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By Meng-Cherng Sun, Fun-Den Wang, David M. Ropchan

A proposed technique for improving coal-mine roof stability by softening parts of coal pillars along the sides of entries developed from structural analysis is presented. This technique is based on the transference of the high stress concentration in the roof near the upper corners of a rectangular opening to the roof rock and coal over the solid away from the opening. This transferral is accomplished by softening parts of the coal pillars by drilling a series of parallel holes into the coal in the ribs and face of the entry prior to advance. The effectiveness of the pillar softening in terms of reducing the opening width (so that the stress in the roof near the corner is equivalent to that of a narrower opening) ranges from 3 to 5 ft for a 16-ft entry using a series of 4 to 5-ft-deep parallel drill holes of 3 to 6-in.-diam on a 1 to 2-ft spacing for a particular geology. Pillar softening should be highly effective in controlling roof where cutter-roof cave conditions exist, because this technique reduces the high stress concentration in the roof at the upper corners of the opening. It may also be effective for reducing tensile roof failure and coal rib sloughing for certain specific geological conditions. This technique appears to be a simple, effective, and practical method that can be used to supplement conventional roof support methods of roof bolting, timbering, roof truss, and other existing methods in underground coal mines. The authors consider the technique feasible and believe that it merits underground trials.

Jan 1, 1975

By Reynold Q. Shotts

Data are presented which show that fractions of varying densities from the same coals are oxidized at different rates by nitric acid. From oxidation data, the approximate quantity of "bright" and "dull" components may be calculated. Definite relationships between oxidation rate and rank are shown for density fractions from at least two bituminous coals.

Jan 8, 1950

By O. C. Ralston

The use of copper sulfate for improving the flotation behavior of sphalerite is probably at least 15 years old. The original discovery of its activating influence is somewhat obscure. The story goes that in the mill at Mascot, Tenn., its favorable action was discovered by accident, early in 1914, as follows: The original laboratory test work on a sphalerite ore gave favorable flotation results, but after a mill had been built the flotation concentration of the ore was very unsatisfactory. In diagnosing the probable reasons, one fact pointed out was that the laboratory test machine had been constructed of bronze whereas the commercial machine allowed pulp to come in contact only with wood and iron. A plate of sheet copper was hung in the flotation machine and results immediately improved. At first fanciful explanations of electrolytic and electrostatic behavior were given credence, but when the copper plate was removed and a small amount of copper sulfate substituted in the pulp an even more favorable result was obtained. Toward the end of 1914 copper sulfate was also adopted in the acid flotation circuit of the Butte and Superior Copper Co. Just who is responsible for the original discovery the present writers do not know. It seems strange that in that era of flotation litigation this discovery was not patented. While for pragmatic purposes it [nay be sufficient to know that the mere addition of copper compounds to a flotation pulp is sufficient to activate the flotation of the sphalerite, for scientific purposes it is quite desirable to know more about how the action takes place. It is the purpose of this paper to present certain evidence dealing with the mechanism of the beneficial effect. The description of the effect as activation in contradistinction to depression is now common in both the English and German languages. It makes no assumptions as to whether the zinc sulfide surfaces have been filmed with copper compounds. In fact, the principal differences of opinion expressed in the literature deal with whether there is an actual formation of CuS (or even Cu2S) on the surface of the sphalerite. Activation of sphalerite takes place in alkaline, neutral or weakly acid solutions and whereas the present day flotation of sphalerite is usually in ah alkaline solution, the early use of copper sulfate was in a sulfate solution.

Jan 1, 1930

By K. L. Woodruff

The first step in processing municipal solid waste (MSW), principally household waste, for resource recovery is usually shredding. A trommel has been investigated as a step to precede shredding. This way abrasive inorganic materials, such as stones and metals, would be removed prior to shredding, thus lowering the amount of feed and hence maintenance on the shredder. In addition, friable materials such as glass would be removed in large pieces, rather than pulverized too mall to process for recovery. The utility of a trommel for these purposes was investigated on a pilot scale using a unit 9 ft diam by 10 ft long with 4-in. square clear openings. Experimental results indicate that up to approximately half of the MSW may be removed as -4-in. material prior to shredding. The -4-in. fraction contains approximately 70% of the metals and 95% of the glass present in the MSW feed to the unit. Scale-up and cost information necessary for the design of a 60 to 70 tph unit is developed.

