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By A. V. Deforest, C. W. Macgregor, A. R. Anderson

One of the important problems in the design of structures and machine parts subjected to rapidly applied loads is the determination of the strength and ductility of the material itself under such conditions. Realizing the need for such information, many investigations have been carried out in the past. Most of these experiments have been made using notched bars in bending either with the Charpy or Izod impact machine. While yielding valuable data on the effect of notches in the energy absorption of the material and on the condition of heat-treatment, this form of test does not lend itself readily to a determination of fundamental stress-strain relations. For this and other reasons, more attention has been paid recently to the tension impact test. An extensive literature already exists on the subject and only those investigations somewhat closely related to the present paper will be mentioned. For a more comprehensive list, the reader is referred to the Symposium on Impact Testing or the A.S.T.M., 1938. The work of Mann.' Clark and Dätwyler,2 Nádai and Manjoine,3 Winlock and Leiter,4 Deutler,5 and Brinkmann,6 however, deserves especial mention. In most of the previous investigations on the subject, when stress-strain relations were obtained under high rates of loading, it was the common procedure to determine stresses based on the original area and strains based on the original length. Stress-strain curves were then constructed by P ALo plotting So = 1/A0 as a function of eo = ALr,o where A0 and Lo refer to the original area and gauge length, respectively. At present there exists a paucity of true stress-strain data in the impact problem. The advantages of constructing so-called true stress-strain curves in order to reveal the fundamental physical properties of the material for the tension test were discussed recently by one of the authors.7'8 It was shown that the true physical behavior of the material in the tension test could best be represented P by plotting the average true stress, S = 2P as a function of 6 = q' = log —r = log ~9L where P, A, L, S, E, and q' refer to the load, the cross-sectioned area while the load P is applied, the actual gauge length, the average true stress, the true strain and true reduction in area, respectively. Besides giving a better physical representation, the method has certain additional advantages in that the stress-strain curve so plotted becomes a straight line from the maximin load point to fracture. The construction of such curves, however, while comparatively simple for the slow rates of loading customarily used in the tension test, presents certain dificulties for tensile impact in that both loads and diameters are required throughout the test. The continuous measurement of test-piece diameters to fracture under impact conditions offers considerable experimental difficulty. In order to make it feasible to

Jan 1, 1942

By A. V. Deforest, A. R. Anderson, C. W. MacGregor

One of the important problems in the design of structures and machine parts subjected to rapidly applied loads is the determination of the strength and ductility of the material itself under such conditions. Realizing the need for such information, many investigations have been carried out in the past. Most of these experiments have been made using notched bars in bending either with the Charpy or Izod impact machine. While yielding valuable data on the effect of notches in the energy absorption of the material and on the condition of heat-treatment, this form of test does not lend itself readily to a determination of fundamental stress-strain relations. For this and other reasons, more attention has been paid recently to the tension impact test. An extensive literature already exists on the subject and only those investigations somewhat closely related to the present paper will be mentioned. For a more comprehensive list, the reader is referred to the Symposium on Impact Testing or the A.S.T.M., 1938. The work of Mann.' Clark and Dätwyler,2 Nádai and Manjoine,3 Winlock and Leiter,4 Deutler,5 and Brinkmann,6 however, deserves especial mention. In most of the previous investigations on the subject, when stress-strain relations were obtained under high rates of loading, it was the common procedure to determine stresses based on the original area and strains based on the original length. Stress-strain curves were then constructed by P ALo plotting So = 1/A0 as a function of eo = ALr,o where A0 and Lo refer to the original area and gauge length, respectively. At present there exists a paucity of true stress-strain data in the impact problem. The advantages of constructing so-called true stress-strain curves in order to reveal the fundamental physical properties of the material for the tension test were discussed recently by one of the authors.7'8 It was shown that the true physical behavior of the material in the tension test could best be represented P by plotting the average true stress, S = 2P as a function of 6 = q' = log —r = log ~9L where P, A, L, S, E, and q' refer to the load, the cross-sectioned area while the load P is applied, the actual gauge length, the average true stress, the true strain and true reduction in area, respectively. Besides giving a better physical representation, the method has certain additional advantages in that the stress-strain curve so plotted becomes a straight line from the maximin load point to fracture. The construction of such curves, however, while comparatively simple for the slow rates of loading customarily used in the tension test, presents certain dificulties for tensile impact in that both loads and diameters are required throughout the test. The continuous measurement of test-piece diameters to fracture under impact conditions offers considerable experimental difficulty. In order to make it feasible to

