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[Trans. No. Place Date Vol. Page 1, Wilkes-Barre, Pa.* .... May, '71.. 1 3 2. Bethlehem, Pa Aug., '71.. 1 10 3 Troy, N. Y Nov.,'71.. 1 13 4. Philadelphia, Pa Feb., '72.. 1 17 6. New York, N. Y •.... May, '72.. 1 20 6. Pittsburgh, Pa..:.Oct., '72.. 1 25 7. Boston, Mass Feb., '73.. 1 28 8 Philadelphia, Pa.' May, '73.. 2 3 9. Easton, a Oct., '73.. 2 7 10. New York, N. Y Feb., '74.. 2 11 11. St. Louis, Mo.* May, '74.. 3 3 12. Hazleton. Pa Oct.. '74.. 38 13. New Haven, Conn Feb., '75.. 3 15 14. Dover, N. J.' May, '75.. 4 3 16. Cleveland, 0 Oct., '75.. 4 9] [ ]

Jan 1, 1925

By Paul A. Beck, John Towers, W. D. Manly

Recent work on grain growth in high purity aluminum and in a solid solution type alloy of aluminum and magnesium1 showed that the isothermal increase of the average grain diameter D with time follows the equation D = K(tg + A)2 Eq 1 Here tg is that portion of the total annealing time 1, which is available for grain growth, that is the annealing time less the time necessary for complete recrystallization. The parameters A and n depend only on the temperature. A has the dimension of time, and is usually of the same order of magnitude as the time for recrystallization: R. In some instances R may be substituted for A in Eq I. This is the case for example at long periods of annealing or at high temperatures, where both A and R become small in comparison with t. In such instances Eq I is simplified to D = K, tn Eq 2 For high purity aluminum the exponent n increases in the ratio of about I to 5 in. the temperature range of 350' to 6w°C. 70-30 brass has been long known to exhibit grain growth of the continuous type, such as occurs in pure metals. For this reason, it was of interest to determine whether grain growth in brass also follows Eq I and 2 as it does in aluminum. Isotherma1 grain growth data for 70-30 brass were published in recent years by R. S. French2 and by H. L. Walker.' Fig I shows a log D vs. log t plot of French's data, together with the 500, 600 and 700°C data by Walker for 42.8 pct reduction by rolling. In such a log D vs. log t plot Eq 2 corresponds to a straight line with a slope of n. As seen in Fig I, the data of French and the 600°C data of Walker can be represented by straight lines. However, the 500 and 7c0°C data of Walker give curved lines and the average slope of his 500°C line is very different from the slope of the line representing French's data for the same temperature. Furthermore the curvature of the 700°C line suggests a tendency for grain growth to stop after 8 hr. If confirmed, this would constitute a definite deviation from Eq 2, not explainable on the basis of the specimen thickness effect found in high purity aluminum.' Walker's specimens were 0.125 in., or 3.18 mm thick, while the deviation occurs at a grain size of approximately 0.4 mm. A further point of divergence arose recently, when J. E. Burke suggested4 on the basis of Walker's data, that, instead of Eq 2, grain growth in 70-30 brass follows the equation D - D, = K . tgn Eq 3 Here D, is the grain size as recrystallized at the temperature in question. Although it was possible to show5 that, for pure aluminum, for which isothermal grain growth has been carefully investigated, Eq 3 is incompatible with the experimental facts, the situation remained somewhat obscure with respect to 70-30 brass. In view of the discrepancies between the published data on brass from different