Jan 1, 1977

By Robert L. Gower, John H. Cash

Interconnections for integrated circuits operating at rnicrowaue frequencies rzust be formed as microwave transmission lines. This paper describes the fabrication of one type of microwave transmission line known as microstrip, which can be fabricated on momlithic integvated circuits by deposition of 0.1- to 2.0-mil-thick metal and dielectric films. A microstrip line consists of a narrow conducting strip separated from a gvound plane by a dielectric material. Thick films of good conducting materials are required for low loss at high frequencies. Vacuum-evaporation methods for depositing aluminum and silver films are described. The narrow conducting strip forming the top conductor is defined by photoresist-etching techniques after the thick rnetal film is deposited. Gold plating with a photoresist-masking technique is also used to forrrz thick metal conductors. The microstrip dielectric layer is formed by deposition of suitable dielectric films 0.1 to 2.0 mils thick. Several deposition techniques were investigated. Electron-beam evaporation of quartz is described. Electrical characteristics of deposited microstrip lines at microwave frequencies are included and the microwave power attenuation as a function of conductor and dielectric thickness is given. It is concluded that the deposition of microstrip transmission lines is a practical way to achieve low-loss interconnections in monolithic integrated circuits. CONNECTIONS between devices in low-frequency and digital circuits are usually made by connecting the devices with a length of conductor such as a metal lead oi- a wire. If this method were applied to microwave integrated circuits, the reactance of the connection due to the series inductance and parasitic capacitance would be very high, in fact too high to permit successful circuit operation. In addition, resonance and antenna effects would occur at high frequencies, especially when the connections approach the wavelength.' Connections which are sections of transmis- sion line will overcome these difficulties. The electromagnetic field is confined to the volume of the transmission line, parasitic effects are not present, and circuit design utilizes familiar transmission-line techniques. TRANSMISSION LINES One type of transmission line geometrically adaptable to integrated circuits is known as micrstri. A microstrip line can be generated from a coaxial line as shown in Fig. l(a). The outer conductor of the coaxial line is distorted into an ellipse (b) and finally separated at the extremities of the ellipse to form the strip transmission line shown in (c). One of the ground planes is then removed, leaving a conducting ground plane and a narrow conducting strip separated by a dielectric. Two configurations of the microstrip line were considered in this investigation, Fig. 2. Type (a) is fabricated from a semiconductor slice with the ground plane and top conductor deposited on each side of the slice. The semiconductor slice serves as the die lec-

Jan 1, 1967

By Grant Buma

The purpose of this paper is to present arguments and evidence that there are natural processes at work which tend to minimize the impact of solution mining on the environment. The contaminants have two sources. First are elements which were present in the roll-front deposit in insoluble compounds, for example, uranium in uraninite and coffinite, molybdenum, arsenic, iron, cobalt, nickel, etc. in sulfide minerals, vanadium in micas and clays, etc. Second are elements introduced by the leach liquor. Precipitation of reduced compounds, scavenging of heavy elements and absorption by quartz and clays, can all reduce the amount of heavy elements in solution. If a roll can be demonstrated to be actively precipitating uranium and heavy metal elements, then the presence of precipitants (pyrite and carbon) can be assumed. Criteria for recognizing an active roll are described.

Jan 1, 1979

By T. T. Quirke, L. C. McCabe

The object of the present investigation was to discover a physical basis for rank differentiation of coals, particularly the coals of the Illinois basin. Vitrainl was selected as the most appropriate coal material to use in the investigation, because of its homogeneity and ease of acquisition and handling. Previous Investigations.—Hoffman and Jenker2 have shown that their index of reflection is a characteristic of coal rank and that the Leitz slit microphotometer may be used in determining the different intensities of reflection. Zhemchuzhnikov3 measured the luster of several Russian coals with a color analyzer and found that the degree of luster was indicative of rank. Luster-volatile matter curves based on data from Sucan and Donetz coals were satisfactorily used for determining the rank or volatile content of other coals after the luster strength was determined. In 1934 Fisher4 reported refractive indices of 1.76 for bituminous vitrain and 1.87 for semibituminous vitrain. Investigation of Angle of Polarization.—Early in the present investigation several determinations of the refractive indices of the vitrains were made by immersing the minus 150 plus 200-mesh powder in oils. It was found that all the samples fell within the range 1.6 to 1.8. However, difficulty was encountered in securing oils in this high index range that were closely enough spaced to separate some of the coals. The writers made a number of determinations of the angle of maximum polarization from the polished surfaces of the vitrains and derived their refractive indices by the procedure described in the following paragraphs. Johannsen5 states the fundamental concepts underlying this procedure as follows: In general, in an isotropic medium light vibrates in all directions at right angles to the direction of propagation, and when it meets with another isotropic medium at an angle, part of the light is reflected and part refracted. It has been found that after reflection or refraction, the vibrations do not move with the same freedom in every