Jan 1, 1942

By D. B. Robinson, J. Lukacs

A knowledge of the equilibrium water content of hydrocarbon systems under pressure is important to the natural gas industry. The information available on the solubility of water in hydrocarbon, hydrogen sulfide, and carbon dioxide systems is reviewed in this paper and the influence of the more important variables such as temperature, pressure and molecular structure on solubility in liquids and gases is discussed. A suitable cbromatographic technique has been developed for determining low concentrations of water. Tailing of the water peaks has been elim inated by adding water to the carrier gas stream The method is applicable for both gas or liquid samples and is effective in the presence of hydrogen sulfide. The experimental study of water solubility in methane-hydrogen sulfide systems at a temperature of 16oF has shown that the presence of hydrogen sulfide causes only a modest increase in water content at pressures up to 1,400 psia. Theoretical considerations and data on pure hydrogen sulfide and carbon dioxide suggest that the effect of both these compounds will be greater at higher pressures and in the liquid phase. INTRODUCTION Before transporting or processing natural gases and gas condensates, it is usually necessary to dry them using suitable dehydration equipment. The design and operation of this equipment requires a knowledge of the amount of water present in the fluid at the reservoir and operating conditions. This is influenced by temperature, pressure and composition, particular1y when certain non-hydrocarbon components are present. Field experience indicates that hydrogen sulfide and carbon dioxide, for example, alter the usual water solubility relationships appreciably. However, an extensive search of the literature does not reveal any quantitative data on such systems. For sweet natural gases, generalized empirical correlations such as the one proposed by Katz, et al,6 can be used to predict water solubility with confidence at most temperatures and pressures of interest. However, existing theoretical relationships do not permit a calculation of the deviation from these curves when polar substances like hydrogen sulfide are present in the system. Thus one must resort to an experimental approach to obtain the necessary information. The fact that laboratory experimental methods frequently involve the use of mercury which reacts with hydrogen sulfide in the presence of water, and that hydrogen sulfide interferes with many chemical reactions specific for water has contributed to the difficulty of studying water solubility in systems containing hydrogen sulfide. In this investigation the water content of a limited member of methane-hydrogen sulfide mixtures was determined using a special technique with gas chromatography. REVIEW OF PUBLISHED DATA Experimentally determined water solubility data have been reported for methane, 14 ethane, 15 propane, 9 n-butane, 16 1-butene, 11 hydrogen sulfide 18 and carbon dioxide. 19 These studies report the effect of pressure, temperature and molecular structure on water solubility in single component gases and liquids. Fig. 1 compares experimentally determined water solubilities in several hydrocarbons, carbon dioxide and hydrogen sulfide at l00F as taken from this

By Philip B. Dettmer

In the last two decades we have witnessed many new developments in the art and science of mineral beneficiation. Competition and the pressures of inflation have caused operating managements to search for every possible way to squeeze out a few more cents savings per ton of product. One illustration of this is the trend toward the use of larger grinding mills. A few years ago a 1000 hp ball mill was considered a giant. Now we have many examples of successful grinding mill installations of 3000 to 4400 hp connected load per mill. The trend toward these larger mills is increasing every year, and we have not seen the upper limit yet. For example, three 6600 hp cement finish mills are presently being built for a plant in Missouri.