Jan 1, 1949

By John Towers, Paul A. Beck, W. D. Manly

Recent work on grain growth in high purity aluminum and in a solid solution type alloy of aluminum and magnesium1 showed that the isothermal increase of the average grain diameter D with time follows the equation D = K(tg + A)2 Eq 1 Here tg is that portion of the total annealing time 1, which is available for grain growth, that is the annealing time less the time necessary for complete recrystallization. The parameters A and n depend only on the temperature. A has the dimension of time, and is usually of the same order of magnitude as the time for recrystallization: R. In some instances R may be substituted for A in Eq I. This is the case for example at long periods of annealing or at high temperatures, where both A and R become small in comparison with t. In such instances Eq I is simplified to D = K, tn Eq 2 For high purity aluminum the exponent n increases in the ratio of about I to 5 in. the temperature range of 350' to 6w°C. 70-30 brass has been long known to exhibit grain growth of the continuous type, such as occurs in pure metals. For this reason, it was of interest to determine whether grain growth in brass also follows Eq I and 2 as it does in aluminum. Isotherma1 grain growth data for 70-30 brass were published in recent years by R. S. French2 and by H. L. Walker.' Fig I shows a log D vs. log t plot of French's data, together with the 500, 600 and 700°C data by Walker for 42.8 pct reduction by rolling. In such a log D vs. log t plot Eq 2 corresponds to a straight line with a slope of n. As seen in Fig I, the data of French and the 600°C data of Walker can be represented by straight lines. However, the 500 and 7c0°C data of Walker give curved lines and the average slope of his 500°C line is very different from the slope of the line representing French's data for the same temperature. Furthermore the curvature of the 700°C line suggests a tendency for grain growth to stop after 8 hr. If confirmed, this would constitute a definite deviation from Eq 2, not explainable on the basis of the specimen thickness effect found in high purity aluminum.' Walker's specimens were 0.125 in., or 3.18 mm thick, while the deviation occurs at a grain size of approximately 0.4 mm. A further point of divergence arose recently, when J. E. Burke suggested4 on the basis of Walker's data, that, instead of Eq 2, grain growth in 70-30 brass follows the equation D - D, = K . tgn Eq 3 Here D, is the grain size as recrystallized at the temperature in question. Although it was possible to show5 that, for pure aluminum, for which isothermal grain growth has been carefully investigated, Eq 3 is incompatible with the experimental facts, the situation remained somewhat obscure with respect to 70-30 brass. In view of the discrepancies between the published data on brass from different

Jan 1, 1949

THE first session was held in the small hall of the Academy of Music, on Tuesday evening, February 18th, 1879. The proceedings were opened by the reading, by President Eckley B. Coxe, of the following Address : SECONDARY TECHNICAL EDUCATION. Technical education is a subject to which both the American Institute of Mining Engineers and the American Society of Civil Engineers have of late years given much attention, and deservedly so. We all remember the admirable address of our former President, Mr. Holley, at the Washington meeting, upon this subject, and the very interesting reunion of the two societies in Philadelphia for its discussion. The problem to the solution of which the meeting devoted its attention was, "Shall the practical education of the engineer in the mine, in the rolling-mill, in the workshop, or in the field, precede, be contemporaneous with, or follow his theoretical studies in the technical school ?" I do not propose to add anything to what was so admirably said by so many of our leading engineers on that occasion ; but I shall ask your attention to another question in technical education, which seems to me equally worthy of our consideration, and which, I am sorry to say, has as yet attracted but little attention in this country. It is, "Shall the apprentices (I call them so for the want of a better general name), who are growing up and learning their trades in and around our mines and works, and from whose ranks the master mechanics and foremen of the future must be taken-shall they be provided with some means of obtaining as much theoretical training as may be necessary to enable them properly to understand the various processes and operations that they may be called upon to superintend, and not be obliged to pick up, as best they may, here a little and there a little truth mingled with much error?" In the former case, those who have the ability and industry to avail themselves of the advantages that should be offered to them would fit themselves to become real foremen, men who would understand and appreciate the true engineer and his methods. Of late years the young men of this country who have wished to enter our profession have had great facilities offered to them for so doing ; there have been undoubtedly great improvements in the methods of instruction; and although I am very far from imagining that no further progress can be made, or is demanded, yet I feel sure that

