphia. Harrington, Dr. Bernard J.,. .. Montreal, Canada. Hayden, Wm. B.,.....Columbus, O. Hill, Leslie C.,.....Capelton, Quebec, Canada. Land, W. J.,......Atlanta, Ga. May, Wm. A.,.....Scranton, Pa. Mills, James E.,.....St. Louis, Mo. Moore, Charles W.,.... Montezuma, Ind. Page, William Byrd,.... Lexington, Ky. Putnam, Douglas, Jr.,.... Ashland, Ky. Richards, Henry,.....Dover, N. J. Boberts, Percival, Jr.,. .. . Philadelphia. Sackett, S. G.,......Brooklyn, N. Y. Schley, Wm. S.,.....Atlanta, Ga. Setz, Gustav,......Mine La Motte, Mo. Talhutt, John H.,.....Lexington, Ky. Torrey, Herbert G.,.... U. S. Assay Office, New York City. Wernlitz, Fred. W.,..., Cartersville, Bartow Co., Ga. Wiestling, Geo. B.,.....Mont Alto, Franklin Go., Pa.

By Mark I. Copeland

This study was conducted by the Bureau of Mines to determine the effect of steel reheating practices in burning natural gas on the amount of silicon required to prevent the formation of copper on steels containing up to 1 wt-pct Cu. Formation of copper, which causes surface hot shortness, was readily prevented by as little as 0.3 wt-pct Si and by 2 vol-pct excess oxygen in the furnace atmosphere when reheating steels containing up to 0.8 wt-pct Cu. Up to 0.8 wt-pct Si content and careful control of reheating conditions were necessary for steels containing 1 wt-pct Cu. Best conditions for these steels were reheating to 2,200° F (1,205° C) in burning gases containing 2 vol-pct excess oxygen, and then to higher temperatures in gases of 6 vol-pct excess oxygen. Slag and mold wash were not detrimental on steels reheated for 8 hr by a soaking-pit-type furnace schedule, but they were problematical on steels heated for 2 hr by a pusher-type furnace schedule. The effect of silicon contents on scaling rates also was determined.

Jan 1, 1974

By M Furche, U Noell, C Grissemann, J A. Meima, T Graupner, A Romero-Baena

The mining residues at the abandoned copper mine site Pe±a de Hierro, located at the headwaters of the Rio Tinto, contribute substantially to the pollution of the river with high loads of Fe, As, Pb, Zn and Cu. The pH of the outflow ranges from 0.5 to 2.4 in the dry and wet season, respectively. One heap composed of alternating layers, which were deposited parallel to the slope, was investigated in detail. Unsorted blocky to fine materials including gossan material, pyritic volcanics, ashes from pyrite combustion and slate were observed here. The top of the heap has a gentle slope and a hill contouring channel-rip morphology. The initially rugged surface was smoothed by heavy rainfalls filling up the pores of the blocky material with fines. These fines are capable of storing the water for a prolonged time, providing an extended reaction time close to surface in a dry climate at extremely low pH conditions (one to four). All minerals, pyrite, mica, barite and even quartz (probably due to F released from dissolved mica) have been digested and silica gel precipitates have formed a stable and quasi impermeable 100 ¦m layer with very low porosity (<5 area per cent, estimated using scanning electron microscopy (SEM) imaging). The silica layer itself is covered by Fe-oxy-hydroxide (ie FeOOH) coating (10 ¦m) and seals a 1 - 5 mm thick stable hardpan. This hardpan covers the channels and part of the rips almost entirely, guiding the rainwater subhorizontally towards slopes and sinkholes. By geoelectrical measurements, a 3D-resistivity model of the internal structures and the bedrock relief underlying the heap was generated. Internal structures relate to lithological changes in a number of layers. Zones of low resistivity may be attributed to washed-in fines within the mega pore system, whilst zones of high resistivity close to the surface probably reflect the advanced stage of drying beneath aging hardpans. The water movement at the surface was investigated by an artificial precipitation experiment with monitoring of the subsequent changes in resistivities.

Jan 1, 2008

By Robert J. F. Goodfellow, William A. T. Meakin, Kevin Clarke, Eric Cole

INTRODUCTION New York City Water Supply—Background and History Since the 1840s New York City has been developing the largest, and perhaps, the best urban water supply and distribution system in the world in terms of quality and reliability. One of the engineering marvels of the modern world, the New York City water supply and distribution system serves a population of almost nine million, including residents in nearby Westchester, Putnam, Ulster, and Orange Counties of New York State. The average daily supplies presently are running at almost 60 m3/sec(about 1,350 million gallons per day). The watershed for the New York City water supply system, under the jurisdiction of the New York City Department of Environmental Protection (NYCDEP), consists of19 reservoirs and three controlled lakes, and covers an area of approximately5,000 square kilometers (about 2,000 square miles) north of New York City. The watershed total available storage capacity is about two billion cubic meters (560 billion gallons) and is divided into three reservoir systems: the Catskill and Delaware watersheds located West of the Hudson River; and the Croton watershed, located east of the Hudson River, see Figure 1. The first element of the system, the Croton Aqueduct, started operations in 1842.Through several updates and expansions, the present-day Croton system was in place by 1911, providing a potential maximum supply of about 15 m3/s (about 340 mgd). The system includes ten reservoirs and three controlled lakes. In the late 1800s, with the tremendous growth of the City, New York City water engineers began to look for additional sources. Between 1907 and 1929, the City acquired water rights and constructed a new 148 km (92 miles) Catskill aqueduct to convey water from the Ashokan Reservoir to the City. The Catskill system also included the construction of the Kensico and Hillview Reservoirs just north of the City,

