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By William H. Schiffbauer, Ph. D. Mowrey

Proximity warning devices can improve workplace safety by alerting workers when they are in a hazardous area near moving equipment. Industrial work sites often present extreme challenges to safety-based proximity warning devices. Many commercially available types of proximity warning sensors and systems can be rendered useless when covered with mud, ice, snow, ore, rock, and other material. The list includes radar, ultrasonic, capacitive, and visual types of sensors and systems. Addressing these shortcomings, NIOSH personnel have developed a patented active proximity warning system called HASARD (Hazardous Area Signaling and Ranging Device) which employs lowfrequency, low-power magnetic fields which are quite impervious to severe environmental conditions. A shapeable wire loop antenna which provides the marker of dangerous work areas, has been mounted on a continuous mining machine and was mounted inside 1.3-cm thick angle iron. This loop antenna was exposed to more than six months of active underground coal production, which included being covered by and scraped over with tons of rock, sprayed by a continuous stream of water, and immersed in thick mud. After six months the loop antenna showed signs of wear, but was still capable of performing its intended function. The HASARD system is now being applied to other industrial applications and is showing much promise, especially in harsh environments. This paper details the system, describes the tests that have been done, and mentions other areas where it can benefit the safety of industrial workers.

By Paul McIlroy

Costs of producing lead from various known resources in the United States are developed by the Bureau of Mines to define the future availability of domestic lead at various price levels. It is estimated that 60 million tons of primary lead (75 percent of the total resource) is available at $0.20 or less per pound; 72 million tons (90 percent of the total) is available at $0.50 or less per pound; and the 79 mil- lion ton total estimated resource can be obtained at a price or $1.82 or less per pound. The supply available at $0.20 per pound or less will meet demand for over 78 years at the 1970 annual consumption rate of 763,000 tons.

Jan 1, 1974

By L. C. Marchont

This Bureau of Mines report tabulates data on nitrogen-gas reservoirs and isolated occurrences of inert gases in several Williston basin oilfields. Recoverable reserves of nitrogen gas in the Minnelusa nitrogen interval within the areas of five oilfields on the Nesson anticline in North Dakota are estimated at about 1.27 trillion standard cubic feet, based on computer analyses of logs from over 300 wells. This volume of nitrogen represents a large source of high-pressure inert gas and warrants consideration of possible application in oil-production operations. Drill-stem tests made in two of the fields indicated that nitrogen can be produced at rates up to 28 million cubic feet per day.

Jan 1, 1966

By Roy L. Wilfong, LeRoy R. Furlong, Louis P. Domingues

The bulk and apparent densities , particle size , and surface area of ceria powders derived from the ammonium sulfate , carbonate , nitrate , oxalate , and sulfate salts and heated at 950 ° to 1,500 ° C for 1 to 24 hours were studied . The bulk and apparent densities and particle size generally increased , and surface area decreased with increase in temperature and time of heating ; surface area was more sensitive to changes in temperature and time than the other properties studied . These properties of the ceria powders had a marked dependence on temperature and a lesser dependence on duration of heating at a given temperature ; and the source of oxide and thermal treatment cannot be considered optional in the preparation of refractory powders by thermal decomposition . The ammonium sulfate and sulfate salts heated at 950 ° and 1,200 ° C produced oxide powders with the lowest bulk density , the smallest particle size , and the highest surface area . The highest apparent densities were achieved for oxides resulting from the carbonate and the sulfate but the carbonate - derived material was considerably coarser . The surface areas of ceria powders derived from cerium salts decrease in the order of sulfate , ammonium sulfate , nitrate , oxalate , and carbonate . The observation of these physical properties are useful in predicting the sintering behavior of various oxide powders .