Jan 1, 1938

By T. T. Quirke, L. C. McCabe

The object of the present investigation was to discover a physical basis for rank differentiation of coals, particularly the coals of the Illinois basin. Vitrainl was selected as the most appropriate coal material to use in the investigation, because of its homogeneity and ease of acquisition and handling. Previous Investigations.—Hoffman and Jenker2 have shown that their index of reflection is a characteristic of coal rank and that the Leitz slit microphotometer may be used in determining the different intensities of reflection. Zhemchuzhnikov3 measured the luster of several Russian coals with a color analyzer and found that the degree of luster was indicative of rank. Luster-volatile matter curves based on data from Sucan and Donetz coals were satisfactorily used for determining the rank or volatile content of other coals after the luster strength was determined. In 1934 Fisher4 reported refractive indices of 1.76 for bituminous vitrain and 1.87 for semibituminous vitrain. Investigation of Angle of Polarization.—Early in the present investigation several determinations of the refractive indices of the vitrains were made by immersing the minus 150 plus 200-mesh powder in oils. It was found that all the samples fell within the range 1.6 to 1.8. However, difficulty was encountered in securing oils in this high index range that were closely enough spaced to separate some of the coals. The writers made a number of determinations of the angle of maximum polarization from the polished surfaces of the vitrains and derived their refractive indices by the procedure described in the following paragraphs. Johannsen5 states the fundamental concepts underlying this procedure as follows: In general, in an isotropic medium light vibrates in all directions at right angles to the direction of propagation, and when it meets with another isotropic medium at an angle, part of the light is reflected and part refracted. It has been found that after reflection or refraction, the vibrations do not move with the same freedom in every

Jan 1, 1938

By D. Swan

Industrial research may be defined as a critical and exhaustive investigation to create new and better ways of doing things. The results of industrial research are new and improved products, processes, and techniques. This broad definition, of course, covers investigation of all subjects by either individuals or groups of people, and this chapter aims to examine the purpose (what research tries to do), and methods (or how research is done) as applied in the mineral industries. Concepts and History The idea or concept of organized research probably originated in the universities of Europe. There, groups of scholars banded together for discussion and application of their particular specialty to a common problem. Publication of the conclusions drawn from such investigations gave scholars in other areas the opportunity to review and criticize the work of their colleagues, and one of the hallmarks of scientific research work is the publication and criticism of the results of the investigation. It was not until the late nineteenth century that the concept of organized research for the profit of industry was recognized. During the late nineteenth and early twentieth centuries, a large number of industrial enterprises sponsored organizations to study the application of the physical sciences with the aim of making discoveries that would result in profit to the sponsoring organization. The tangible benefits accruing from these activities were so great that they, in turn, fostered several other methods for the support of organized research activities. For the large problems involving public interest, United States Government scientific research laboratories were set up. As the demand of smaller enterprises for research activities increased, research institutes and consulting laboratories were organized. In Europe the idea of common industry sponsorship of research centers grew and many large research organizations there were sponsored by associations of manufacturers. Finally, in the United States

Jan 1, 1964

By Roger E. Barthelemy

PRIMITIVE mining and metallurgy has today almost disappeared. Probably the only remaining tribal tin mining and smelting is practiced by the Laotian natives in one of the less known tin areas of the world. This district lies almost a thousand miles from the sea along the Mekong River, one of the longest rivers in the world, that marks the border between Siam and Laos, one of the five states forming French Indo-China. Less than twenty years ago it took more than two weeks' travel on elephant-back to reach the spot and today it still takes many days of travel, using all kinds of transportation from automobiles to native