Jan 1, 1879

Jan 1, 1879

Jan 1, 1884

The Committee on Technical Nomenclature, of which John T. Faig, Professor of Mechanical Engineering at the University of Cincinnati, is Chairman, appointed by the Society for the Promotion of Engineering Education, has recently issued a report advocating uniformity in the use of symbols to designate engineering and mathematical terms: The selection of the symbols was based upon a canvas of a considerable number of engineers, editors of engineering papers, and professors of engineering throughout the United States. The list, as finally accepted by the Committee and recommended for universal adoption, is as follows: Concept Symbol I Concept Symbol Acceleration due to gravity 'g Length L Acceleration, linear a Mass m Area A Modulus of section Z Breadth b Modulus of elasticity, Young's... E Center of rotation 0 Moment of force M Coefficients and constants C, K Moment of inertia, polar J Deflection of beam y Moment of inertia, rectangular.. I Depth : d Quantity of liquid flowing Q Diameter D . Radius r Distance passed over s Radius of gyration k Distance of extreme fiber from Reactions R neutral aids C Revolutions per unit of time.... N Eccentricity of application of load e Stress, unit S Efficiency (hydr., mech., vol.)...er,.em, e9 Time t Force F Torque T Friction, coefficient of f Velocity, angular :. W Head H 'Velocity, linear V Height h Volume V Horsepower : Hp Weight W Hydraulic radius Re Previous lists of symbols have not secured wide acceptance in, this country; some that have been proposed by prominent writers are familiar to very few engineers. The above list is presented in the hope that it will assist in the evolution of a standard list. It is short; it contains no Greek letters; it is mnemonic to a considerable degree, though not by

Jan 1, 1918

NORTH AMERICA ALASKA Anchorage.-Culver, H. W. Geehan, R. W. Strandberg, H. Chicagof.-Russell, J. C. Tracy, Q. S. College.-Dorsh, J. B. Fox, E. F. Joesting, H. R. Smith, M. C. Wilcox, H. G. Douglas.-Cahill. W. E. Fairbanks.-Adams, J. M. Barber, R. J. Beistline, E. H. Crawford, J. D. Doheny, L. C. Earling. R. B. Greves, J. H. Harris. Q. P., Jr. Henton. H. M. Herbert, C. F. Nester, W. B. Hopkins, J. E. CANADA ALBERTA Calgary.-Allen, R. E. deHart, J. B. Dunn, W. Gray, J. G. Johnson. R. V. Link, T. A. Slipper. S. E. Soul, N. Thorne, B. L. Thorne, H. L. Edmonton.-Ball, M. W. Lilge, E. O. Pitcher, N. C. Nordegg.-Shanks, J. Turner Valley.¬MacKenzie, W. D. C.

Jan 1, 1941

By H.A. Bedworth

AlloTs of copper and silicon have been known for one hundred years or more but the commercial development of this type of alloy has taken place during the past few years. In 1905, Sperry l proposed the use of copper-silicon alloys for springs and other purposes for which copper-tin bronzes were used. Some attention was given to this proposal at the time but no one succeeded in producing a practical alloy containing more than a fraction of a per cent. of silicon. The equilibrium relations of the copper-silicon system were studied first by Rudolfi2 and later by Sanfourche 3 and Corson. 4 The constitution of the system has also been recently investigated by Matuyama, 5 and in the laboratories of the American Brass Co. by Smith. 6 Some of the physical properties of the copper-silicon alloys have been investigated by Norbury7 and by Geiss and Van Liempt.8 Summarizing the results of various investigators of the constitution of copper-silicon alloys, the solubility reaches its maximium value, 6.7 per cent. silicon, between 721" and '782" C. At 852" (1. the solubility is 5.25 per cent., while at 400" C. it is only 4.1 per cent. silicon. The copper-silicon alloy begins to get so hard at about 3 per cent, silicon that it is difficult to manage. It was found by Jacobs that the addition of manganese to this alloy considerably improved the working