Jan 4, 1965

By J. F. Kemp

Introduction The Bulletin of the Institute for March, 1911, is chiefly devoted to papers upon the iron ores of northeastern Cuba. At that time information about the new developments in the peculiar brown hematites of the region was becoming widely circulated and interest was especially keen. For some years exploration had been conducted with pits and trenches and so great an area had been shown to contain ore in the Mayari, Moa, and Cubitas or San Felipe districts, that the reserves conveniently situated for the consumption of American furnaces were estimated as quite two billions of tons. In the subjoined footnote will be found a list of the principal papers of special interest which have already been published.1 The further remark may, however, be made that the

Jan 2, 1915

By H. F. Yancey, M. R. Geer, C. L. Allyn, R. H. Eckhouse

W. M. Bertholf—This is an excellent report of a well-conducted investigation, of sufficient scope to provide generally useful information. Some years ago we had occasion to test the Humphreys spiral on the middling from our table plant. The conclusions reached in this investigation come as no surprise to us. In certain applications it is virtually impossible to improve on the spiral from the monetary returns point of view even though its "efficiency" may be low. We have noted that in all successful applications of the spiral the feed is "classified," hence we were somewhat disappointed in the showing the spiral made on the Poplar Ridge coal, the only one of the four which could really be considered the equivalent of a classified feed. As was noted in the paper, however, this coal contained a considerable amount of middle and high-gravity material, apparently more than enough to make up for the theoretical advantage of small particles in these categories. A comparison of particle size in the various specific gravity classes of the four coals is given in table XXV. Table XXV. Comparison of Particle Size in Various Specific Gravity Classes. (Unit size, 150 m to 0.105 mm) Black Eagle Clements Poplar Ridge Rosly,n 1.3 Float 7.47 10.60 8.68 9.66 1.3 x 1.4 7.89 7.96 7.58 8.20 1.4x1.6 7.24 8.36 5.58 6.85 1.6 x 1.8 7.98 8.31 3.42 7.33 Sink 1.8 7.85 7.13 5.09 7.41 Avg 7.69 10.08 7.15 8.38 This tabulation indicates that there was very little difference in the size of the various gravity fractions for three of the coals, Poplar Ridge varying the most. Examination of figs. 3, 6, 7, and 8 reveals a general similarity of behavior for all coals except Black Eagle. Would the authors care to speculate on the reasons for the difference in the distribution curve for the sink 1.60 material in the washed coal of fig. 3 as compared to the others? This difference is particularly noticeable in the 8xl4-mesh size. Was there a "shape effect"? J. D. Price and W. M. Bertholf—The performance data on three of the coals studied appear to be typical, but there are certain departures from the general pattern in the case of the Poplar Ridge coal which are large enough to deserve special consideration. For example: 1. Despite the high proportion of sink 1.60 material in the feed, it was not possible to make a corresponding proportion of high-ash reject. (See table XVI.) 2. Even though approximately 70 pct of the feed was 1.40 float with an ash content of 6.6 pct, and this

Jan 1, 1951

By R. H. Eckhouse, M. R. Geer, H. F. Yancey, C. L. Allyn

W. M. Bertholf—This is an excellent report of a well-conducted investigation, of sufficient scope to provide generally useful information. Some years ago we had occasion to test the Humphreys spiral on the middling from our table plant. The conclusions reached in this investigation come as no surprise to us. In certain applications it is virtually impossible to improve on the spiral from the monetary returns point of view even though its "efficiency" may be low. We have noted that in all successful applications of the spiral the feed is "classified," hence we were somewhat disappointed in the showing the spiral made on the Poplar Ridge coal, the only one of the four which could really be considered the equivalent of a classified feed. As was noted in the paper, however, this coal contained a considerable amount of middle and high-gravity material, apparently more than enough to make up for the theoretical advantage of small particles in these categories. A comparison of particle size in the various specific gravity classes of the four coals is given in table XXV. Table XXV. Comparison of Particle Size in Various Specific Gravity Classes. (Unit size, 150 m to 0.105 mm) Black Eagle Clements Poplar Ridge Rosly,n 1.3 Float 7.47 10.60 8.68 9.66 1.3 x 1.4 7.89 7.96 7.58 8.20 1.4x1.6 7.24 8.36 5.58 6.85 1.6 x 1.8 7.98 8.31 3.42 7.33 Sink 1.8 7.85 7.13 5.09 7.41 Avg 7.69 10.08 7.15 8.38 This tabulation indicates that there was very little difference in the size of the various gravity fractions for three of the coals, Poplar Ridge varying the most. Examination of figs. 3, 6, 7, and 8 reveals a general similarity of behavior for all coals except Black Eagle. Would the authors care to speculate on the reasons for the difference in the distribution curve for the sink 1.60 material in the washed coal of fig. 3 as compared to the others? This difference is particularly noticeable in the 8xl4-mesh size. Was there a "shape effect"? J. D. Price and W. M. Bertholf—The performance data on three of the coals studied appear to be typical, but there are certain departures from the general pattern in the case of the Poplar Ridge coal which are large enough to deserve special consideration. For example: 1. Despite the high proportion of sink 1.60 material in the feed, it was not possible to make a corresponding proportion of high-ash reject. (See table XVI.) 2. Even though approximately 70 pct of the feed was 1.40 float with an ash content of 6.6 pct, and this