Jan 1, 1964

By W. W. Adams

"Accidents at coal mines in the United States in September 1926 resulted in the loss of 170 lives, according to information furnished to the Bureau of Mines, Department of Commerce, by State mine inspectors. Of this number 125 occurred at bituminous mines and 45 in the anthracite field. As the bituminous output of coal for September was 48,976,000 tons, and the production of anthracite was 8,444,000 tons, the fatalities reported represented a death rate of 2.55 per million tons for bituminous mines and 5.33 for anthracite mines. The industry as a whole showed a fatality rate of 2.6 per million tons of coal produced in September 1925 the rate for bituminous coal mines was 3.29; the anthracite mines were idle in September last year due to a strike.During the first nine months of the present year 1,759 men have been killed by accidents at the coal mines throughout the United States, resulting in a death rate, per million tons of coal produced, of 3.76 as compared with 3.95 for the same period in 1925. Reports for bituminous mines alone showed a nine-month fatality rate of 3.53 which was about the same as the corresponding rate from January to September in 1925. The anthracite rate for the present year, however, shows a decrease of about 17 per cent; that is, the rate has declined from 6.36 to 5.28.Records covering the first nine months of 1926 show that 12 ""major"" disasters, that is, disasters in which five or more men were killed at one time, have resulted in the loss of 271 lives as against 10 disasters and 199 deaths in the corresponding months in 1925. The fatality rates for these disaster: alone were 0.579 and 0.465, respectively. One major explosion occurred at Tahona, Oklahoma, on September 3, 1926, in which 16 men lost their lives.An analysis of the principal causes of the 1,759 fatalities for the first nine months of the present year shows a reduction in the death rate as a whole and for falls of roof and coal and for explosives, but an increase in haulage, gas and dust explosions, and electricity. The comparative rates for these accidents were:"

Oct 1, 1926

By B. H. Caudle, A. D. PUCKETT

This paper summarizes precent knowledge of the ignition qualities of pure hydrocarbons likely to be present in modern Diesel engine fuels, as shown by an extensive search of the technical literature. The report also discusses the possible significance of cetane number and hydrocarbon struc- ture. Cetane or cetene numbers, and other physical properties, are tabu- lated for about 100 hydrocarbons, and a bibliography is appended. In recent years the Diesel engine has enjoyed increasing popularity due to its dependability, inherent characteristics of fuel economy, and the fact that it operates on a fuel that hitherto has been available in comparatively large quantities at a low price. These qualities have en- abled the compression-ignition engine to compete very favorably with other types of prime movers in many fields and have led to predictions of fur- ther rapid expansion in the application of Diesel power. In a survey of the field of all petroleum fuels for combustion engines, Holaday et al (9) have predicted that by 1948 railroads will be using 10 times as much Diesel fuel as was used in 1939 and that over-all consumption will have doubled that of 1939. Other estimates of the yearly demand for Diesel fuels five years hence vary from 2,6 to 5 times the amount used in 1944. Into this picture has come the question of whether the greatly in- creased production to meet this estimated demand is compatible with the maintenance and possible improvement in quality of fuels necessary to satisfy future engines. Unfortunately perhaps for the Diesel engine, factors other than those of simple arithmetical multiplication must be considered. For example, the consumption of oil in central heating plants doubled from 1935 to 1943, and a further increase of 57 percent of the 1943 demand is expected by 1950. Jet propulsion has been developed to the stage where it is entirely practical for military aircraft. Catalytic cracking plants, many of which were constructed to meet the war- time accelerated demand for high-octane gasoline, are taking their place in the refining industry. All these developments, as well as the Diesel engine, require material of approximately the same boiling range. Virgin gas oils make excellent burner fuels, perform most satisfactorily in the gas-turbine units for aircraft according to present information, and are at a premium as catalytic cracking stock.

Jul 1, 1948

By E. V. Cilento, R. C. Laotz, K. A. DiGregorio

"PULMONARY ALVEOLAR macrophages (PAM) protect the lungs by providing a first line of defense against inhaled foreign debris and bacteria. In this role PAM phagocytize foreign matter, secrete enzymes that augment microbial killing and digestion, and produce reactive oxygen me-tabolites (2, 3, 18, 19, 22, 26). However, in addition to this antibacterial function, PAM participate in a diversity of functions, such as tissue repair, lipoprotein metabolism, and immunoregulatory activities (11, 22).Studies have suggested the existence of a heterogeneous population of PAM with respect to immunologic function, enzyme release, phagocytosis, morphological characteristics, expression of membrane receptors, ad-herence, and superoxide (O2•) release (4-7, 10, 16, 21, 23, 28). This heterogeneity has been observed by analyz¬ing subfractions of PAM separated by cell density frac-tionation. For example, using guinea pig PAM, Dauber et al. (7) showed heterogeneity in cell density and size, morphological characteristics, and cytochemical properties, whereas Holian and co-workers (16) reported variations in migration, chemotaxis, O2• release, and pinocytosis among subfractions collected. Similarly, O'Neill et al. (21) observed functional heterogeneity in rat PAM with regard to phagocytosis, O2 • release, and lysosomal enzyme activity.Several investigations have reported a correlation between PAM activity and cell volume. Most studies have shown that O2 release from PAM increased with decreasing cell size (15, 21, 25), although Bielefeldt Ohmann and Babiuk (4) reported a decreasing trend. However, Gallin (13) has suggested that significant variability may even exist within density-defined or cell-volume subfractions that could lead to misinterpretation of results concerning PAM heterogeneity.A better understanding of the heterogeneity in O2 production may be obtained by using single cell meas-urements to evaluate whether functionally distinct sub-populations actually do exist. As such, the present study was designed to examine heterogeneity in O2 • release from single PAM using a recently developed electrooptical technique (8). The initial oxygen metabolite, O2•, produced by NADPH oxidase at the surface of the plasma membrane, was measured by quantifying the reduction of nitro blue tetrazolium (NBT I to a diformazan precipitate. Measurements were made from video recordings of individual cells stimulated by their adherence to the bottom of a culture dish. The cell volume and degree of spreading also were determined directly from the same video recordings, and the data were correlated with the initial rate and maximum amount of diformazan produced by the same cell."

