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By Maurice Magee

The Ducktown ore deposits have been known, explored, and mined for 120 years. Eight massive sulfide ore bodies occur in highly folded and metamorphosed graywacke, graywacke conglomerate, mica schist, chloritegarnet schist, and staurolite schist of Precambrian age. The ore deposits are tabular bodies that have been extensively folded, generally conform to the enclosing rocks, but show local complex differences. The ore deposits, ranging in size from 250,000 tons to over 20 million tons, are composed principally of the minerals pyrrhotite, pyrite, chalcopyrite, sphalerite, and magnetite. Gangue minerals are quartz, calcite, actinolite, tremolite, hornblende, garnet, and masses of schistose wall- rock. Three fault systems are present that have influenced ore control and ore body configuration. Hydrothermal effects are evident in wall-rock alteration. Evidence of retrograde metamorphism is extensive in the wall and ore associated rock. Preliminary isotopic age dates have indicated four possible metamorphic events during the Paleozoic Era. Ore genesis is considered to be hydrothermal replacement of receptive beds, predominantly highly calcareous zones, quartzitic zones, and brecciated shear zones. Ore deposition is thought to have occurred during the Devonian Period, with later mobilization and recrystallization of the ore and gangue during Middle and Late Paleozoic times.

Jan 1, 1968

By L. A. Wright, J. F. Emerson

The Pine Creek mine, owned by Union Carbide Nuclear Co., Div. of Union Carbide and Carbon Corp., is one of the world's largest producers of tungsten. The mine is located on the eastern slope of the Sierra Nevada Mountains, about 25 miles north- west of Bishop, Calif. Prior to 1948, production from the property came either from surface pits or from underground workings above A level haulage tunnel. The tunnel is at an elevation of 10,900 ft, which left 500 to 600 ft of vertical backs to the surface outcrops. Heavy production demands during World War II hastened the planning for long range development of orebodies below A level. A 7000-ft haulage tunnel, 1500 ft below A level, was started in 1943 and completed in early 1947. This haulage tunnel is at an elevation of 9400 ft and is known as Zero tunnel.

Apr 1, 1956

By D. M. Davidson, P. F. Kerr

The Permian Cutler Formation in Kane Creek, Utah bears uranium ore in fissure-type vertical veins. This fissure vein formation and its associated host rock bleaching, weak argillic alteration, and base-metal sulfide mineralization along with the development of hydrothermal minerals, a 60 m.y. isotopic Pb/U age, and well-crystallized uraninite's structural control, give evidence of ore deposition in a hydrothermal environment consistent with Laramide mineralization. Mica polymorph studies indicate first, that temperature during the hydrothermal alteration or subsequent ore deposition did not exceed 200°; hence Cutler deposits are classified telethermal; and secondly, that rock alteration and ore deposition are closely related both in time and space, as is seen in argillic alteration sequence. Ore deposition in an alkaline to slightly acid reducing environment is postulated. Ore textures and mineral associations and distributions also indicate that carbonate complexes may have been transported with the deposing ores. Bleached rock formations are not primary strati-graphic phenomena. Bleaching, or changes in ferric iron content, results from a chemical process involving reduction and conversion of hematite to a soluble aqueous ion. Nearby Chinle bedded deposits (Moss Rack sandstone), containing shale lenses, fossil wood, organic debris and minor fractures, overly the Cutler formation. Chinle ores have a single reported isotopic age of approximately 200 m.y. Their chemical environment is assumed similar to that of the Cutler ores, though slightly more acidic. Two genetic, paradoxically divergent interpretations of the bedded deposits are derived from available spectrographic, petrographic, X-ray and chemical analyses. Kane Springs canyon is located southwest of Moab, Utah, south of the Colorado River and northwest of the Lisbon Valley mining district (Fig. 1). Uranium deposits occur along the northeast flank of a Kane Creek salt anticline where two geologic formations bear ore, the Permian Cutler and the Triassic Chinle. The Cutler deposits' fissure vein formation is an unusual occurrence in the Colorado Plateau. The Chinle deposits appear to be of the normal sedimentary type. Associated with the vein deposits are a number of features, including argillic alteration of sedimentary strata. The minerals of these deposits and their associated features have been studied in detail in a two year program entailing both field and laboratory techniques. STRATIGRAPHY A stratigraphic section of the lithologic units in the Kane Creek area is given in Table I.