Jan 1, 1929

By H. A. Bedworth

AlloTs of copper and silicon have been known for one hundred years or more but the commercial development of this type of alloy has taken place during the past few years. In 1905, Sperry l proposed the use of copper-silicon alloys for springs and other purposes for which copper-tin bronzes were used. Some attention was given to this proposal at the time but no one succeeded in producing a practical alloy containing more than a fraction of a per cent. of silicon. The equilibrium relations of the copper-silicon system were studied first by Rudolfi2 and later by Sanfourche 3 and Corson. 4 The constitution of the system has also been recently investigated by Matuyama, 5 and in the laboratories of the American Brass Co. by Smith. 6 Some of the physical properties of the copper-silicon alloys have been investigated by Norbury7 and by Geiss and Van Liempt.8 Summarizing the results of various investigators of the constitution of copper-silicon alloys, the solubility reaches its maximium value, 6.7 per cent. silicon, between 721" and '782" C. At 852" (1. the solubility is 5.25 per cent., while at 400" C. it is only 4.1 per cent. silicon. The copper-silicon alloy begins to get so hard at about 3 per cent, silicon that it is difficult to manage. It was found by Jacobs that the addition of manganese to this alloy considerably improved the working

Jan 1, 1929

By M. J. Stewart, F. Weinberg

PREVIOUS investigations into convective flow in molten metals have examined systems in which the length-to-height ratio of the enclosure is large, usually using long graphite boats.''2 In normal castings this ratio is generally small and it is not possible to extrapolate the results of previous work to casting configurations. The present investigation was undertaken to examine liquid flow in systems of low length to height ratio. The apparatus used for the experiments is shown in Fig. 1. The molten zone of tin is contained in an aluminum mold of inside dimensions 6.4 by 6.4 by 0.31 cm. A heating block containing a resistance coil is attached to one end of the mold and a cooling block is attached to the other end. These are used to produce a wide range of temperature differences across the mold. The mold is contained in a stainless steel tank which is heated from the outside by resistance heaters to give the required operating temperature during the experiment. Temperature measurements in the molten tin are made with an iron-constantan thermocouple PT equal to 5 atm. The phase diagram derived by us was the same as that found by Krivsky and Schuhmann, except for a similar discrepancy in one boundary line representing the gas composition in equilibrium with SO a. The vapor pressures of the pure components can be neglected at 1700°K, 1 atm and 2500°K, 5 atm. There-fore, in these cases PT is essentially the total pres-sure in the system. This is valid for all the diagrams presented by Krivsky and Schuhmann except for the one at 2500°K and 0.01 atm, where the vapor pressure of silicon is comparable to PT.6 This work was supported in part by the American Iron and Steel Institute. 'C. E. Wicks and F. E. Block: Thermodynamic Properties of 65 Elements, U S. Bur Mines, Bull. No. 605, 1963. R. P. Elliott: Constitution of Binary Alloys, 1st supplementary, McGraw-Hill Book Co., New York, 1965. 3W. A. Krivsky and R. Schuhmann, Jr.: Trans. TMS-AIME, 1961, vol. 221, pp. 898-904. 4M. F. Ancey-Moret, M. Olette, and F. D. Richardson: Mem. Sci. Rev. Met., 1964, vol. 61, pp. 169-76. 5J . F. Elliott and M. Gleiser: Thermochemistry for Steelmaking, vol. 1. Addison-Wesley, Reading, Mass. 1960. 6 J.Drowart, G. De Maria, and M. G. Ingraham: J. Chem. Phys., 1958, vol. 29, p. 1015. probe of 0.4 mm diam inserted into the open top of the mold. Radioactive sn113, in the form of a small sphere, was gently lowered into the molten tin at point A in Fig. 1 THERMOCOUPLE> WATER ARGON END HEATER QUENCH ARGON Fig. 1—Apparatus for detecting liquid flow. Point A indicates position the tracer was introduced.