Mar 1, 1992

By D. H. Baker

THIS REPORT presents the technique and equipment used in determining the hardness of titanium sponge. Detailed descriptions are given of the methods used in preparing test samples for chemical analysis and hardness testing, the method of melting and surfacing test ingots, and the technique of reading Brinell-hardness impressions. The arc-melting furnace described, for which engineering drawings are included, will produce from 70 to 90 double-melted buttons each 8 hours of operation. Experimental data are also presented depicting the effect on hardness of the methods of surfacing specimens, temperature of test specimens, and the effect of time at test load. These data show that surfacing of the specimen involves no critical machining operations but that the test surface must be paralleled by a relatively flat surface for contact with the anvil of the Brinell tester. The heating of a specimen to 150° C. during surfacing does not materially affect the results if the ingot is cooled to room temperature before the hardness impressions are made. The optimum time at load appears to be approximately 30 seconds, but load times of as much as 1/ ½ minutes will not cause major errors.

Jan 1, 1959

By E. M. Tignor

As a part of the program of promoting the conservation and efficient utilization of petroleum, studies are being made by engineers of the Bureau of Mines on secondary oil-recovery projects throughout the United States. In furthering that aim, engineering data concerning the reservoirs, methods of stimulating the production of oil, and other pertinent facts are collected, studied, and subsequently published so that others may profit by the experience gained. This report presents the results of a study made by engineers of the Franklin, Pa., office of the Bureau of Mines of secondary oil-recovery operations in the Boggs field, Spencer district, Roane County, W. Va., whore natural gas is injected into the reservoir to stimulate the production of oil from a so-called stripper field. The Boggs field, like most others in the Appalachian region, is one in which the major part of the natural energy that caused oil to flow through the reservoir to the producing wells during the primary stage of oil production has been dissipated. For all practical purposes, most of the oil produced in the Appalachian region at the present time can be considered to be from stripper fields. Consequently, secondary recovery methods are being used extensively in the oil-producing areas of New York, Pennsylvania, West Virginia, Ohio, and Kentucky for recovering some of the oil that was not produced by primary production methods.

Jan 1, 1949

By F. D. Stevenson

A metal diaphragm pressure relay system was constructed to measure vapor pressures of the metal halides, oxyhalides, and other substances at temperatures up to 700° or 800° C. The vapor pressure of arsenic (III) oxide (As2O3) was determined to verify the reliability of the apparatus for such measurements. The data for the liquid AS2 Os (2820 to 4830 C) are represented by the equation, log Pmm = 6.875 - 2,929/T, from which the normal boiling point was calculated to be 461° C. The heat of vaporization calculated from this equation was 13.40 ±0.09 kcal/g mole As4OS and is essentially constant over the interval studied. The melting point of the octahedral arsenic (III) oxide was determined to be 278° C from the inter-section of the solid and liquid vapor pressure curves, A thermal analysis apparatus is also described by which melting and transition temperatures could be checked by a method independent of vapor pressure data. The melting points of the monoclinic and octahedral forms were determined to be 314.4 ±1.4° C and 278 ±5° C, respectively.