Jan 1, 1967

By D. W. Jessup

THE handling of native labor is offering an interesting problem that requires diplomacy. It is difficult to induce many of the men to leave their villages and enter into regular work. They do not feel the necessity of manual labor other than to obtain sufficient money to pay the annual hut tax and to buy a little clothing. The ground provides mealies (corn) which means food and beer, he hunts and catches fish, so why work? But gradually, as the native becomes more civilized, his wants increase and his ideas change; he now needs money to supply his desires and eventually he must work more. So in time it is hoped that the labor market will be better supplied.

Jan 1, 1931

Howard N. Eavenson, Gary, W. Va. (communication to the Secretary*):—For some time before the publication of Mr. Scholz's paper, I had been collecting data bearing upon its subject, and I now take pleasure in presenting to the Institute my results in the form of a discussion. It has long been a matter of common opinion among mining-men that mine-explosions are more frequent during the colder, or winter months, than during the warmer ones, and it is a matter of common knowledge among them that the air-ways and road-ways in most mines are much drier and are more inclined to be dusty during the winter than during the summer. In many mines, places which are wet and sloppy in the summer are dry and sometimes dusty during the winter. These changes, of course, can only be due to atmospheric conditions, and are caused by differences in temperature and humidity. Until recently, however, very little attention has been paid to the part that atmospheric conditions may play in mine-explosions, or, rather, to the effect they may have in rendering mine-conditions peculiarly dangerous, and in spreading and rendering more disastrous the effects of what otherwise probably would have been small explosions. To show the difference in mine-conditions during summer and winter months, I have tabulated in Table I. the results of 24 observations of hygrometric conditions in several different mines at different times of the year. Mines Nos. 1, 2, and 6 are located in the Pocahontas coal-region, in McDowell county,w.Va., the first one being a shaft-mine and the others drift. Mines 1A and 2A are drift-mines located in Logan county, W. Va. All of these are mines of fair size, but none of them has been in operation more than six years,

Jan 1, 1910

By Clyde E. Williams, JAMES L. GREGG

THIS review of the past year's progress in iron and steel metallurgy presents examples of only a few of the interesting or important accomplishments made in the United States. In the field of iron ore concentration increased attention was given to the study of the more difficultly separated wash ores and some progress was made in tabling. One difficulty with the table, in concentrating iron ore where the percentage of concentrate in the feed is large, has been the removal of fine silica from the thick layer .of concentrates in the cleaning zone. One company has -Made an important contribution toward the solution of this problem by an extension of the well-known plateau principle. By a special riffling of the plateau section of the table, the concentrates are crowded together. This action forces the fine silica to the top of the bed in the cleaning zone, whence the cross-flowing currents of water -can wash it into the middling product. Some work has been done on the application of froth flotation to the concentration of iron ores. Laboratory experiments were made at the Colorado School of Mines in which hematite was, successfully floated. Using oleic acid as a frothing and collecting agent and sodium carbonate as the conditioning agent, a high recovery of rich ,concentrate was obtained. A laboratory flotation unit is in use at Taconite, on the Mesabi range, and a commer-

Jan 1, 1932

By Kirtley F. Mather

FROM almost every point of view, petroleum was "strategic mineral number one" during the World War that ended in 1945. Even the spectacular advent of the atomic bomb in the final days of the conflict did not displace it from its position of prime importance, although within a few years uranium will almost certainly be the "number one" material in the minds of military strategists, if it is not even now in that position. But both as fuel and as raw material for chemical industries, petroleum will hold the center of the stage for many years to come. Hardly any other substance illustrates so fully the manner in which science and technology may be combined to achieve the utmost success in contributing to human efficiency and comfort. Fundamental to any understanding of the problems implied by my topic

