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Coal Division Industrial Minerals Division Minerals Beneficiation Division Mining, Geology and Geophysics Division Established as a Society February 26, 1957 OFFICERS AND COMMITTEES J W Woomer, President A B Cummins, President-elect S D Michaelson, Past President C E Lawall, Eastern Regional Vice-President D W Scott, Central Regional Vice-President 3 D Forrester, Western Regional Vice-President R B Ladoo, Treasurer John Cameron Fox, Secretary

Jan 1, 1959

By W. A. Krivsky, R. Schuhmann

Jan 1, 1962

By R. G. Turner, M. G. Hubbard, A. E. Dukler

Gas phase hydrocarbons produced from underground reservoirs will, in many instances, have liquid phase material associated with them, the presence of which can affect the flowing characteristics of the well. Liquids can come from condensation of hydrocarbon gas (condensate) or from interstitial water in the reservoir matrix. In either case, the higher density liquid phase, being essentially discontinuous, must be transported to the surface by the gas. In the event the gas phase does not provide sufficient transport energy to lift the liquids out of the well, the liquids will accumulate in the wellbore. The accumulation of the liquid will impose an additional back pressure on the formation that can significantly affect the production capacity of the well. In low pressure wells the liquid may completely kill the well; and in the higher pressure wells there can occur a variable degree of slugging or churning of the liquids, which can affect calculations used in routine well tests. Specifically, the calculated bottom-hole pressures used in multirate backpressure tests will be erroneous if the well is not removing liquids on a continuous basis, and gas:liquid ratios observed during such a test may not be correct. Several authors1,3,8,14 have suggested methods to determine if the flow rate of a well is sufficient to remove liquid phase material. Vitter14 and Duggan' proposed that wellhead velocities observed in the field would be adequate for keeping wells unloaded. Jones8 and Dukler3 presented analytical treatments resulting in equations for calculating, from physical properties, the minimum necessary flow rate. An analysis of these studies indicates the existence of two proposed physical models for the removal of gas well liquids: (1) liquid film movement along the walls of the pipe and (2) liquid droplets entrained in the high velocity gas core. Although there probably is a continuous exchange of liquid between the gas core and the film, they will be treated separately for the purposes of this study. The development and comparison of these separate models with experimental data will permit the determination of which, if either, is the controlling mechanism for the removal of liquids from gas wells. The Continuous Film Model Liquid phase accumulation on the walls of a conduit during two-phase gas/liquid flow is inevitable due to the impingement of entrained liquid drops and the condensation of vapors. The movement of the liquid on the wall is therefore of interest in the analysis of liquid removal from gas wells. If the annular liquid film must be moved upward along the walls in order to keep a gas well from loading up, then the minimum gas flow rate necessary to accomplish this is of primary interest. The analysis technique used follows Dukler2 and Hewitt5 and involves describing the profile of the velocity of a liquid film moving upward on the inside of a tube. The minimum rate of gas flow required to move the film upward is then calculated.

Jan 1, 1970

MR. Woo's succinct description of the mining and smelting of silver-lead in Mongolia, with the roasting-and-reduction process and cupellation, has much interest as a picture of methods that not only may have been in use, as he suggests, a thousand years ago, long before the existence of mining schools or chemical laboratories, but probably vary little, if at all, from the practice of prehistoric times, when King Priam's handsome silver vases, cups and bowls were formed. For it is highly improbable that such large objects were made from comparatively rare native silver, and the metal must have been smelted from ore, and most likely in great part from galena,, with cupellation of the lead. Dr. W. A. P. Martin, in his excellent book on the Lore of Cathay, points out that Chinese alchemy is over 2000 years old, antedating the European by at least six centuries; and he infers that the Chinese skill in metallurgy and many branches of practical chemistry owes its origin to " those early devotees of the experimental philosophy who passed their lives among the fumes of the alembic." Those alchemists, however, may have more likely derived some of their leading ideas from the mys terious, and at that time wholly unexplainable results observed in already very ancient metallurgical processes; in which, for example, certain stones were transmuted, as it were, into metals widely divergent in character from their ores, and even silver and gold were obtained from the most unlikely-looking mate rials. It is therefore, in any case, not improbable that the Chinese may have preceded western nations in the discovery of metallurgical methods. At all events, it is now evident that the Japanese acquired these arts from China, the former source of all their higher civilization. My own observation of old-fashioned silver-smelt ing at Hosokura, on the main island of Japan, and about 220