Jan 1, 1970

By G. Thomas, O. Johari

MEIERAN and Richman' have proposed a method for the determination of electron-diffraction patterns from twinned bcc crystals. It is the purpose of this note to present a general method capable of predicting the positions of all reflections from both matrix and twin regions for all possible orientations of cubic crystals. The method has been verified for twinning in explosively deformed copper, and is found to be a very useful tool when used in conjunction with stereographic projection, and dark-field electron microscopy. Let an isometric crystal be twinned in any (hkl) plane. The twinning can be considered either as a reflection in the twin plane or as a 180-deg rotation about the twin axis. In reciprocal space, the 180-deg rotation about the twin axis would place a given point p, q, Y to a new position P, Q,R, such that both will be equally inclined to the twin axis. This is represented in Fig. 1. If the coordinates of three such pairs of points are determined, the matrix of the transformation can be obtained.' It is also seen that such pairs would satisfy another condition, i.e., the vector [p,q,r] plus the vector [P,Q,R] will yield a multiple of hkl, i.e., the indices of the twin plane, because in isometric systems the axis [hkl] is perpendicular to the plane (hkl). This can be simplified by taking the points along the three axes. If a point h2 + k2 + 12, 0, 0 is taken along the x axis, it is seen that its new indices should be so as to yield a sum 2h2, 2hk, 2hl,i.e., 2h(h,k,1). (Also the points h2 - k2 - 12, 2hk, 2h1, and h2 + k2 + 12, 0, 0 are equidistant from the origin and both points make equal angles with the twin axis, i.e., cos-' h/dh2 + k2 + l2.) Similar operations for the points yield respectively, after the 180-deg rotation about the twin axis. Following the method due to Buerger,' the matrix of the transformation is obtained as follows: Using this matrix the indices of any other point in reciprocal space can be determined. This matrix is much simplified for (111) twinning commonly encountered in fcc metals, since are each equal to —1; hence

Jan 1, 1964

Jan 1, 1886

By W. R. Hibbard

It has been proposed1 on the basis of slip and flow that the ideal deformation texture of drawn wire for face-centered cubic metals is a (111) direction parallel to the wire axis. Under these considerations, an intermediate [loo] texture is permissible but should eventually change to the stable [Ill] orientation. This theory does not explain why copper and its alloys containing up to about 30 pct nickel, 5 pct zinc and 1 pct aluminum were found to have a double [Ill], [100] texture, while alloys with at least 8 pct zinc and 2 pct aluminum developed essentially a single [Ill] texture.1,2 It does suggest, however, that the [loo] component of the former alloys should disappear with additional deformation.3 Some evidence exists to support this suggestion. Howald4 reported that annealed copper wire previously drawn 93.8 pct and 98.5 pct developed a single [Ill] texture. Since, in wire, the drawn and annealed textures are similar, these wires probably had a single [Ill] deformation texture before annealing. In addition, although cold rolled polycrystalline copper and 80-20 brass were found to form different types of pole figures,5,6 single crystals of these metals when rolled from the stable (110) [112] orientation were found to produce essentially the same polo figure.7.8 It may be, therefore, that while the addition of solute elements changes the path by which the final texture is obtained, the final texture is not changed. Experimental Results The wires remaining from the previous investigation1 already drawn about 50 pct reduction in diameter were further drawn to 86 pct and then to 96.4 pct total reduction in diameter. The textures were determined after these stages by transmission X ray photograms taken with a copper K-alpha beam rotated 0 degrees toward the wire axis. It was found that the ratio of the [111].] and [100] intensities of the double texture in copper and its alloys containing 0.94 pct aluminum, 30.70 pct nickel, 2.61 pct zinc and 4.99 pct zinc increased from about 3:l for the 50 pct reduction to about 9:l for the 86 pct reduction. After 96.4 pct reduction, these wires exhibited essentially a single [lll] texture. Summary Thus, the drawn wire deformation texture of copper and its alpha solid solution alloys containing aluminum, nickel or zinc is essentially a single [Ill] texture as predicted by theoretical considerations of slip and flow.' For copper and its alloys containing up to about 1 pct aluminum, 5 pct zinc and at least 30 pct nickel, an intermediate [loo] component is found after about 50 pct reduction in diameter, but disappears after about 95 pct reduction in diameter. For alpha solid solution alloys containing at least about 2 pct aluminum and 8 pct zinc the single [Ill] texture is developed considerably more easily and is found after about 50 pct reduction in diameter. No explanation of this compositional effect is apparent. Similar work is contemplated for cold rolled and cold compressed alloys. References 1. w. R. Hibbard, Jr. and M. K. Yen: Trans. AIME 175, 126. Metals Tech., Feb. 1948, TP 2334. 2. W. R. Hibbard, Jr. and D. E. Trout, 11: Trans. AIME 185, 620. Jnl. of Melals, Sept. 1949, TN 18. 3. W. R. Hibbard. Jr.: Disc. of R. M. Brick's paper on Deformation Textures, ASM Symp. on Cold Working of Metals, Oct. 1948. 4. T. S. Howald: Disc. of Ref. 1. Trans. AIME, 175, 126. Melals Tech. Aug. 1948, TP 2449. 5. R. M. Brick, D. L. Martin and R. P. Angier: Trans. ASM (1943) 31, 675. 6. 0. Dahl and F. Pawlek: Zlsch. Melall. (1936) 28, 266. 7. C. S. Barrett and F. W. Steadman: Trans. AIME (1942) 147, 57. 8. J. E. Burke and C. S. Barrett: Trans. AIME 175, 106. Melals Tech., Feb. 1948. TP 2327.