Jan 1, 1963

By H. Kenworthy

A zinc-pyrite ore from the Gray deposit in Jo Daviess County, Ill., was successfully concentrated on a laboratory scale. Initially, drill cuttings were submitted for separation of zinc and iron concentrates. Subsequent to mine development, a large sample of coarse ore was submitted to ascertain its amenability to sink-float treatment to produce a low-grade zinc-iron concentrate and discard a clean tailing. The samples of ore were submitted to the Rolla Metallurgical Branch by the Mining Division of the Federal-Bureau-of Mines. They were obtained during the recent war as a part of the extensive government program to increase metal production through exploration for new mineral deposits and investigation of old mineralized areas. The first sample consisted of about 3,000 pounds of drill cuttings collected, during the Bureau?s churn and diamond- drilling program. The second sample was taken at a later date, after Tri-State Zinc, Inc., had opened the deposit and commenced milling the ore. This sample consisted of a ?ton-of mill feed crushed through 2 inches and collected over a period of 3 days.

Jan 1, 1949

By Brian G. White

The Coeur d'Alene Mining District of northern Idaho is remarkable for its number of large ore bodies and for the amount of its historical production of lead, zinc and silver (Fig. 1). Since veins were first discovered in 1884, more than 127 Mt (140 million st) of ore have been produced from narrow, high-grade veins. Mining continues at the Lucky Friday, Galena and Sunshine mines (Fig. 2). All have been in production for decades. At these mines, more efficient mining and exploration techniques have reduced costs while adding significant new reserves. Even the old Bunker Hill Mine, where ore was first found in 1875, continues operation on a limited basis, partly involving production of world-class pyromorphite specimens. Until recently, the Coeur Mine was also a profitable silver producer. Other large producers have included the Star-Morning, Hecla, Page, Standard-Mammoth, Hercules and Gold Hunter mines (Fig. 2). The first deposits were discovered by prospectors who spilled over from the Murray gold mining district, 24 km (15 miles) to the north. The Bunker Hill Mine was founded the year after the first veins were discovered. Bunker Hill has now operated for more than 100 years. Production includes 2.3 Mt (2.6 million st) of lead, 1.1 Mt (1.2 million st) of zinc and 4.1 kt (132 million oz) of silver. Total district production through 1996 (Springer, 1997) amounted to 7.3 Mt (8.1 million st) of lead, 3 Mt (3.3 million st) of zinc, and 34.5 kt (1.109 billion oz) of silver. This record establishes the district as the largest recorded producer of silver in the world, while also yielding major quantities of lead and zinc. Only Potosi, Bolivia, may have produced more silver, although records are unclear. Despite the district's longevity, historic production and current activity, the published literature on the district lags behind with regard to recent concepts of district geology. The most recent comprehensive US Geological Survey (USGS) bulletins (Hobbs et al., 1965; Fryklund, 1964) are dated. Much research in the last half century has been short-lived or geographically restricted because the district is large and its geology is complex - and even this research tends to remain unpublished. Thus, it has been difficult for in- [ ]

By V. A. Nieberlein

This paper presents the results of research undertaken to recover titanium and columbium by low-temperature chlorination of low-grade columbium-bearing ilmenite concentrates, and to simultaneously remove chlorinated impurities from the volatile chlorides without resort to distillation. Coke-reduced ilmenite was chlorinated at 400° to 500° C., and the resulting TiC14 was free of most impurities before condensation. A heated purification column was used wherein various packing materials reacted chemically or physically with the impurities which passed through them in the vapor phase. A nearly water-white TiC14 product was obtained directly. The principal impurities in the titanium tetrachloride were: 0.02 percent Fe, 0.01 percent V, 0.05 percent A1, 0.04 percent Si, and 0.07 percent Cb. This is a less pure product than commercial TiC14. Most of the columbium was recovered as crude CbC15, requiring further refining.

Jan 1, 1960

By J. M. Mutmansky, S. Padmanabhan

"The subject of quartz occurrences in respirable coal mine dusts has been of increasing concern in recent years. The primary impetus for this concern has been provided by better measurement technology that has detected an increased number of mines with high quartz content in their respirable dusts. This paper presents the results of statistical analyses of quartz levels in multi-stage impactor samples from eighteen different coal mining sections located in Pennsylvania, West Virginia, Ohio, Illinois, Kentucky, Colorado and Ucah. The quartz and kaolinite determinations were then determined by combining impactor stage loadings to provide larger dust masses and applying the infrared spectrometry procedure outlined in Bureau of Mines/MSHA Method P7.The results will be presented using two categories of data collected during two separate phases of the research:(l) quartz concentration data from mines where quartz was known to be present in relatively high concentrations, and(2) quartz concentration data from mines chosen at random.The aspects of the occurrence of quartz in coal mine airborne dusts that will be reported include the size dependence of the quartz content, quartz variations with location in the mining section, and variations due to mining region. The results of the study show a strong pattern of size dependence of the quartz content in mines for which high quartz concentrations exist. A similar, though less pronounced, pattern exists in mines chosen at random. Quartz levels appear to have a varying relationship to section location and strong geographical patterns do not appear to exist in the data collected. Kaolinite content was found to be similar to that of quartz with patterns that are somewhat more consistent."