Jan 1, 1938

By Louis Katona

The practical execution of the design for rolling-mills presented by the writer at the Paris meeting* of thc Iron and Steel Institute in 1900 involves the determination of some questions not yet discussed, among which is the determinatioir of the amount of power required to perform the rolling of pieces of iron and steel of given dimensions. It is necessary to know this factor if we would put motors of proper capacity to the respective pairs of rolls, or, rcciprocally, if, having standard motors at our disposal, we would design grooves to suit them. Moreover, this factor is involved in giving right dimensions to every part of the rolls and housings. Expert designers of engines for driving rolling-mills of the present type receive very indefinite directions, such as: that the motor is to drive a light, medium or heavy train; that it must work with fly-wheel or reversing gear; that the number of revolutions per minute should not exceed 40 or 60, and that at a given speed the power developed should be from 100 to 200 H. P., or from 1,000 to 2,500 13. P. It frequently happens, however, that an cngine of 200 H. P. is forced under the circumstances to press or develop as much as 300 H. P., while, on the other hand, the ,1,500-11. P. engine may be rolling-stock which could be worked with a maximum expenditure of 60 to 80 H. P. Of course such variatior~s as these do not permit the best adjustment of parts or the best economy of power and fuel. The design of roll-trains is even more vaguely limited. Every part of a train, from the point where it connects with the engine to the last groove in the rolls, bears evidence that there are no rules for calculating even approximately the dimensions of the main-shafts, couplings, pinions, gears, rolls, trunnions,

Jan 1, 1904

By J. A. Herbst, K. Rajamani

INTRODUCTION Recent research has shown that popu- lation balance models hold considerabl e promise as a basis for accurate mill scale-up from laboratory batch grinding tests. It has been shown that entire product size distributions from large ball mills can be predicted from data obtained in tests in small mills with errors of less than one or two percent. This level of accuracy has been demonstrated for batch grinding scale-up (Herbst and Fuerstenau, 1980; Austin, 1973; and Malghan and Fuerstenau, 1976) and for continuous grinding scale-up (Herbst, et a1., 1976; Herbst, Rajamani and Sanchez, 1982; and Herbst, Rajamani and Lo, 1982) in commercial mills up to 14.5 x 32 feet. A procedure which has been proposed for commercial mill design using the population balance approach and specific power information is shown in Figure 1 (Herbst and Fuerstenau, 1980). Here batch grinding data (size distributions for various energy inputs) obtained in a small batch mill is input to an estimation program which determines the "best" set of breakage rate parameters from the data provided. In turn, these breakage rate parameters are input to a scale-up program along with traditional inputs such as: a) desired circuit throughput and product size b) circuit operating conditions including fraction of critical speed and fractional ball load, size distribution and % solids in feed and circulating load (if closed circuit). In addition, since the population balance approach relies on more detailed models of the grinding circuit sub- processes than the classical design methods do, it is necessary to provide input to the scale-up program on the nature of material transport through the mill (e.g. residence time distribution information) and classifier performance characteristics (e .g. selectivity functions). The scale-up program will make the design calculations including the selection of mill dimensions and drive requirements, will predict product size distributions throughout the commercial circuit and will provide information on the sensitivity of the design to errors in the design assumptions. In order to implement such a scale- up scheme it is necessary to have a computer program for parameter estimation and a program for scale-up prediction. A program which is suitable for parameter estimation, ESTIMILL, has been developed and tested on a wide variety of ores at the University of Utah. This program has been in use in

Jan 1, 1982

TO THE BOARD OF DIRECTORS AND THE MEMBERS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS Gentlemen -It is pleasant to be able to report that the year just closed has been a prosperous and successful one for the Institute As is shown by the reports of the Treasurer and the Finance Committee, the business affairs of this organization are in excellent condition With property valued at more than three-quarters of a million dollars, and with con¬siderable sums in various funds and endowments, it is possible to spend on each member of whatever class $22 65 each year, more than the maxi¬mum amount of dues received from any one, and substantially twice the average amount, $10.94, received from all To do this has required close management and a strict regard for our limitations In 1926, when the Budget was made up, the estimated expenditures for the work which it was felt the Institute must do exceeded the estimated receipts by some $14,000. At the close of the year, despite a` number of unexpected decreases in receipts, it had proved possible to accomplish substantially all the work laid out and close the books with the usual transfer of initia¬tion fees to the General Reserve, and still only reduce the cash balance $2,074 54. This was made possible by the hearty and loyal cooperation of the whole staff of employees and the extremely large amount of gratui¬tous service rendered by the officers, the members of the Divisions and technical Committees, and the membership generally Even so it was impossible, because of limitations of funds, to undertake many things it is highly desirable for the Institute to do, and it was necessary to refuse the publication of important papers and committee studies, because of the lack of funds.