Jan 1, 1903

By L. W. Berger, and R. I. Jaffee, D. N. Williams

The effects of hydrogen on the properties of binary Ti-A1 alloys containing 2.5, 5, and 7 pct aluminum and ternary alloys of the same compositions with added interstitial elements oxygen, nihrogen, and carbon were stzdied. Aluminum increases the apparent hydrogen solubility of the a-phase, resulting in a marked increase in resistance to impact embrittlement. In the Ti-5Al and Ti-7Al alloys, for example, the addition of 180 and 305 ppm hydrogen, respectively, did not cause embrittlement, while unalloyed titanium was embrittled by as little as 75 ppm. The role of aluminum in increasing hydrogen solubility of the a-phase probably accounts for the excellent hydrogen tolerance of a-ß alloys containing considerable amounts of aluminum. There is some evidence that aluminum retards the rate of hydride precipitation. If so, these alloys may be susceptible to slow-strain embrittlement. UNALLOYED a-titanium is extremely sensitive to small amounts of added hydrogen in that there is a marked decrease in notch properties. For example, as little as 100 ppm hydrogen is sufficient to lower the room-temperature notch-impact strength from over 100 to less than 20 in.-lb.' This loss of impact Strength has been associated with the Presence of hydride phase in the microstructure. Hydrogen in the amounts encountered in commercial practice

Jan 1, 1959

By L. W. Berger, R. I. Jaffee, D. N. Williams

The effects of hydrogen on the properties of binary Ti-A1 alloys containing 2.5, 5, and 7 pct aluminum and ternary alloys of the same compositions with added interstitial elements oxygen, nihrogen, and carbon were studied. Aluminum increases the apparent hydrogen solubility of the a-phase, resulting in a marked increase in resistance to impact embrittlement. In the Ti-5Al and Ti-7Al alloys, for example, the addition of 180 and 305 ppm hydrogen, respectively, did not cause embrittlement, while unalloyed titanium was embrittled by as little as 75 ppm. The role of aluminum in increasing hydrogen solubility of the a-phase probably accounts for the excellent hydrogen tolerance of a-ß alloys containing considerable amounts of aluminum. There is some evidence that aluminum retards the rate of hydride precipitation. If so, these alloys may be susceptible to slow-strain embrittlement. UNALLOYED a-titanium is extremely sensitive to small amounts of added hydrogen in that there is a marked decrease in notch properties. For example, as little as 100 ppm hydrogen is sufficient to lower the room-temperature notch-impact strength from over 100 to less than 20 in.-lb.' This loss of impact Strength has been associated with the Presence of hydride phase in the microstructure. Hydrogen in the amounts encountered in commercial practice

Jan 1, 1959

Jan 1, 1970

By Frederick Rhines

PURE copper that has been allowed to oxidize at an elevated tempera-ture in the air is found to be covered with two distinguishable layers of oxide scale. The outer of these, which is very thin, is composed of cupric oxide, while the inner layer, comprising the bulk of the scale, is made up chiefly of cuprous oxide (Fig. 1a). If a small quantity of an alloying element, such as silicon, is present in the copper, silica particles are found disseminated through the cuprous oxide, deposited most abundantly near the metal surface, and, in addition, silica particles occur to a limited depth within the copper itself (Fig. 1b). It is this inner layer, composed of oxide particles precipitated in a matrix of metallic copper that is known as the "subscale" or the zone of internal oxidation. Under a low oxygen pressure it is possible to produce the subscale without the formation of external layers of copper oxides, thus leaving the metal surface bright and apparently clean while oxidation has occurred, in fact, to a considerable depth within the metal (Fig. 2). Although little is yet known in a detailed way of the mechanism of internal oxidation, the general nature of the process is evident. By virtue of the considerable solubility of oxygen in copper,1 it is possible to bring the alloying element in contact with oxygen within the metallic solid solution. If the oxide of the alloying element is more stable than cuprous oxide, the foreign oxide may form and, since most oxides are relatively insoluble in copper, it will not long remain in solution, but will separate as a precipitate. As the metallic solute is exhausted in the zone of precipitation, oxygen that is constantly being supplied at the surface diffuses farther into the alloy and thus produces an ever-thickening shell of subscale. The distribution of the reacting elements in the subscale and adjoining zones must be somewhat as indicated in Fig. 3. The conditions requisite to internal oxidation to be anticipated are thus: (1) a solubility of oxygen in the alloy, (2) the ability of oxygen to diffuse at an appreciable rate into the alloy, (3) the possibility of the