Jan 1, 1989

By D. R. Dolinar, J. Pablic, D. C. Oyler, T. P. Mucho

At a mine in central PA, high horizontal stresses have caused long running roof falls resulting in hazardous conditions for the miners and the premature abandonment of panels. Because of these conditions, the mine requested assistance of the National Institute for Occupational Safety and Health (NIOSH) in utilizing the 'advance and relieve method to mitigate the affects of horizontal stress on the mine roof. "Advance and relieve" mining involves the removal of a pillar or a portion of a pillar during development, thereby creating a cave along one side of the panel. Following cave development, the horizontal stress is relieved over the workings adjacent to the cave in the active panel. The mine has used this system in three panels with a significant reduction in stress damage and no large roof falls.

By G. R. Fitterer, C. H. Herty

"INTRODUCTION Manufacturers and consumers of steel have come to realize during the past few years that cleanliness is of great importance in steels which must meet rigid specifications for various physical properties. Of equal importance is the consistent production of steel which is uniform in these properties. For maximum utility steels should be uniform not only from heat to heat, but also from ingot to ingot and within each ingot. In the manufacture of killed steels such as the higher carbon forging grades, uniformity as indicated by the usual chemical analysis in easy to obtain, provided that a normal top discard is taken, as is always the case in steels poured with hot—top practice. No such uniformity, however, holds true for the nonmetallic matter, which consists for the most part of the products of deoxidation of the steel.For a large tonnage of steels which go into articles manufactured by deep—drawing processes, killed steel has never been successfully applied because with the present deoxidation practice, low—carbon killed steel is almost invariably extremely dirty. To obtain the desired qualities for deep drawing, the steel is rimmed, — that is to say, deoxidized with manganese and perhaps a small amount of aluminum, — the resultant product being of high purity in the skin of the ingot, but very badly segregated at the center of the ingot, particularly in the upper—central section. This segregation necessitates a very heavy top discard, and one of the major segregates is carbon which renders the steel too hard to draw properly. If clean, low—carbon killed steel could be made successfully, much better ingot yields would be obtained than by the present rimming steel practice. Furthermore, banded structures and outside and inside seams, which are undoubtedly due in a large measure to blowholes in the ingot, are defects which are very difficult to control in rimmed steel. These defects would be minimized by clean killed steel."

Feb 1, 1931

By Charles L. Kimbell

Comprehensive world mineral industry investment data do not exist, but limited material published on aggregates of in vestment in some elements of the world mineral industry suggest a continued up-turn in the investment level, at least in market economy countries in 1989. Steel industry investments in Organization for Economic Cooperation and Development (OECD) countries are not yet available for 1989 but, as shown in table 6, increased by 22.1% in 1988, after showing a decrease of 5.2% (revised) in 1987. The pattern of investment ups and downs varied during 1988 within country blocs and economic alliances showing no particular trends. Investment in the steel industry by the United States increased by 58.3% between 1987 and 1988 and was 1 1.9% higher than the previous highest amount invested during the 1984-88 period but was still 41.5% less than the amount invested in 1983. Investment in the steel industries of the European Coal and Steel Community (ECSC) dropped again in 1988 from the revised amount for 1987, which became the first drop after several years of steady growth in what became the expanded ECSC in 1986. This drop in 1988 was the result of lower investments by Denmark, France, the Federal Republic of Germany, Ireland, Italy, Luxembourg, the Nether- lands, and Spain, investments grew or remained level in Belgium, Portugal, and the United Kingdom in 1987 and 1988. A decrease in investment in the Canadian (-26.6%) steel industry was offset by in- creases registered by the members of the European Free Trade Association (EFTA) of 31.7%, by Japan of 19.8% by Turkey of 22.4%, and a slight increase by the nations of Latin America. If data for the world steel industry as a whole, including those of the centrally planned economy countries, were available, the same pattern presumably would be shown as that reported; that is, it would remain fairly stable, with increases in some countries being offset by decreases in others. However, the lack of comprehensive information on the centrally planned economy countries makes it impossible to determine whether the overall trend was up or down despite recorded increases or decreases in production of the materials involved. Preliminary data show that investment levels in industries dealing with the production and/ or processing of mineral commodities for