Jan 1, 1951

ENGINEERS AVAILABLE (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Graduate mining engineer, with 10 years' experience, having an office in New York, would like to represent a mining company as selling and purchasing agent, and general supervision if desired. Machinery agency considered. No. 259. Member, technical graduate, with several years' experience as engineer for a pyrites company, and as geologist and engineer for copper, nickel, and silver companies, desires a position as engineer or superintendent of mines. No. 260. Member, technical graduate, aged 29, with experience as draftsman, surveyor, and superintendent of iron and gold mines, and as construction engineer, is open for a position as mine superintendent, or in mine examination or construction. No. 261.

Jan 11, 1915

FOR two days preceding the Colorado Mining Association annual meeting, officers representing all interests of the lead and zinc producers hammered away at remedies for the ills of the industry behind closed doors at the University Club in Denver. For once in the stormy history of the industry, large and small producers alike came to agreement with an automatic sliding scale stabilization import tax. The proposal set forth in full on the following page, is not new being merely an amplification of the tariff arrangement whereby tariffs are imposed when the price drops below ceiling. Its advocates claim that it is simple, automatic, and flexible. It will give stability to the industry without subsidies and since no government bureaus will be required to administer it, there will be no cost to the taxpayer.

Jan 3, 1953

By J. A. Berger, R. J. Towner

A method for determining the disorientation between sub-grains that .share a common tilt or twist boundary from measurements on X-ray micrographs is described. The method may be applied to subgrains of almost any orientation having boundary angles in the range from about 1 min to 1 deg of arc. An adaption of the Berg-Barretl method has been made to allow calculation of small angles of about 1 min to 1 deg of arc: between adjacent subgrains from the relative displacement of their images on X-ray micrographs. schulz4 gave equations for determining subgrain disorientation where the axis of subgrain rotation and the reflecting crystal planes were parallel to the specimen surface. In our method, however, they need not be parallel and, indeed, may have va:rious orientations. His camera setup, involving a fine-focus X-ray tube for obtaining high resolution with continuous radiation, was different from the one used in the present investigation (a 1.2 x 1.2 mm effective source and characteristic radiation). The X-rays produced a slight magnification in the subgrain images in the Schulz method, but not in the present method. The commonly available type of X-ray tube used permitted relatively short exposure times with a fine-grained photographic plate, which could be magnified optically many times for the examination of small subgrains. The method is illustrated by results obtained on {110} tilt boundaries in a polygonized aluminum single crystal of 99.994 pct purity. The flat crystal was stretched 6 pct in tension and then heated at 500°C for a cumulative time of 5 hr. Earlier, cahn5 studied subgrains formed by polygonization in stretched and heated aluminum crystals. He observed kink bands to have well defined boundaries lying in (110) planes, at least in the early stages of deformation. Cahn found that the (110) tilt boundaries formed by polygonization were directly related to the lattice bending about the <211> axis which lay in the (111) slip plane perpendicular to the <110> slip direction. DESCRIPTION OF THE CAMERA Our camera was similar in detail to Honey-combe&apos;s.6 Unfiltered copper radiation was used at 35 kv, and 20 ma. With the particular specimen used here to illustrate the method, a 1.2 by 1.2 mm effective source and a distance of 780 mm from target to specimen were employed, giving a convergence of 5 min of arc in the primary beam. The distance was 9.5 mm from the specimen to film. The upper 1/2- by 1-in. portion of the front surface of the specimen was irradiated with the film in parallel position. Since the specimen had been inhomogeneously deformed, many regions were in a position to reflect characteristic radiation at the Bragg Angle. Five minute exposures were satisfactory with Kodak Single Coated X-ray Film, 1 1/2 hr