Jan 1, 1940

By H. T. Kennedy, J. E. Little

An empirical equation for the prediction of the viscosity of several pure paraffin hydrocarbons and nitrogen is presented. It involves temperature, pressure and six constants of the material, and it applies reliably to both liquids and gases. The equation is similar in form to van der Waal's equation of state. For the paraffin hydrocarbons methane through r-hexane and nitrogen, an average absolute deviation of 1.9 percent was obtained on 1,006 data points described in the literature by 14 authors. When this equation is extended to complex, liquid hydrocarbon mixtures, a correlation was obtained with an average absolute deviation of 9.9 percent. INTRODUCTION Equations describing the flow of gas and liquid through porous media contain the viscosity coefficient of the fluid. If other pertinent variables remain constant, the volume rate of flow is inversely proportional to this coefficient. In dealing with condensate fluids and volatile oils, however, the compositional effects resulting from changing pressure materially affect the viscosity. The effect of compositional changes also may be significant in certain secondary recovery or pressure maintenance processes, notably miscible displacement or gas injection. Early attempts to describe the performance of reservoirs utilized a volumetric material balance method wherein gas and liquid in the reservoir were identified as produced gas and liquid at the surface. This method of analysis proved adequate for reservoirs at moderate temperature and pressure that contained gas with moderately low amounts of condensable materials. The volumetric material balance procedures for "black oil" reservoirs leave much to be desired when applied to condensate and volatile oil reservoirs because phase behavior and compositional changes are relatively more important in these cases. The alternative is a compositional material balance, which in turn, requires a correlation of properties of the reservoir fluid with composition. This paper supplies this correlation in regard to viscosity, for reservoir crude oils. REVIEW OF LITERATURE The literature contains many empirical equations describing the effects of composition, temperature and pressure on the viscosities of pure liquids and binary liquid mixtures. However, the applicability of a majority of these equations is limited to very low pressures and to a small number of systems. Most of them, when applied to complex hydrocarbon systems, are of little value. The lack of utility of the majority of equations results from the fact that they were developed to show the separate effect of temperature, pressure or composition on viscosity, but not to predict the viscosity as a function of all three variables. And with the few exceptions noted below, they were developed to apply to much simpler systems than hydrocarbon mixtures. Eakin1 developed an equation for the viscosity of pure light hydrocarbons applicable in the gas, liquid and dense fluid regions, and in its most general form is written as µ - µo =A(ebP - e-cpk) The pure component viscosity at atmospheric pressure and temperature T, µo, was calculated using the Sutherland equation: µo = BT3/2/T + S The constants in Eakin's equation permitted the term e-CPk to become quite small at high densities (above 0.215 gm/cc), and the general equation would simplify to

Jan 1, 1969

By Ott F. Heizer

The mines and the mill of the Nevada-Massachusetts Co. are on the east slope of the Eugene Mountains, in Pershing County, Nevada, 8 miles northwest of Mill City, a station on the Southern Pacific R.R. and on the Victory Highway. Fig. 1. Supplies and, concentrate are transported by truck over an automobile road of easy grade. The property is at an average elevation of 5500 ft. and climatic conditions are generally favorable for continuous operation throughout the year. The ore treated is supplied by two adjoining mines, the Stank and the Humboldt. Physical and mineral characteristics of the ores produced by these two mines are substantially similar, although variations occur in hardness and mineral distribution.' The economic mineral is scheelite (CaWO4), composed, when pure, of 80.6 per cent tungstic trioxide (WO3) and 19.4 per cent lime (CaO).

Jan 1, 1935

The income of the Institute is derived mainly from dues, advertising in MINING AND METALLURGY and sale of publications. These sources are fortunately supplemented by the interest from invested funds now amounting to over $500,000, a considerable portion constituting endowments for especial purposes. Aside from the medal funds the principal endowments are the James Douglas Fund for support of the Library, the Rocky Mountain Fund and the Seeley W. Mudd Memorial Fund. The income from the two last named is available for the support of research and a variety of other purposes. It is allocated by the Board of Directors upon recommendation of standing committees in each case. An active effort is being made to increase the endowments of the Institute, it being felt that unusual opportunities exist for research and public and professional service through the organization.