Jan 1, 1950

By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By Irving Fatt, Herman Dykstra

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members) The following is a partial list of members and guests who called at Institute headquarters during the period Mar. 10, 1917, to Apr. 10, 1917. Frederick R. Ahbe, Athens, Pa. Frank M. Leland, San Francisco, Cal. J. L. W. Birkinbine, Philadelphia, Pa. Edwin Ludlow, Lansford, Pa. Samuel D. Bridge, Monterrey, Mex. E. P. Mathewson, Toronto, Canada. J. R. Buchanan, Pasadena, Cal. E. V. Matlack, Webster Grove, Mo. G. M. Colvocoresses, Humboldt, Ariz. E. C. Potter, Clearwater, Mont. F. G. Cottrell, Washington, D. C. R. B. Stanford, Bluefields, Nicaragua. H. N. Eavenson, Gary, W. Va. R. S. Ransom, Jr., Newark, N. J. H. T. Fisher, Englewood, N. J.. M. L. Requa, San Francisco, Cal. E. P. Fleming, Salt Lake City, Utah. John A. Rice, El Paso, Tex. F. L. Garrison, Philadelphia, Pa. W. E. Rice, Ringwood, N. J. W. M. Grant, So. Bethlehem, Pa. Lewis A. Riley, Philadelphia, Pa. J. F. Hanst, Negaunee, Mich. Hallet R. Robbins, Vancouver, B. C. H. D. Hibbard, Plainfield, N. J. Allen H. Rogers, Boston, Mass. B. B. Hood, Chrome, N. J. A. A. Stevenson, Philadelphia, Pa. Henry M. Howe, Bedford Hills, N. Y. Wm. Huff Wagner, Johnstown, Pa. Hennen Jennings, Washington, D. C. E. E. Watts, Denver, Colo. Oscar Lachmund, Greenwood, B. C. Samuel S. Wyer, Columbus, Ohio. H. W. Aldrich, after ten years of service with the Anaconda Copper Mining Co., at Anaconda, has resigned and accepted a position as general superintendent for the Ladysmith Smelting Works, at Ladysmith, B. C. Charles E. Bunker, formerly superintendent of the Keystone mine, has been appointed superintendent of the Bunker Hill mine near Amador City, Cal.