Jan 1, 1923

By David H. Carlson, John H. Johnson

The paper presents background information, a description of mine characteristics that affect air monitoring techniques, and a review of Portable measurement techniques and instruments for gas and particulate matter sampling. A general review of the laboratory and field research being conducted at Michigan Technological University in the area of diesel emissions is presented. The facilities involved with this research are also described. These are the experimental mine, the diesel dilution tunnel test cell, the mine air monitoring lab (MAML), portable instruments, and the production mines used.

Jan 1, 1982

The practice of fine-grinding is now being so succeesfully carried on in some fields, notably in West Australia, and its advisability has been so frequently pointed out,l that the matter in this paper is not put forward as new; its chief object being to call attention to the importance of fine-grinding in the treatment of comparatively low-grade oree. I' have been engaged daring the last five years in the cyanide-treatment of ores in the Ohinemuri district (North Island), New Zealand, and I consider that, in the near future, extremely fine-grinding (almost sliming) will become a very im-

Jan 1, 1906

By David R. Maneval, Sylvester Lemezis

All acid mine drain waters, regardless of source, share certain characteristics; but they do differ in exact chemical composition, degree of acidity, and total solids content. Any serious program to treat such waters must recognize these differences and apply to each specific case the technique which offers the best promise of each specific case the technique which offers the best promise of technical and economic success. The Pennsylvania Dept. of Mines and Mineral Industries has originated and funded studies of many different treatment means. Neutralization with lime is now being used on 200 different polluted streams in Pennsylvania, and multistage flash evaporation has been selected for a particularly large and troublesome outfall near Wilkes-Barre, Pa. A 5 x 106 gpd plant for this latter site is now being designed by Westinghouse Electric Corp. which developed a concentration process based on multistage flash evaporation as part of the State's research program.

Jan 1, 1973

By R. N. Schulz

The recently completed modifications and additions to Reserve Mining Company's taconite concentrating process incorporate a totally new control system. Design of the new control scheme is centered on reliability, versatility, centralization, and optimization. The design objectives were achieved through a distributed control system based on a network of independent field located microprocessor based control system connected to a central control room. Operation of each micro-processors can be interrogated and modified from the central control room by the operator or by either of two computer systems. The two computer systems handle logging, alarming, specialized sequenced controls, and complex process optimization routines.

Jan 1, 1984

By John Birkinbine

An item of considerable importance to the producers of pig-iron is the disposition of the slag or cinder from the blast-furnace; and various plans have been adopted at different works to care for the rapid accumulation of this generally waste material. The charge per ton of iron made which must be allowed for the care of cinder is sufficient in times of business depression to give plants having facilities for disposing of their slags an advantage over others less favorably arranged, and to allow iron to be produced profitably in the one case and prevent a profit in the other. The varied methods employed and the means of conveyance utilized need not be detailed. It is sufficient to say that the large outputs of American blast-furnaces, and consequent rapidly augmenting dump-piles, have brought into general favor the use of cars carrying the slag in a liquid condition. The advantages of this method are the prompt removal of the slag, the reduced space occupied by the dump-piles, and the facility of converting the slag into such forms for use as may be desired. The progress in iron-manufactlire is also marked by a more general adoption of methods by which molten metal is carried in vessels away from the point of its production; and, anticipating the prospective advance in pig-iron manufacture, it does not seem unreasonable to prophesy the early abolition of casting-houses at blastfurnaces, particularly where several are grouped together; or the casting of steel ingots away from the converters or furnaces. In some large blast-furnace plants, the iron is carried molten from the blast-furnaces to the converters or other furnaces. Even where it is cast into pigs, casting-sheds removed from the immediate vicinity of the furnace-stack would, perhaps, be superior to casting in beds in front of the furnaces. The idea of casting-sheds appears to present the following advantages : 1st. The equipment of boilers, hot-ovens, and blowing-machinery could be closely grouped around the blast-furnace stacks, permitting