Jan 1, 1948

By C. W. Davis

THE name fuller's earth, which was derived from its early use in "fulling" or removing grease from woolen goods, is a term that is generally considered to designate mineral matter, containing hydrous aluminum silicates of the clay group, which has a high capacity for removing colors from oils, whether of animal, vegetable, or mineral origin. Fuller's earths are usually dried and may be "tempered" by heating or may be treated with water or reagents to improve their efficiency. For our purpose the term "acid-treated earths" will include those products from the partial decomposition of mineral water -by acid which are equal to or more efficient than an untreated fuller's earth from Quincy, Fla., when used in bleaching mineral oil by the "contact" process. In general, the contact process for treating oils consists of heating and agitating a mixture of oil and finely divided adsorbent, the latter being subsequently removed by filtration. The term "adsorbent" is used because, although there has been a great deal of controversy over the mechanism of removal of impurities from oils by mineral matter, there is no doubt that adsorption, which involves the surface of the solid, plays a major part.1 The properties that make fuller's earth useful in the treatment of petroleum products by "percolation" and in the purification of edible oils by the contact process have long been studied, but the comparatively recent adaptation of the contact process to the bleaching of petroleum products has made desirable the further investigation of fuller's earth and other, adsorbent earths.

Jan 1, 1929

By Dever C. Ashmead

COAL companies in the anthracite region are studying various methods of mining that will permit a considerably shorter life of gangway and therefore a decrease in the maintenance charges. Maintenance charges in the upkeep of gangways where the measures are steeply pitching are high due to the excessive cost of the replacement of timbers and the cleaning up of falls. Therefore, if the length of gangway in the coal beds can be decreased and the mining more concentrated, the life of the coal gangways will be decreased and consequently the maintenance charges will be lower per ton of coal produced. Customary practice in the anthracite region is to drive long coal gangways and to work the breasts as the gangway from which they were driven is advanced.

Jan 1, 1925

By Robert Pack

INTRODUCTION SOONER or later in the development of any natural resource it becomes highly desirable to know the quantity of this resource in the country as a whole, as well as of the part that is being developed, for the general course and. conduct of the development work must be governed to some extent by the total supply available. An accurate estimate of the quantity of any natural resource is difficult to make; yet if one is diligent enough one can obtain a pretty accurate idea of the quantity of marketable timber, the acreage of tillable land, or the horsepower that may be developed from the streams, for these are things that may be measured. But any attempt to estimate the quantity of some mineral in the ground appears to enter the realm of imagination and it seems that the estimate can be nothing more than a blind guess. It may appear to be especially futile to attempt to determine the quantity of oil and gas that is available in the ground, for these minerals are so vagrant that even if the quantity now available should be known quite exactly, the quantity that will eventually be obtained may be much less, for certain losses in the extraction of both oil and gas are unavoidable, and just what these losses will be cannot be predicted. Though necessarily inaccurate, estimates of such mineral reserves are, however, of distinct value, for they summarize the existing knowledge of the deposits of the mineral and thus enable those who are interested in some industry that depends in one way or another on this mineral to formulate a rational commercial policy. Some time ago, when the price of gasoline suddenly rose in a rather spectacular manner, the writer was one of the U. S. Geological Survey geologists called upon to help to estimate the quantity of oil that could be obtained in the United States, for the fear had become widespread that perhaps the rate of increase in the price of gasoline was a measure of the rate of depletion of the supply of petroleum. It thus became his

Jan 8, 1917

By GEORGE H. DERN

IF THE engineer is to go into politics, as I think he should, I believe the curriculum of every engineering school should be amended to include a good stiff course in public speaking. My observation has been that the engineer in private conversation can scintillate as brightly as a life insurance agent or an oil stock salesman, but before an audience, with rare exceptions, he is a total loss. He will not get up and talk. He hides his light under a bushel, and sits on the bushel as dumb as an oyster. I have seen meetings of the Utah Section at which some topic of general interest to the members was up for discussion, and where an animated debate was the logical thing to expect. After the chairman states the subject and invites discussion, there is dense silence. Finally a member, bolder than the rest, gets up and with trembling voice and knees makes a motion. The motion carries, the meeting adjourns, and then the members gather into groups and begin to discuss the question seriously -and intelligently, giving cogent arguments on either side and embellishing their remarks with appropriate or inappropriate epithets illustrations and figures of speech. Now, I am not pleading for more speechmaking. The good Lord knows we have too much of this great American indoor sport already. But I think every man ought to be able and ready to express his opinions at the proper time. Some men have a reputation for wisdom because they do not talk much. We speak of the wise old owl because she never speaks, but in my opinion the owl's reputation for wisdom is vastly overrated. silence is more apt to be a cloak for stupidity than for wisdom. The person who has ideas can- not exert any influence by keeping them locked up in his own mind. The great motive force of the world is not muscle, but ideas, and ideas in order to get in their work must be released.