Jan 5, 1917

THE opening session was held on Tuesday evening, February 17th, in the house of the American Society of Civil Engineers. The President of the Institute, Mr. E. B. Coxe, after a few introductory remarks, congratulating the members on the general prosperity in all the branches of the professions and manufactures represented by the Institute, called on Mr. E. F. Loiseau, of Philadelphia, for the first paper, On the Successful Manufacture of Compressed Fuel at Port Richmond, Philadelphia. Professor Prime called attention to the fact that the work of the United States Testing Board had been left unfinished at a point when valuable results had just been reached, and offered the following resolutions: WHEREAS, The American Institute of Mining Engineers has seen with regret that the work of the United States Testing Board has been suspended through the lack of an appropriation by Congress, which appropriation dues not seem likely to be renewed, and WHEREAS, It seems most important to the vital interests of our iron and steel manufactures that the experiments commenced by the United States Testing Board should be carried to successful completion ; Resolved, That a committee of three be appointed, to act with a like, committee to he appointed by the American Society of Civil Engineers, to carry out to completion the work commenced by the United States Testing Board. Resolved, That the American Society of Civil Engineers be requested to cooperate with this society by the appointment of a like committee. Resolved, That the committee have authority to request, in the name of the American Institute of Mining Engineers, contributions to a fund to be devoted to the completion of the experiments aforesaid. Resolved, That the Council of this Institute be authorized, whenever requested by the committee so appointed, to petition Congress for the free use of the testing machine at the United States Arsenal at Watertown. Resolved, That a committee be appointed by the President, to select the afore-said committee of experts. Resolved, That the President of the Institute have authority to fill any vacancies which may occur in the committee. The resolutions were unanimously adopted, and President Coxe appointed the following committee in accordance with the resolutions : Messrs. A. L. Holley, James Park, Jr., and J. F. Holloway. The President also appointed Messrs. Heinrich, Mickley, and Spils-

Jan 1, 1880

By Morris Cohen

STAFF: Editor, Gerhard Derge Acting Editor, Paul G. Shewmon Carnegie Institute of Technology Schenley Park Pittsburgh 13, Pa. Editorial Assistant, M. A. Redmerski Production Editor, Otto T. Johnson THE METALLURGICAL SOCIETY: Karl L. Fetters, President; J.S. Smart, Jr., Past-President; R. C. Cole, Vice President; R. L. Hennebach, Treasurer; R. W. Shearman, Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: W. O. Phil-brook, Chairman; H. L. Bishop, R. C. Cole, J. N. Hobstetter, W. A. Krivsky, E. R. Morgan, F. C. Langenberg, R. E. Lund, Paul Queneau, L. L. Seigle, R. L. Smith, and T. V. Wainwright. Review and selection of manuscripts is under the supervision of the following Publicotions Committes: Extractive Metallurgy Division: R. E. Lund, Chairman; M. E. Wadsworth, Vice Chairman; D. H. Baker, Jr., G. M. Bell, R. E. Grace, W. A. Krivsky, R. A. Lewis, Charles O'Neill, A. W. Schlechten, R. E. Shinkoskey, and W. W. Stephens. Iran and Steel Division: T. V. Wainright, Choirman; H. L. Bishop, R. E. Boni, T. E. Dancy, D. W. Murphy, Johannes M. Uys, J. B. Wogstoff, and R. G. Ward. Institute of Metals Division: J. N. Hobstetter, Chairman; P. A. Beck, J. J. Becker, G. F. Bolling, J. 0. Brittain, J. B. Clark, R. S. Davis, A. E. Dwight, R. W. Fountain, L. R. Girifolco, J. C. Gurland, H. S. Kalish, E. L. Harmon, J. J. Heger, A. A. Hendrickson, L. Himmel, J. P. Hirth, H. H. Johnson, Jr., R. R. Nosh, T. N. Rhodin, R. H. Richman, H. C. Rogers, W. Rostoker, C. Sherby, C. W. Spencer, L. Slifkin, J. K. Stanley, R. Steinitz, H. C. Stumpf, and R. Swalin. Published bimonthly by the Americon Institute of Mining, Metallurgicol, and Petroleum Engineers, Inc., 345 East 47th Street, New York 17, N. Y. Telephone PLaza 2-6800. Subscription $30 peryear for non-AIME members in United States and North, South, and Centrol America; $32, foreign; $30per$7.50 for AlME members. Single copies, $6.00, single copies foreign, $6.50. The AlME is not responsible for any stotement made or opinion expressed in its publications ... Copyright 1962 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . . . Registered cable address, AlME New York . . . Indexed in Engineering Index, Industrial Arts Index, and Chemical Abstracts . . . Second class postage paid at New York, N. Y., and Ann Arbor, Mich. Volume 224, Number 4.

Jan 1, 1962

Jan 1, 1880