Jan 1, 1887

By J. G. Thompson

THE methods employed for the determination of oxides and oxygen in ferrous materials may be roughly classed in two groups, "wet" methods and "hot" methods, the first group including the iodine, electrolytic, mercuric chloride, hydrochloric acid, nitric acid, and chlorine methods; the second group including the vacuum-fusion and hydrogen-reduction methods. The wet methods depend upon preferential solubility in a selected medium to separate the metallic portion of the sample from the oxygen-containing constituents. Subsequent analysis of the insoluble residue permits the isolation and separate determination of individual oxides and compounds. The hot methods depend upon the reduction of the oxide constituents of the sample by means of carbon or hydrogen at elevated temperatures. With the exception of the recently developed fractional vacuum-fusion method, the hot methods do not identify individual oxides and compounds but yield only a single value represent-ing the sum of the oxygen contents of several or all of the oxide con-stituents present. With such diversity in the principles and. aims of the different groups, it is not surprising that concordance of results by differ-ent methods has usually been difficult to obtain. The present cooperative attempt to define more rigorously than has been possible heretofore the accuracy and limits of usefulness of the vari-ous methods, originated in correspondence between Dr. John Johnston, Director of Research of the United States Steel Corporation, and other interested metallurgists. The plan was, briefly, to submit identical samples to a number of laboratories for analysis by different methods and to collate the results of these analyses. The project was endorsed by the Iron and Steel Division of the American Institute of Mining and Metal-lurgical Engineers at the annual meeting in February, 1933, and has been conducted under the joint sponsorship of the Iron and Steel Division and the National Bureau of Standards. The latter organization undertook

Jan 1, 1936

By A. Romero-Juarez

This paper is concerned with the effect of propping-agent concentration on flow capacity of a fracture in the case in which there is embedment of the propping agent. Previous published studies have shown definitely that there is a relationship between fracture flow capacity and prop ping-agent concentration, and it has been shown that the theoretical results are confirmed by laboratory experiments. The problem of directly finding sand concentration for maximum flow capacity of a sand-propped fracture is solved, and formulas and charts are given to obtain this concentration under various conditions of effective overburden pressure, medium sand-grain diameter and rock properties. It is shown that, for the same effective overburden pressure and the same rock characteristics, optimum sand concentration in pounds per gallon does not depend on medium sand diameter. For conditions met in bydraulic fracturing operations, it is found that sand concentration in grains per square inch for maximum flow capacity varies within a wide range of values; this indicates the convenience of using data of fracturing pressure and rock characteristics for calculating sand concentration in order to achieve the best results in fracture treatments. INTRODUCTION It has been pointed out in the published literature1 that one important factor controls the success of a hydraulic fracturing operation — the propping of the fracture. The main effect of the propping agent is to hold the fracture open by means of the reaction forces that oppose the pressure due to the overburden. It is assumed in this paper that the propping agent is sand, that the grains are spherical and uniform in size, and that this sand is distributed in a monolayer in the fracture. The existence of a sand concentration value for maximum fracture flow capacity has been recognized since the publication of one of the first studies on the subject.2 In the reference cited, flow capacity was assumed to be proportional to the cube of the fracture volume per square inch not filled by sand. The obtained experimental curves relating to flow capacity and sand concentration had the same appearance as the curves obtained with the afore-mentioned assumption. Recent work3 has shown that fracture permeability, in the case of a monolayer, can be calculated accurately by means of a modified Kozeny-Cacman equation; thus, it can be shown that fracture pqmeability is a function of free volume in the fracture and of the rock and sand wet surfaces. The flow capacity of a fracture is dependent on the permeability of the fracture and on the fracture width. If all excessive quantity of sand is present in the fracture, its width may be large but its permeability i:; low due to the greater flow resistance; too few grains of sand per square inch are present in the fracture, sand embedment in the rock is greater and the width becomes small enough to appreciably decrease the rate of flow. To determine optimum conditions of flow, therefore, it is necessary to know the dependence of fracture width on density or concentration of propping agent. This relation is given in a study4 in which the approach to embedment is similar to the one made in a penetration hardness test of metal. With the equacions presented by Darin and Huitt,3 the number of sand grains per square inch that results in maxirnum fracture capacity can be determined graphically by plotting fracture capacity vs sand concentration. Since the relationship between fracture capacity and sand concentration may be considered known, one is led to formulate the analytical problem of directly determining sand concentration for maximum fracture flow capacity, in order to study the effect of the various quantities that come into the process. The solution of this problem appears to be interesting both from the viewpoint of fluid mechanics and from the practical viewpoint of oil production in hydraulic fracturing treatments. EQUATION FOR FRACTURE FLOW CAPACITY It can be shown3 that the fracture flow capacity of a monolayer is given by the following expression,