Jan 1, 1925

By A. L. Holley

There is a growing demand for pure and cheap material for fine open-hearth steel; a material not only very free from phosphorus, but from carbon and silicon; so that it may he rapidly converted into steel. Iron and steel scrap are not trustworthy as to quality, and they are often dear. There are three methods of purifying cheap materials for the open hearth. 1. Mechanical puddling, as done at Creusot, which removes 90' per cent. of the phosphorus from the pig iron. 2. Krupp's washing process (the conduct and results of which 1 fully described in a former paper*), which eliminates 70 to 80 per cent. of the phosphorus and most of the sulphur and silicon from pig iron. Neither of these processes would sufficiently purify, for very fine steel, those very impure pigs which are cheapest in many parts of the United States. 3. The process of producing directly from the ore an iron which is practically pure chemically, although mechanically mixed with the impurities of the ore. This is the oldest of iron processes ; one form of it, the CataIan forge, employed to produce charcoal blooms, is still in use, but its great cost is rapidly throwing it out of competition. Among the modern attempts to produce iron direct from the one, on a large scale and at a cheap rate, several have been in various respects successful. Dr. Siemens's process of treating a ton and a half or more of ore and the coal to deoxidize it, in a rotating gas furnace, and bringing out, in some four hours, a ball of chemically pure iron so soft that the fluid and impure slag may be sqneezed out of it, is the most attractive and the most highly developed of all the modern direct processes. I hare watched it, from time to time, since 1874, and have noted a steady improvement. It may now be said to have passed the experimental stage, although, like older processes, it must be adapted by practice to special materials. The cause which has been more potent than all others, including the defects of the best direct processes, to bring these processes into disrepute, is the wasteful treatment of the direct product. With one or two exceptions (when failure mas due to other and obvious causes), the direct product has been made into wrought iron (weld iron). Even Dr. Siemens has, at Towcester, in England, and at Park, Bro. & Co.'s, in Pittsburg, set up his apparatus for this purpose. Is it likely that

Jan 1, 1880

PAUL. D. MERICA, Bayonne, N. J. (written discussion*)..-The mode of intercrystalline oxidation which the authors" have so well observed and described is characteristic of nickel that has been exposed' to: the action of an oxidizing atmosphere at higher temperatures, such as, those at which; it is annealed or heated for rolling or forging. Oxidation under such conditions proceeds inward from the surface along the, crystal boundaries' producing a net-work, probably of oxide; which causes a very brittle condition of this surface material. This, in turn, generally results in surface cracking and checking during further, rolling and a defective sheet or other product is produced. An example of this is shown in Fig. 2, which shows the surface, of a badly surface-cracked sheet of nickel produced by incorrect heating con-ditions. A cross-section of this sheet etched with nitric acid is shown in Fig. 1, which reveals the intercrystalline oxidation network adjacent to both surfaces.These layers are so brittle that it is not possible to deform them by rolling without severe cracking along these lines or, planes of weakness. The best, and possibly only, remedy for this condition lies in its prevention by the maintenance of a neutral soft flame for heating and annealing nickel during the entire course of its manufacture. I should like to suggest that, those making microscopic investigations of nickel and nickel-rich alloys try the use of acetic-acid .solutions of nitric acid for etching these metals rather than aqueous solutions, of nitric acid. I have found that a solution containing 50 per cent. nitric acid, from 25-45 -per. cent. acetic acid, and from 25-5 per cent. water gives excellent results with. Wrought and cast nickel and Morsel metal and superior results to those obtained with nitric acid, alone. The acetic. acid seems to inhibit the passivity that nickel often assumes toward nitric acid and much more uniform etching may, be obtained. The proportions of nitric and acetic, acid may be varied somewhat from those given without mate-rially altering the quality of the etching, although without any distinct improvement in it.