Jan 1, 1961

By F. C. Sturges

[CONTENTS PAGE ................. Introduction-Grouting in Mines. By F. C. STURGES. I Use and Technique of Pressure Grouting in the Construction Industry. By V. L. MINEAR . 3 Technique of Pressure Cementing in the Petroleum, Mining, and Construction Industries. By WY. D. OWSLEY and R. E. MOELLER. ..................... 9 An Example of Controlled Pre-grouting in Shaft Sinking. By R. H. ALLEN and J. W. GALPIN. 15 ........ Solidifying Mines and Shafts Areas by Pressure Grouting. By B. H. MOTT 17 .............. Grouting in Southeast Missouri District. By W. W. WEIGEL 20] Introduction-Grouting in Mines By definition the word "grout" means a thin mortar, or a kind of plaster or cement, and "grouting" means to fill up or finish with grout. The words "cement," "plaster" and "mortar" mean a substance that is used in a soft state which subsequently hardens. Thus, grouting is the filling of void space with a substance that hardens. Construction cements are the most common substances used, either by themselves or in mixtures, but the term grouting is applied quite correctly when other substances such as plastics and certain chemicals are used. Also, the use of the term grouting to cover the filling of voids with materials that do not actually become hard, such as the flotation tailings used in grouting in the southeast Missouri lead district, should be considered correct, as some stiffening does take place and, anyway, it is a better descriptive term than any substitute. Engineers are interested in grouting because some of the materials with which they must work contain voids, and certain conditions can be improved if these voids can be filled with something solid and permanent. Grouting is done to accomplish several purposes: I. To stop the passage of fluids and gases, 2. To cement materials together to make them stronger, and 3. To prevent consolidation of materials by filling void space with something solid as a replacement for the air and water that could be forced out under load. The construction industry uses grouting extensively for all three purposes. Grouting is used to stop water percolation under and around dams. It is used to control water flow in tunnel driving and in shaft sinking. It is used to improve foundation conditions under civil engineering structures by permanently filling void space and thereby reducing settlement, or by cementing broken rock together and increasing its supporting strength. The oil and gas industry does a lot of grouting, primarily to stop the passage of gases and fluids. The search for oil at increasingly greater depths has meant greater investment per well, and the oil industry has spent large sums on development of improved drilling methods. This

Jan 1, 1947

By G. Sachs, G. Espey

SIMPLE methods can be used for the determination of the residual stresses in thin-walled tubing if the stresses consist of high tensile stresses at the one surface and high compressive stresses at the other surface Such a stress distribution is approximated in sunk tubing and in deep-drawn shells It is possible to cut sections from such articles in such a manner that a major part of the residual stress is relieved by a bending of the part that is separated from the adjacent metal The circumferential stress is evaluated from the change in diameter D, occurring on splitting a length of tubing (Fig Ib),1-5 or from deflection resulting from the cutting out of a circumferential tongue (Fig Ia) G The bending moment M released by such a flexure is [ ] The release of this bending moment corresponds to the release of stresses, which, in a thin section, vary linearly from one surface to the other, and have the following value in a particular fiber a certain distance (zx from the surface [ ] where C is the section modulus and d is the thickness of the section, the ratio AI C being d 2 for a rectangular section* The maximum stress values at the surfaces are [ ] For most purposes the simpler equations [ ] will be satisfactory, where Dm is the average of the mean diameters of the tubing

Jan 1, 1941

By J. Henry Harden

I desire to call the attention of the Institute to a new form of drawing-board trestle. With the ordinary four-legged trestle, commonly used, one has not the means of adjusting the height of the board to the draughtsman. To obviate this inconvenience, and at the same time to enable one to incline the board, I have devised an arrangement of curved and straight slots and thumb-screws, by means of which the hoard can be raised three or more inches, and placed at any desired angle of inclination on either side. Figures 2, 3 (Plate I) show side and end elevations of the trestle for a single board, and Figure 4 for two boards. The latter form is adapted for use in schools, or where it is desired to economize space.