Jan 1, 1992

By Alice M. Chieruzzi

This Country Documentation Report presents the development of economic indices for Zambia for the period from 1970 through 1981. The work done through the Bureau of' Mines, Minerals Availability Program, under Contract number J0225001. This contract calls for the development of twelve index time series describing factor input costs in the mining sector of 95 countries. The twelve index time series describe the costs of: 1) mining wages, 2) construction wages, 3) equipment and repair parts, 4) bits and related steel, 5) timber and lumber, 6) fuel, 7) powder and blasting agents, 8) tires, 9) construction materials, 10) industrial materials, 11) transportation, and 12) electrical power. These indices combined with weight factors being developed by the personnel of the Minerals Availability Field Office (MAFO) of the Bureau of Mines in Denver, Colorado, will be used to perform instantaneous updates of all costs relating to the mining industry. The indices were developed primarily for use in the Bureau's Minerals Availability Program in assessing the worldwide availability of nonfuel minerals.

Jan 1, 1983

By H. R. Hardy Jr., E. J. Kimble Jr., H. W. Shen

"The primary objective of this research project is to study the character of the bit-coal interaction during coal cutting and its influence on the size and shape distributions of the generated dust. Secondary objectives include the investigation of the acoustic emission technique as an indirect method for coal dust characterization and remote bit wear monitoring. The results of the project will be useful in developing efficient coal cutting techniques which significantly reduce the harmful coal dust components, and in providing methods for remote monitoring of bit condition and associated coal dust character. This paper will outline recent experiments carried out on coal under uniaxial compression, linear single-bit cutting, and cutting using a laboratory-scale, single-bit shearer. During the experiments acoustic emission and a variety of other mechanical parameters were monitored. · A commercially available artificial intelligence computer package, namely: JCEPAK (Intelligent Classifier Engineering Package), has been utilized to provide a powerful and objective means for AE waveform analysis. This program is able to evaluate a number of features of each AE event and to make objective comparisons between AE signals associated with different loading or cutting parameters. Finally, the paper will discuss the results obtained from a variety of coal breakage tests.INTRODUCTIONStudies to date clearly indicate that the reduction of the severity, and eventual elimination, of Coal Workers' Pneumoconiosis (CWP) depends on gaining fundamental understanding in a number of major areas. These include dust generation and entrainment, transportation, suppression, medical effects of dust and possible treatment. At present a project is underway by the authors to investigate the character of the bit-coal interaction during coal cutting and its influence on the size and shape distributions of the generated dust. An important aspect of this on-going project is the development of acoustic emission (AE) criteria which will make it possible to carry out remote monitoring of coal cutting operations. Suitable on-line analysis of monitored AE data would allow engineers to evaluate factors such as shearer bit condition and cutting efficiency, and to quantify the particle size and shape distribution of the generated dust. The on-going AE studies are fundamental in form and were undertaken to evaluate the general feasibility of AE monitoring techniques using simplified coal cutting procedures. This paper will outline recent experiments on coal under uniaxial compression, linear single-bit cutting, and cutting using a laboratory-scale, single-bit shearer. Additional information on these studies are presented elsewhere [4]."

Dec 1, 1996

By Jr. Smith

To investigate the effects of flow geometry on laminar flames, studies are in progress in this laboratory employing Bunsen-type burners with rectangular cross section. Interpretation of these studies requires a determination of the flow velocity at all points of the rectangular cross section for one dimensional steady laminar flow. In addition, values of the velocity gradient at the boundary for such flows are needed in the interpretation of blow-off and flash-back studies with burners of rectangular cross section. The hydrodynamical problem of steady laminar flow of a viscous fluid in channels of rectangular cross section was solved by Stokes. His results have been quoted by Love21 and by Dryden, Murnaghan, and Bateman,§/ and they have been discussed by Boussines and by Paschoud. It may be noted that the steady laminar flow of a viscous fluid in channels of rectangular cross section constitutes a hydrodynamical analogue for the problem of the torsion of an isotropic prism of rectangular cross section.

Jan 1, 1952