Jan 1, 2005

By K. A. Lewandowski

Leach heaps are plagued with problems due to fine material migrating downwards, clogging the spaces between the coarser ore particles, resulting in decreased metal recovery rates. The use of a binder in agglomeration would allow the fine material to be immobilized, increasing the availability for the solution to come in contact with all the ore. As much as 1.64*1012 BTU per year would be able to be saved if a 25% increase in copper recovery was experienced, assuming that 70% of heap leaching units converted to using agglomeration technology. This is equivalent to approximately 18% of the energy currently being used in leaching heaps.

Jan 1, 2008

By M. Leroux, S. R. Rao, J. A. Finch

"Poor Pb-Zn selectivity during Pb flotation in laboratory tests on a Mississippi Valley-type Pb-Zn ore was traced to apH effect. In the pH range, 9.5 to 11.0 sphalerite floated readily without copper activation. Compared to sphalerite flotation with copper activation this procedure gave equivalent selectivity but reduced flotation rate.Possible mechanisms of this sphalerite flotation without copper activation are discussed. Activation by Fe(OH)2 is suggested, the Fe- + ions being derived from superficial oxidation of pyrite in the ore. IntroductionGalena and sphalerite commonly occur together. A typical procedure, using xanthate collectors, is to float the galena first, at pH - 8, followed by flotation of sphalerite after activation with copper (II) sulphate at pH - 10 (to depress pyrite).Flotation tests following this procedure in an undergraduate laboratory course with a Pb-Zn ore from Polaris failed to achieve consistent selective flotation of galena. Occasionally a considerable amount of sphalerite, even though unactivated with CUSO4, floated. This was traced to accidentally high pH. A systematic study was carried out which revealed that sphalerite floated readily in the pH range 9.5 to 11.0 without activation by CuSO4 This paper describes the results of the study and discusses a possible mechanism of this flotation of sphalerite."

Jan 1, 1987

By O. E. Palasvirta

Several drum-type, low-intensity dry magnetic separators have recently been described 1,2,3,4 all of which share at least two generic similarities. The magnet consists of a multiplicity of poles of alternating polarity and, the speed of the drum shell, relatiw to the magnet, is such that the magnetics are agitated through rotation of the magnetic particles around their individual axes. The speed of the drum relative to the magnet (differential speed) determines the frequency of the field reversals. For effective agitation this frequency generally has to be above a specific value, which varies according to the mean particle size of the magnetics. With separators of small diameter, say less than 11/2 ft., a sufficient differential speed for treatment of fine magnetite can be attained only by rotating both the magnet and the drum separately; separators of large diameter may attain sufficiently high differential speeds with stationary magnets. Separators of large diameter thus have the advantage of simplicity of design. The capacity of a separator of this type is directly proportional to the speed of the shell. As the centrifugal force opposing the magnetic force increases at a slower rate than the peripheral speed of the shell when drum diameter is increased, large drums can be operated with higher peripheral speeds. Thus they have a higher capacity than smaller drums. Separation is also a statistical phenomenon, i.e. the grade of concentrate improves as the number of agitations or rotations of the magnetic particles per separation increases. As separators of large diameter have space for a large number of magnets they are best suited for production of optimum grade concentrate. The statements above are general clues For separator design. In the following an expression IS derived showing a more exact relationship between the pertinent separator variables. As both magnetic attraction and centrifugal forces are directly proportional to the volume of the affected bodies, complications in mathematical analysis, arising from variable particle size, are avoided by considering the force per unit volume of affected material. For the magnetic force per unit volume Runolinna (3) gives the following equation: V " 1 + N(ur, - 1) uo dr (1) where ur and uo stand for the relative permeability and the permeability of vacuum, respectively, N is the demagnetization factor, B the intensity of the magnetic field, and r the distance from the face of the magnetic pole. The permeability of a specific magnetite ore can generally be considered as a constant. For ground, liberated material N can also be treated as a constant, and the first simplification can be made by writing ur-1 1=k1. 1 + N(ur - 1) uD k1. Fig. 1 shows the field intensity curves for two U-magnets of different size, but of roughly similar geometry of cross-section as plotted against the distance from the plane of the pole faces. The curves

Jan 1, 1961