There&apos;s a right way and a wrong way to store diesel electric systems and similar equipment for generating on-site power, according to James Frankow, service manager for Allis-Chalmers Corp&apos;s Engine Division. In any event, the less storage the better. Many generating sets are stored before installation, especially when new construction is underway. Improper storage, or mothballing, can create initial reliability problems. Therefore; arrange for inside storage with no drastic extremes in temperature or humidity. If engines and alternators are stored in areas other than inside a dirt-free and temperature-controlled building, the unit or engine should be completely covered and protected against the environment. Before covering it with a canvas or with plastic, the unit should first be sealed at the following critical engine openings:

Jan 3, 1978

By J. Henry Harden

I DESIRE to call the attention of the Institute to a new form of drawing-board trestle. With the ordinary four-legged trestle, commonly used, one has not the means of adjusting the height of the board to the draughtsman. To obviate this inconvenience, and at the same time to enable one to incline the board, I have devised an arrangement of curved and straight slots and thumb-screws, by means of which the board can be raised three or more inches, and placed at any desired angle of inclination on either side. Figures 2, 3 (Plate I) show side and end elevations of the trestle for a single board, and Figure 4 for two boards. The latter form is adapted for use in schools, or where it is desired to economize space.

Jan 1, 1874

OFFICIAL Washington is gravely concerned over the adverse military situation caused by the all-out intervention of the Chinese Communists in Korea. What the policies of the United Nations and the United States will be in the new crisis is unknown. However, Stuart Symington, chairman of the NSRB, set the general pattern for mobilization in the near future when he said that this country would move from a "light gray to a dark gray mobilization." The implications of accelerated mobilization for the mining industry are particularly apparent with respect to the manpower situation. Revised policies recently initiated for the recall of reservists may be abrogated, in which case key personnel in the mining industry may face calls to active duty with insufficient consideration given to their indispensability to national defense in their present positions.

Jan 1, 1951

By Fred C. Bond

DISCUSSION Milton C. Shaw and Donald R. Walker (Massachusetts Institute of Technology)—For many years the two empirical rules of comminution bearing the names of Rittinger and Kick have been applied to grinding processes to account for the energy required to crush brittle materials. The basis for Rittinger&apos;s rule was the thought that the energy to grind a substance went largely into supplying the additional energy associated with the new free surface, while Kick&apos;s law was prompted by the concept of dimensional similarity and is a special statement of the concept of constancy of strain energy to cause rupture. According to Rittinger the energy to grind a given volume varies as the change in the square of the mean particle size, v - A (D2), while according to Kick this energy varies

Jan 1, 1953

By Fred C. Bond

DISCUSSION Milton C. Shaw and Donald R. Walker (Massachusetts Institute of Technology)—For many years the two empirical rules of comminution bearing the names of Rittinger and Kick have been applied to grinding processes to account for the energy required to crush brittle materials. The basis for Rittinger&apos;s rule was the thought that the energy to grind a substance went largely into supplying the additional energy associated with the new free surface, while Kick&apos;s law was prompted by the concept of dimensional similarity and is a special statement of the concept of constancy of strain energy to cause rupture. According to Rittinger the energy to grind a given volume varies as the change in the square of the mean particle size, v - A (D2), while according to Kick this energy varies