Jan 1, 1939

By John R. Eckel

A Iaboratory drilling rig has been devised and placed in operation which permits the application of hydrostatic, terrastatic, and formation pore pressures to a rock sample for drilling under controlled conditions. Calibrated rests of this equipment in-dicate qualitative agreerment with field results on the effect of weight on bit, rotary speed, and rate of circ~~lation on drilling rate. Tests under pressure, using water and air as the drilling fluids, indicate that when drilling saturated limestone samples, a pressure differential between hydrostatic and formation pressure is the only pressure which affects drilling rate. A differential in either direction causes a reduction in rate, but the same diflerential from the wellbore into the formation causes the greater reduction. Also, in lime.stone, air favorably affected drilling rote only when compared to water at high hydrostatic pressurre, all other conditions remaining constant. Large increases in drilling rate with air could be obtained in the laboratory only while drilling a shale, which offered a limited permeability to nitrogen and which could be drilled with a differential from the formation into the wellbore. In general, the magnitude of the changes due to the pressure effect were small compared to changes in drilling rate obtainable by changing either bit weight or rotary speed. INTRODUCTION In the course of Humble's drilling research program, the desirability of investigating several factors which lend themselves to laboratory rather than field study became obvious. Principal reasons for this are the expense involved in field studies and the difficulty of exercising the required degree of control. Of primary importance are investigations of the effect of fluid pressure on rock rate, the effect of pressure on rock drillability, and a study of the fundamental mechanics of rock failure and chip generation. Several years ago some work in the laboratory on the effect of mud properties on drilling rate was re- ported to the API', but the completion of this work and the investigation of the other variables affecting drilling rate required equipment somewhat more elaborate than that used on these earlier tests. This equipment has been assembled to form Humble's Drilling Engineering laboratory. To date only the effect of pressure on rock drillability while using water and air has been investigated, and this work is not yet complete. Facilities are available to investigate the effect of fluid properties on rate of penetration, and information is being assembled on a current basis on the mechanics of drilling. The sequence of presentation in this progress report is somewhat different from that in which the data were obtained since the order of ex-

By Pierre de P. Ricketts

Having had occasion while in Europe during the past summer to visit some of the foreign mints and assay offices connected with the same, I thought a brief description of the general process of coining employed, and such items connected with assaying as were new, might prove interesting to the Institute. The principal foreign mints are: the Royal Mint, London; and the mints in Paris, Brussels, Utrecht, Berlin, Vienna, Copenhagen, St. Petersburg, Stockholm, Madrid, Milan, Rome, and Constantinople. My time only permitted my visiting a few of the principal and largest given in the list, and for a description of the remainder I am indebted to the kindness of Mr. James M. Napier, who in company with the deputy master, and chemist of the Royal Mint, made a complete inspection of all the European Mints in 1870.

By E. Douglas, D. N. Collins, J. R. Stevens

E. Douglas (Dept. of Scientific and lndustrial Re-search, Warren Spring Laboratory, Hertfordshire, England) — The authors are to be congratulated on the considerable improvements they have made in tailoring efficiency and selectivity terms which are generally superior to the alternative forms in current use. However, I feel that their efficiency expression is limited to lower-grade feeds; its accuracy reduces as the feed grade increases. For example, its application to such processes as the beneficiation of glass sands, refractories and clays will invoIve considerable inaccuracies. The reason for this lies in the direct use of recovery, which, with high-grade feeds, biases their empirical expression, R(1 - c/h). With a 90% grade feed, the recovery weighting for the slightest degree of beneficiation, over a zero efficiency sampling operation, will be 90+%+ I disagree with their second basic requirement which states that there can be no fundamental basis for any single quantifying expression. A formula giving a comprehensive representation of concentra- tion efficiency can be derived fundamentally accord-to the procedure outlined in the literature. '' This formula, called the Basic Efficiency formula, is

Jan 1, 1963

By Pierre de P. E. M. Ricketts

HAVING had occasion while in Europe during the past summer to visit some of the foreign mints and assay offices connected with the same, I thought a brief description of the general process of coining employed, and such items connected with assaying as were new, might prove interesting to the Institute. The principal foreign mints are: the Royal Mint, London; and the mints in Paris, Brussels, Utrecht, Berlin, Vienna, Copenhagen, St. Petersburg, Stockholm, Madrid, Milan, Rome, and Constantinople. My time only permitted my visiting a few of the principal and largest given in the list, and for a description of the remainder I am indebted to the kindness of Mr. James M. Napier, who in company with the deputy master, and chemist of the Royal Mint, made a complete inspection of all the European Mints in 1870.