Jan 12, 1919

By R. L. Caldwell, E. E. Glenn, L. J. Norton, A. J. D. Straus, S. V. Holcomb, J. Zemanek

A new and unique logging tool, called the Borehole Televiewer (BHTV), has been developed to inspect boreholes and to evaluate formations. Even though geologists and engineers have had only about 3 years' experience with the BHTV, the thinking of many of them has been radically influenced by the fascinating and revealing "log-picture" recorded with the tool. The BHTV fills a need for a logging tool that can produce a direct and descriptive record of the physical properties of the borehole environment. Although primarily developed to evaluate fractured reservoirs, the BHTV has been used successfully to solve a variety of problems related to formation evaluation and borehole inspection. Geologists and petroleum engineers have been confounded for many years by the problems of locating and evaluating fractures. Interpretation of the usual resistivity, acoustic or radioactivity logs, as well as the analysis of cores, for evaluation of fractured reservoirs is extremely difficult and often not definitive. This is understandable since analysis of cores from fractured formations has reported variously: (a) low porosity, (b) no effective permeability, (c) lack of any matrix oil saturation and (d) oil stains on fracture planes as the only indications of potential production.14 In recent years acoustic amplitude logs have been introduced and used with varying degrees of success to locate fractures.8'9'11"13 Conventional amplitude logs at best give only qualitative answers where quantitative ones are desired. The logs reveal nothing of the orientation of the fractures. In addition to these logs, various types of cameras, television, and rubber impression packers have been used for borehole inspection. (See Appendix.) The BHTV logging tool supplies both the quantitative and the orientation answers about fractures. The borehole can be filled with any homogeneous, gas-free liquid such as fresh water, saturated brine, crude oil or drilling muds. This tool takes an "acoustic picture" of the borehole wall. The resulting log is a representation of the borehole wall as if it were split vertically and laid flat. The log is oriented with respect to magnetic north. Any physical changes in the borehole wall are seen as changes in picture intensity. In this way, fractures, deformation or pits are reflected on the log. Tool Description The fundamental parts of the BHTV are shown in Fig. 1. A piezoelectric transducer probes the borehole wall with bursts of acoustic energy. A flux-gate magnetometer senses the earth's magnetic field and provides the means for determining the orientation of the log. A motor rotates the transducer and mag-

Jan 1, 1970

NEW YORK SECTION J. E. JOHNSON, JR., Chairman EDGAR RICKARD, Vice Chairman D. M. LIDDELL, Secretary, 7 Wall St., New York, N. Y. C. A. BOHN, Treasurer JOHN V. N. DORR LEWIS W.. FRANCIS The following minute was unanimously passed at a meeting of the NEW YORK SECTION AMERICAN INSTITUTE OF MINING ENGINEERS held on the evening of June 6, 1917, two regular meetings having been adjourned by unanimous consent until this date out of respect to the memory of the late Chairman of the Section. Minute The death of our beloved fellow member DR. DAVID H. BROWNE one of the foremost metallurgists and one of the most brilliant and original thinkers in the profession of mining engineers, the chairman for the past two years of this section, has caused throughout a wide circle of

Jan 9, 1917

By AIME AIME

THE PAPER, "Surface Effects on Assay Beads Caused by Metals of the. Platinum Group," presented by J. L. Byers, before the Institute of. Metals Division at the February meeting of the Institute, is the subject of interesting discussion, an abstract of which follows. The original paper is available at Institute headquarters as a Preprint. Member-What assurance have you that the percentage of metals, as stated, is really an accumulation?

Jan 1, 1932

By O. J. Hollister

Jan 1, 1888

By R. P. Fischer

The Colorado Plateau region has been the principal domestic source of uranium, vanadium, and radium. The value of these commodities produced from the region through 1964 slightly exceeds $2 billion. Most of the deposits occur in streamlaid lenses of sandstone in the Chinle and Morrison Formations. The ore minerals below the zone of oxidation are low-valent oxides and silicates of uranium and vanadium; all of these, except the quite stable vanadium silicates, oxidize readily to a variety of high-valent uranium and vanadium minerals. The ore minerals partly replace fossil wood but mainly impregnate sandstone, typically forming tabular ore bodies that are nearly concordant to the bedding of the host rock. The deposits range in size from those containing only a few tons of ore to those containing more than 1 million tons. Stratigraphic, lithologic, and sedimentary structural factors obviously influenced the localization of these deposits, but igneous activity, hydrothermal mineralization, and tectonic structures show no similarly consistent influence on localization. The deposits are epigenetic, but the source of the ore metals, the nature of the ore-bearing solutions, and the time of ore emplacement are uncertain. A few uranium deposits in the region are dominantly discordant to bedding and occur in collapsed breccia pipes or along linear fractures. Their origins are also uncertain.