Jan 1, 1953

By R. A. Greenkorn, R. C. Smith

Hele-Shaw cells are used to model creeping flow through porous media (where Darcy&apos;s law is valid). The effects of inertia on flow about obstructions in a Hele-Shaw cell can be calculated by a perturbation method if one can determine a solution to Laplace&apos;s equation. Results of a computer solution for flow about circular, square and elliptical obstructions are presented. These results show that or a modified Reynolds number of less than I, the inertia terms are small; and for values of less than 3, the average streamline predicts the ideal flow. Therefore, the analogy might be used for studying flow in porous media up to a modified Reynolds number of at least 3. INTRODUCTION The nature of fluid flow in porous media is of interest in the fields of soil mechanics, ground water flow, petroleum production, filtration and flow in packed beds. Because it is very difficult to study the phenomenological behavior of flow in porous media, homologs and analogs are used to study flow characteristics. A Hele-Shaw model, made of two closely spaced plates - usually glass — is often used as an analogy to two-dimensional flow in porous media. Hele-Shaw2 showed experimentally that the streamline configuration for creeping flow around an obstacle located between two closely spaced parallel plates is the same as for two-dimensional, ideal flow about the same obstacle. Stokes7 verified these observations mathematically. The usual equation of motion for flow in porous media is Darcy&apos;s law. The form of the mathematical statement of Darcy&apos;s law is identical, within a multiplicative constant, to the expression for the average velocity over the plate gap in the plane of a Hele-Shaw model. These models may be used to describe flow in both homogeneous and heterogeneous porous media. In the mathematical proof of the Hele-Shaw analogy it is assumed that the convective terms in the Navier-Stokes equations are negligible and that the equations of motion degenerate to Laplace&apos;s equation, with pressure the dependent variable. Whenever a Hele-Shaw model is used as an analogy to flow in porous media, .the validity of this assumption is in question. Riegels5 showed that if convection is not neglected, the velocity distribution around a cylindrical obstruction in the flow field depends on a Reynolds number, the plate spacing, and a dimension characteristic of the obstacle. Riegels&apos; solution, a perturbation solution, uses the boundary condition that the flow rate into the obstacle averaged over the plate gap at any point on the obstacle is zero. The method requires that a solution to Poisson&apos;s equation for the perturbation pressure be found. Riegels evaluated this solution for the case of the cylindrical obstruction. His method may be simplified by eliminating the need for solving Poisson&apos;s equation for the perturbation pressure. Instead, an analytic expression for the perturbation pressure gradient is obtained (valid for arbitrary shapes) and used to eliminate pressure from the equations for the perturbation velocities. The results show, for symmetrical shapes, that if NRe < 1, the convective acceleration terms are small, and that the average velocities represent ideal flow up to at least NRe = 3, where: L is a characteristic dimension of the obstacle perpendicular to flow, b is the plate spacing, u is viscosity, v, is velocity of approach and p is density. THEORY* Incompressible fluid flow through a Hele-Shaw model and a porous medium are analogous because the equations for the average velocity components in two-dimensional flow are identical if:

Jan 1, 1970

By Stephen L. Bolivar, Susan H. Balog, Thomas A. Weaver

A data-classification scheme was developed to detect potential uranium mineralization in the Montrose l º x 2º quadrangle, Colorado. The methodology developed is a rapid and efficient method of resource evaluation on a reconnaissance scale. The necessary techniques were developed and refined to digitize, integrate, and register various large geological, geochemical, and geophysical data sets for the Montrose quadrangle, Colorado, using a grid resolution of 1 km. All data sets for the Montrose quadrangle were registered to the Universal Trans- verse Mercator projection. The data sets include hydrogeochemical and stream sediment analyses for 23 elements, uranium-to-thorium ratios, airborne geo- physical survey data, the locations of 90 uranium occurrences, and a geologic map (scale 1:250 000). Geochemical samples were collected from 3965 locations in the 19 200 km2 quadrangle; aerial data were collected on flight lines flown with 3-5 km spacings. These data sets were smoothed by universal kriging and interpolated to a 179 x 119 rectangular grid (each grid block is 1 km2). A mylar transparency of the geologic map was prepared and digitized. All possible combinations of three, for all data sets, were examined for general geologic correlations by utilizing a color microfilm output. Subsets of data were further examined for selected test areas. A classification scheme for uranium mineralization, based on selected test areas in the Cochetopa uranium district, is presented. Areas favorable for uranium mineralization, based on this scheme, were identified and are discussed.

Jan 1, 1982