Jan 1, 1876

By S. P. Holt

The chief use of scrapers at this mine has been on lead ore of milling grade, clean and dry, in stulled stopes, 50-100 ft. long, 5-12 ft. high, and pitching 20-30°. Scrapers have also been used to fill these stopes with waste. The first scraper used (Fig. 1) is modified from a Cleveland-Cliffs design, being only 30 in. wide. It is light, weighing but 95 lb., handles well, and-digs itself in; but it spills part of its load on a long haul. It could be improved by lengthening the side plates, but because of the double bent angle irons, it is difficult to make at mine shops and has been discarded. Fig. 2 shows where the light angle irons have failed, spoiling

Jan 1, 1923

By S. P. Holt

The chief use of scrapers at this mine has been on lead ore of milling grade, clean and dry, in stulled stopes, 50-100 ft. long, 5-12 ft. high, and pitching 20-30°. Scrapers have also been used to fill these stopes with waste. The first scraper used (Fig. 1) is modified from a Cleveland-Cliffs design, being only 30 in. wide. It is light, weighing but 95 lb., handles well, and-digs itself in; but it spills part of its load on a long haul. It could be improved by lengthening the side plates, but because of the double bent angle irons, it is difficult to make at mine shops and has been discarded. Fig. 2 shows where the light angle irons have failed, spoiling

Jan 1, 1923

The following record of the important responsibilities already shouldered by Dr. Ricketts will give some indication of the trust and confidence reposed in him by his colleagues. The Institute is to be congratulated that a man who is already so much engaged should be willing to assume the further responsibility of guiding the Institute's Ship of state during the ensuing year. Louis Davidson Ricketts, who is brother of Professor Palmer or Chamberlaine Ricketts, President of Rensselaer Polytechnic Institute, was born at Elkton, Md., Dec. 19. 1859, was graduated from Princeton University in 1881 with the degree, Bachelor of Science, chosen a Fellow in Chemistry and W. S. Ward Fellow in Economic Geology, and after two years' study given the degree Doctor of Science. Following the completion of Iris work at Princeton, Dr. Ricketts went to Colorado and started to work as a mine surveyor. For the 15 years following, his time was chiefly occupied in reconnaissance work, geological work and mine examination. From 1887 to 1890 Dr. Ricketts was Geologist for Wyoming, and at, the end of that period transferred his operations to the Southwest. where he has since been steadily engaged in large mining projects. He was identified with the acquisition of the property now owned by the Moctezuma Copper Co., a , subsidiary of Phelps, Dodge & Co., at Nacozari, Sonora, Mex. From 1899 to 1901 he was General Manager of the property and during his administration the concentrator and reduction works were completed and the mines put on a dividend-paying basis

Jan 3, 1916

By J. P. Neumann, L. Raymond

At temperatures near 1000°C, only the (112) (111) slip systems are operatire in tungsten. Therefore, the substructure introduced into the billet upon rleforming a single crystal by rolling at 1000 "C can be controlled by proper selection 01. processing ral'iubles. Using a reduction of 10 pct pel- pass, the (001)[110] and the (110)[001] crystals will deform by duplex slip rip to a 50 pet reduction in thickuess. These rolled single-crystal sheels are characlerized by anisotropic hardening, retention of ductility with warm working, lattice bending which is related to the conlacl (angle, and macroscopic dimensional changecs in the length bid not the width of the billet. When several slip systems become operative, a greater degree of work hardening is itztvoducetl into the crystal. This rolling- condition is characlerized by isotropic hardening, loss of ductilily with warm working, complex lattice distortions, and macro-scopic dimensional changes in both the length rind Width of the billel. IN tungsten, the {1 10}(111) slip systems are operative below room temperature,' while above 700°C only the {112{ (111) slip systems are observed.2,3 In the transition region, i.e., room temperature. both systems appear. It is the purpose of this investigation to show that tungsten single crystals deformed by rolling at a temperature where only one slip system is operative generate dislocation substructure which depends on the crystal orientation. For a specific crystal orientation. the resulting dislocation substructure can be further influenced by modifying the rolling procedure. Crystals oriented for multiple slip display less substructural sensi- tivity to modifications in processing techniques than do single crystals oriented for duplex slip. Under simple slip modes of deformation, very little work hardening is introduced into a rolled single-crystal sheet. Mechanical properties such as room-temperature strength. ductility, and hardness are used to confirm the existence of the different work-hardened conditions generated within the crystal by modified warm-rolling techniques. EXPERIMENTAL PROCEDURE Material. Single-crystal billets of four different crystal orientations. grown by the Arc-Verneuil technique. were ground to a size of 0.25 by 0.375 by 3 in. In terms of their rolling plane and rolling direction, the billets had the following orientations: (1101 [001 ] (110) [110] (001) [110] (001) [100] The actual orientation of all crystals was within 5 deg of the ideal orientations. The typical impurity content of the crystals is given in Table I. Polishing and Etching. Polishing was done elec-trolytically in a 20 g per liter aqueous solution of NaOH at approximately 10 v. It was established by the Laue back-reflection X-ray technique that the surface damage due to grinding and cutting operations with a diamond wheel did not exceed 0.001 in. Therefore after each cutting or grinding operation at least 0.002 in. was removed electrolytically from the surface in order to eliminate surface effects. By lowering the voltage to 3 v, subgrain boundaries and individual dislocations are identified in agreement with Berlec 4 where the etch-pit traces on a cubic plane form a square. The etching time was about 5 sec at room temperature. Rolling. Rolling was carried out on a Loma 2-high mill (Model 600). The peripheral velocity of the 6-in.-diameter rolls was 500 in. per min, with the surface temperature of the rolls about 400° to 450° C The billets were heated before each pass for 30 min in argon to 1000 C. Oxidation of the crystals during rolling in air resulted in a thin layer of greenish-yellow WO 3 This oxide was removed after each pass by immersing the crystals for a few minutes in a boiling NaOH solution. Prior to the initial rolling pass, a surface layer of 0.001 in. was removed by polishing. The crystals were then annealed in vacuum (10-4 torr) at 2400 C for 30 min. All crystals were rolled in the same direction; i.e., the same end was always introduced into the rolls. The rolling program was conducted in