Jan 1, 1968

By F. C. NINNIS

AT THE Belmont mill, the pregnant solution is de¬livered to a 30 by 10-ft. tank, from which it is pumped to three Merrill clarifying presses of the sluice-bar type, whence it flows through the meter to the precipitation supply tank. ?The solution for precipitation is pumped by a 10 by 10-in. Aldrich triplex pump and delivered through a 6-in. line to the forty-eight triangular frame Merrill presses at the head of the mill. Zinc dust is fed in at the pump suction and the solution precipitated to 0.01 to 0.02 oz. silver. The solution flowing from the presses is tested at 1-hr. intervals with sodium sulfide. All solution is precipitated to the same value; 4J tons of solution are precipitated for each ton of ore treated and the presses are cleaned every 15 days. The product from the presses' is dumped into steel cars having steam-jacketed bottoms, in which they are dried until the moisture content is between 15 and 17 per cent. when 8. per cent. of soda and .3 per cent. of borax are added and the contents thoroughly mixed. In the case of special clean-ups, the precipitate is tested and the flux is added to meet the requirements.

Jan 1, 1921

By E. A. Hopkin

Laboratory tests conducted by the author. together with actual field experience in Canada. have indicated the magnitudc of some of the factors affecting ability of drilling mud to clean the hole. A correlation was observed between funnel viscosity and particle slip velocity. A relationship was also observed between the Bingham yield value of the mud and the particle .slip velocity. Laburatury tests indicated little change in slip velocity with funnel viscosities up to ahout 80 sec/qt or to yield values of aboul 15 lb/100 .sq ft. The lip velocity of the partic1e.s. studied vuried from 160 ft/min with water to neerly zero for high mud viscositie. lncreasing the mud density, creating laminar annular mud flow or rotating the drill pipe Mlay also improve the carrying capacity of mud. Field tests indicated that during fast upper-hole drilling, the rate of cutting removal must he sufficien to maintain the concentration of cuttings in the annulus at less than 5 percent by volume to prevernt balled-up drill collars and .stuck drill pipe. INTRODUCTION In the Mid-Continent area, hole cleaning during rotary drilling normally involves the use of low-density drilling muds with funnel viscosities varying from 26 to 80 sec/qt. However, frequently it is necessary to raise the mud viscosity in excess of 200 sec/qt to clean the hole. In addition, field experience has indicated that during very fast upper-hole drilling, annular mud velocities considerably in excess of the maximum slip velocity of the cuttings (normally considered to be 120 to 150 ft/min) are necessary to prevent balling the bit and drill collars. In view of these variations in mud properties and circulation rates necessary to clean the wellbore, a study of factors affecting hole cleaning and the relative magnitude of each was undertaken. The study was also prompted by the knowledge that a drilling mud with properties close to those of water would drill at rates several times that of a viscous mud. The carrying capacity of these near-water muds was not clearly understood, however, and many drillers were reluctant to use them. DISCUSSION EFFECT OF MUD PROPERTIES ON DRILLING RATE The effect of mud properties on drilling rate has been studied by a number of investigators. 1t is clear from their work that mud properties close to those of water will significantly improve drilling rate and bit life. If the water-type mud will also effectively clean the hole and cause no logging or formation impairment problems, the choice of an appropriate drilling fluid is clear—use water. Often, however, a water-type drilling fluid is not capable of effectively cleaning the hole. THEORY OF PARTICLE SETTLING The forces acting on a particle that is allowed to settle through a fluid quickly reach equilibrium, and the particle settles at some constant velocity referred to as the slip velocity. The slip velocity of any particle depends upon a number of factors such as density and viscosity of the fluid, the volume, specific gravity, shape and roughness of the particle, and upon the shape and area of the projected face of the particle at right angles to the direction of relative fluid solid movement. Brown' expressed this relationship for spheres in Newtonian fluids in the following equation. where v, = slip velocity D, — diameter of sphere p, = density of spheye p, = density of liquid /a = friction factor g = constant. The friction factor f, varies as the size, shape, surface roughness and slip velocity of the body, and as the density and viscosity of the fluid varies. WaddelV ound experimentally that where dynamic similarity exists. f, was a function of the particle Reynolds number (NRe) of the sphere (Fig. 1). Fig. 1 shows that f, for spheres varies from over 10 for low NKe numbers to 0.44 for N,,. over 600.