Jan 1, 1965

By Phillip E. Deering, Robert M. Cox

A model pillar study was conducted in which the engineering principles of dimensional analysis were applied to the problem of coal mine pillar design. The paper reviews the theory of similitude as applied to the model pillar study conducted in the investigation. An example solution of a design problem is included to indicate how the results of the study may be used as a first approximation in the design of coal mine pillars. The design of mine pillars for adequate support with minimum loss of valuable raw materials has always presented a problem to the mining engineer. Most often, for lack of a better method, past practice has influenced the design of new mine pillars. This process has always left doubt as to the safety factor of the pillars. The work presented in this paper is an initial attempt toward adapting the engineering principles of dimensional analysis to the problem of pillar design in underground mines. The use of the dimensional analysis technique is advantageous because all the variables associated with the problem are considered, and by systematic analysis the relative influence of each variable is determined. The model material utilized in this study was taken from the Helena seam of the Cahaba coal field located in central Alabama. The research study was sponsored by The Southern Electric Generating Co. as part of an over-all rock mechanics investigation of the Helena seam area. THEORY OF SIMILITUDE Model analysis is used extensively in engineering today, particularly in the solution of design problems that defy the classical methods of analysis. Such problems arise when materials with a nonlinear stress-strain relationship are involved, when geo- metric boundaries are difficult to define in simple form, when strains become large, or when partial failure occurs. All of these difficulties usually exist in pillar design problems. Those principles which underlie proper design and construction of models, and the interpretation of test results, comprise the theory of similitude. That is, the theory of similitude includes a consideration of the conditions under which the behavior of two separate entities or systems will be similar, and the techniques of accurately predicting behavior of one from observation of the other. The theory of similitude may be developed by dimensional analysis. Dimensional analysis, as a powerful analytical tool, is developed from a consideration of the dimensions in which each of the important quantities involved in a phenomenon is expressed. It is based on two axioms: 1) Absolute numerical equality of quantities may exist only when the quantities are similar qualitatively. 2) The ratio of the magnitudes of two like quantities are dependent on the units used in their measurement, provided that the same units are used for evaluating each. Dimensional analysis, developed from these two axioms, differs from other types of analysis in that it is based solely on the relationships that must exist among the pertinent variables because of their dimensions, rather than on the relationship of natural laws. In itself, dimensional analysis ~rovides qualitative, rather than quantitative relationships, but when it is combined with experimental procedures, it may be made to supply quantitative results and accurate prediction equations. APPLICATION OF THEORY The design of an adequate mine pillar requires the determination of a design equation and the selection of a dimensional system with which to work. Since force plays an important part in the design of mine support, the FLT (force, length, time) system has been used. The factors involved in the dimensional analysis of mine pillars and their dimensions are: A = cross-sectional area L Cp = design strength FL- E, = tangent modulus of elasticity FL

Jan 1, 1969